example of problem solving in economics

Examples of economic problems

The fundamental economic problem is the issue of scarcity but unlimited wants. Scarcity implies there is only a limited quantity of resources, e.g. finite fossil fuels. Because of scarcity, there is a constant opportunity cost – if you use resources to consume one good, you cannot consume another. Therefore, an underlying feature of economics is concerned with dealing how to allocate resources in society to make the most efficient and fair use of resources. The main issues are:

• What to produce?
• How to produce?
• For whom to produce?

Examples of economic problems include

• How to deal with external costs/pollution , e.g. pollution from production.
• How to redistribute income to reduce poverty , without causing loss of economic incentives.
• How to provide public goods (e.g. street-lighting) which are usually not provided in a free market.
• How should we measure economic welfare? Is it wrong to focus on ouptut and income? (as economics has in the past) – New measures of economic welfare try to include broader range of factors, such as environment, education, health care.

Video summary

Micro economic problems

1. The problem of externalities

The economic problem of pollution

One of the most frequent problems is that economic decisions can have external effects on other people not involved in the transaction. For example, if you produce power from coal, the pollution affects people all over the world (acid rain, global warming). This is a particular problem because we cannot rely on the free market to provide the most efficient outcome. If we create negative externalities , we don’t take them into account when deciding how much to consume. This is why we can get overconsumption of driving a car into a city centre at peak hour. If everyone maximises their utility, it doesn’t lead to the most efficient outcome – but gridlock and wasted resources.

Externalities, usually need some kind of government intervention. For example, taxes on negative externalities (e.g. sugar tax) or subsidies on positive externalities (e.g. free public education) even banning cars in city centres.

But, even the solution to market failure (e.g. taxes), creates its own potential problems, such as how much to tax? will there be tax evasion? The administration costs of collecting tax.

Environmental issues

Economics is traditionally concerned with utility maximisation – allowing individuals to aim at increasing their economic welfare. However, this can ignore long-term considerations of environmental sustainability. If we have over-consumption in this century, it could cause serious problems for future generations – e.g. global warming, loss of non-renewable resources. The difficulty is that the price mechanism doesn’t take into account these future costs, and policies to reduce consumption may prove politically unpopular.

– How to deal with potential future environmental costs?

Monopoly was an economic problem that Adam Smith was concerned about in his influential book of economics “A Wealth of Nations.” For various reasons firms can gain monopoly power – and therefore the ability to set high prices to consumers. Given a lack of alternatives, monopolies can make high profits at the expense of consumers, causing inequality within society. Monopoly power can also be seen through monopsony employers who pay lower wages to their workers.

How to deal with the problem of monopoly? – A government may seek to encourage competition, e.g. rail franchising, or price regulation to prevent excessive prices.

Inequality/poverty

This shows that 10% of the world population still live on below $1.90 a day – though the figure has reduced in past three decades.

Inequality is considered a problem because of normative opinions such as – it is an unfair distribution of resources. Also, you could argue there is a diminishing marginal utility of wealth . If all wealth is owned by a small percentage of the population, this reduces net welfare. Redistributing the money to the very poor would enable a greater net utility to society.

Five of the world’s largest companies  Apple, Microsoft, Alphabet, Cisco and Oracle, have a total of $504bn cash savings (2015) This is money unused, whilst people around the world have insufficient food.

Inequality is a problem. However, it is also a problem to know how much we should seek to reduce poverty. Many will agree on the necessity of reducing absolute poverty – but how far should we take it? Should we aim for perfect equality (Communism) or should we aim for equality of opportunity?

Another issue with reducing poverty is that measures to reduce poverty may cause unintended consequences – e.g. higher income tax on high earners may create disincentives to work. Giving benefits to the low paid may reduce incentives to work.

Volatile prices

Some agricultural markets can have volatile prices. A glut in supply can be bad news because the fall in price can lead to lower revenue for farmers. It could even cause some to go out of business because of a bad year. These volatile markets can cause swings in economic fortunes.

Irrational behaviour

In some asset markets, we have seen volatile prices exacerbated by irrational exuberance . Consumers have often been caught up in a market frenzy – hoping that rising prices will make them richer – and expecting prices to keep rising. We can see this in issues such as tulip mania , the South Sea Bubble, railway mania, and the recent property bubbles.

Macroeconomic problems

Mass unemployment 1933

Unemployment has been a major economic problem in advanced economies. One of the principal causes of unemployment is swings in the business cycle. A fall in demand for goods during a recession, causes people to be laid off. Because of the depressed state of the economy, there is an imbalance between demand and supply of workers.

Unemployment can also be caused by rapid changes in labour markets, for examples, unskilled workers unable to gain employment in a high tech economy. Unemployment is a problem because it is a waste of resources, but more importantly, it leads to very high personal costs, such as stress, alienation, low income and feelings of failure.

A recession is a period of negative economic growth – a decline in the size of the economy. It exacerbates problems of inequality and unemployment. A problem of recession is that it can create a negative spiral. When demand falls, firms lay off workers. The unemployed have less money to spend causing further falls in demand.

In the great depression, unemployment rose to over 20% – the unemployed also had little support and relied on soup kitchens.

High inflation can be a serious problem if prices rise faster than wages and nominal interest rates. In periods of rapidly rising prices, people with savings will see a decline in their real wealth. If prices rise faster than wages, then people’s spending power will decline. Also, rapidly rising prices creates confusion and uncertainty and can cause firms to cut back on investment and spending.

Countries which have experienced hyperinflation , have seen it as a very traumatic period because all the economic certainty is washed away, leaving people without any certainty. Hyper inflation can cause not just economic turmoil but political turmoil as people lose confidence in the economic situation of the economy.

Balance of payments/current account deficit

A current account deficit on the balance of payments means an economy is importing more goods and services than it is exporting. To finance this current account deficit, they need a surplus on the financial/capital account. For many modern economies, a small current account deficit is not a problem. However, some developing economies have experienced a balance of payments crisis – where the large deficit has to be financed by borrowing, and this situation usually leads to a rapid devaluation of the currency. But, this devaluation increases the price of imports, reduces living standards and causes inflation.

Exchange rate volatility

In some cases, the exchange rate can cause economic problems. For example, countries in the Euro were not able to change the value of their currency against other Eurozone members. Because countries like Greece and Portugal had higher inflation rates, they became uncompetitive. Exports fell, and they developed a large current account deficit. The overvalued exchange rate caused a fall in economic growth.

On the other hand, a rapid devaluation can cause different problems. For example, when the price of oil fell, oil exporting countries saw a decline in export revenues, leading to a fall in the value of the currency. A rapid devaluation causes the price of imports to rise and causes both higher inflation and lower growth. A difficult problem for policymakers to deal with.

Development economics

Developing economies face similar economic problems, but any issue is magnified by low GDP and high levels of poverty. For example, unemployment in a developing economy is more serious because there is unlikely to be any government insurance to give a minimum standard of living.

Poverty cycle . Some developing economies may be stuck in a poverty trap. Low growth and low saving ratios lead to low levels of investment and therefore low economic growth. This low growth and poverty cause the low savings and investment to be continued.

More examples

• Problems facing UK economy in 2015
• Economic problems of EU

Last updated: 17th November 2019, Tejvan Pettinger , www.economicshelp.org, Oxford, UK

28 thoughts on “Examples of economic problems”

Scarcity in resource is all over. It could be jobs, skills, capital, land, medicines, equipment, hospitals, universities, schools, houses, food, water etc

Sorry…it is not yet….

Enjoyed the lesson

what does economic mean

That is economic factors are addressed

Can I buy printed materials of this article Economic problems

Hi, Pettinger!

Really nice article, thank you. However, I am not sure I’ve got something you stated: isn’t inequality a macroeconomics issue? Because, you see, the scope of microeconomics is restricted to the individual actions of the economic agents (i.e., the “invisible hand science”) and inequality can only be properly handled by a macroeconomics perspective – or, at least, that’s the way I see it. Can you clarify that, please?

P.S.: if you are interested, I’ve answered this same question at stackexchange ( https://economics.stackexchange.com/questions/41448/is-inequality-a-micro-or-macro-economics-issue )

Govt.is also responsible for inequality , unemployment and low GDP growth by not taking efficient decisions in order to boost the economy.

Comments are closed.

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Documented Problem Solving: Calculating Gross Domestic Product

Gross domestic product (GDP) was introduced in class as a way to determine the value of a country's output. Consumption, investment, government spending, and net exports were discussed as the components of GDP. Items that are excluded from GDP were also discussed.

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Grade level, learning goals.

Students will:

• identify the components of GDP;
• determine items that are not part of GDP;
• calculate GDP.

Context for Use

Description and teaching materials.

A MC, T/F or short answer question can be used for this activity. Below is a short answer question.

Use the information below to calculate GDP. Consumer spending = $200 million Investment spending = $55 million State and local government spending = $120 million Federal government spending = $80 million Imports = $50 million Exports = $45 million Income taxes = $100 million Answer: $450 million

Teaching Notes and Tips

Students are not asked to merely calculate the correct answer, but instead they are asked to write the process they employed to arrive at the answer. For example:

• First I reviewed the definition of GDP including the components.
• Based on my notes, in order to calculate GDP I should add consumption, investment, government spending and net exports.
• Income taxes are not a component of GDP.
• Government spending includes spending at the federal level of $80 million and state and local spending of $120 million.
• Net exports is equal to exports of $45 million minus imports of $50 million.
• Imported goods are part of another country's GDP.
• GDP = consumption + investment + government spending + net exports.
• In this case, $200 million + 55 million + $120 million + $80 million + $45 million = $500 million. Then imports of $50 million is subtracted to get GDP = $450 million.

References and Resources

Angelo, T.A. and Cross, K.P. (1993). Classroom Assessment Techniques: A Handbook for College Teachers . San Francisco: Jossey-Bass.

Business Calculus with Excel

Mike May, S.J., Anneke Bart

Section 2.1 Market Equilibrium Problems

Subsection 2.1.1 supply and demand and market equilibrium.

\begin{equation*} \text{slope of supply curve} = \frac{\text{change in price}}{\text{change in quantity supplied}} = \frac{\Delta p}{\Delta q} \gt 0\text{.} \end{equation*}

\begin{equation*} \text{slope of demand curve} = \frac{\text{change in price}}{\text{change in quantity demanded}}= \frac{\Delta p}{\Delta q} \lt 0\text{.} \end{equation*}

• This intersection of the supply and the demand functions is called the point of market equilibrium , or equilibrium point .
• The price at this point is referred to as the equilibrium price .
• The standard economic theory says that a free and open market will naturally settle on the equilibrium price.

Example 2.1.1 . Starting With Formulas.

Example 2.1.3 . Starting With Data.

Example 2.1.5 . Computing Sales.

Reading Questions 2.1.2 Reading Check

1 . reading check, market equilibrium problems..

• The slope of the demand curve is always positive.
• This intersection of the supply and the demand functions is called the point of market equilibrium, or equilibrium point.
• The law of supply looks at the economy from the supplier’s point of view.
• If the supply and demand curves are unlabeled, there is no way to guess which is which.
• The law of demand looks at the economy from the consumer’s point of view.
• The slope of the supply curve is always positive.
• None of the above

Exercises 2.1.3 Exercises 2.1 Equilibrium Problems

Exercise group..

• Evaluate the curves at \(q_0\text{.}\)
• Find the market equilibrium.

• The market equilibrium happened to show up without requiring any more work. The equilibrium occurs when \(q = 4\) and the price is $22. If we had not seen the equilibrium in the table, we should graph the table and determine what values of \(q\) we should look at. After adjusting the table we can use Goal Seek to find the equilibrium point: Solve \(\text{supply}-\text{demand}=0.\)

• Find equations of the supply and demand curves, assuming they are both linear.

• To find the market equilibrium the column for \(q = 8352\) was copied and used to find the equilibrium point. Note that Goal Seek only works if the entries in the cells are formulas! The equilibrium is at \(q = 8240\text{,}\) with a price of $9.85.
• Supply price of $9.92 when \(q = 8352\)
• Demand price of $10.03 when \(q = 7984\)
• Find the projected supply and demand prices for the extra quantities given.

• The market equilibrium takes place at \(q = 8666.5\) with a price of $ 18.17.

1.1 What Is Economics, and Why Is It Important?

Learning objectives.

By the end of this section, you will be able to:

• Discuss the importance of studying economics
• Explain the relationship between production and division of labor
• Evaluate the significance of scarcity

Economics is the study of how humans make decisions in the face of scarcity. These can be individual decisions, family decisions, business decisions or societal decisions. If you look around carefully, you will see that scarcity is a fact of life. Scarcity means that human wants for goods, services and resources exceed what is available. Resources, such as labor, tools, land, and raw materials are necessary to produce the goods and services we want but they exist in limited supply. Of course, the ultimate scarce resource is time- everyone, rich or poor, has just 24 expendable hours in the day to earn income to acquire goods and services, for leisure time, or for sleep. At any point in time, there is only a finite amount of resources available.

Think about it this way: In 2015 the labor force in the United States contained over 158 million workers, according to the U.S. Bureau of Labor Statistics. The total land area was 3,794,101 square miles. While these are certainly large numbers, they are not infinite. Because these resources are limited, so are the numbers of goods and services we produce with them. Combine this with the fact that human wants seem to be virtually infinite, and you can see why scarcity is a problem.

Introduction to FRED

Data is very important in economics because it describes and measures the issues and problems that economics seek to understand. A variety of government agencies publish economic and social data. For this course, we will generally use data from the St. Louis Federal Reserve Bank's FRED database. FRED is very user friendly. It allows you to display data in tables or charts, and you can easily download it into spreadsheet form if you want to use the data for other purposes. The FRED website includes data on nearly 400,000 domestic and international variables over time, in the following broad categories:

• Money, Banking & Finance
• Population, Employment, & Labor Markets (including Income Distribution)
• National Accounts (Gross Domestic Product & its components), Flow of Funds, and International Accounts
• Production & Business Activity (including Business Cycles)
• Prices & Inflation (including the Consumer Price Index, the Producer Price Index, and the Employment Cost Index)
• International Data from other nations
• U.S. Regional Data
• Academic Data (including Penn World Tables & NBER Macrohistory database)

For more information about how to use FRED, see the variety of videos on YouTube starting with this introduction.

If you still do not believe that scarcity is a problem, consider the following: Does everyone require food to eat? Does everyone need a decent place to live? Does everyone have access to healthcare? In every country in the world, there are people who are hungry, homeless (for example, those who call park benches their beds, as Figure 1.2 shows), and in need of healthcare, just to focus on a few critical goods and services. Why is this the case? It is because of scarcity. Let’s delve into the concept of scarcity a little deeper, because it is crucial to understanding economics.

The Problem of Scarcity

Think about all the things you consume: food, shelter, clothing, transportation, healthcare, and entertainment. How do you acquire those items? You do not produce them yourself. You buy them. How do you afford the things you buy? You work for pay. If you do not, someone else does on your behalf. Yet most of us never have enough income to buy all the things we want. This is because of scarcity. So how do we solve it?

Visit this website to read about how the United States is dealing with scarcity in resources.

Every society, at every level, must make choices about how to use its resources. Families must decide whether to spend their money on a new car or a fancy vacation. Towns must choose whether to put more of the budget into police and fire protection or into the school system. Nations must decide whether to devote more funds to national defense or to protecting the environment. In most cases, there just isn’t enough money in the budget to do everything. How do we use our limited resources the best way possible, that is, to obtain the most goods and services we can? There are a couple of options. First, we could each produce everything we each consume. Alternatively, we could each produce some of what we want to consume, and “trade” for the rest of what we want. Let’s explore these options. Why do we not each just produce all of the things we consume? Think back to pioneer days, when individuals knew how to do so much more than we do today, from building their homes, to growing their crops, to hunting for food, to repairing their equipment. Most of us do not know how to do all—or any—of those things, but it is not because we could not learn. Rather, we do not have to. The reason why is something called the division and specialization of labor , a production innovation first put forth by Adam Smith ( Figure 1.3 ) in his book, The Wealth of Nations .

The Division of and Specialization of Labor

The formal study of economics began when Adam Smith (1723–1790) published his famous book The Wealth of Nations in 1776. Many authors had written on economics in the centuries before Smith, but he was the first to address the subject in a comprehensive way. In the first chapter, Smith introduces the concept of division of labor , which means that the way one produces a good or service is divided into a number of tasks that different workers perform, instead of all the tasks being done by the same person.

To illustrate division of labor, Smith counted how many tasks went into making a pin: drawing out a piece of wire, cutting it to the right length, straightening it, putting a head on one end and a point on the other, and packaging pins for sale, to name just a few. Smith counted 18 distinct tasks that different people performed—all for a pin, believe it or not!

Modern businesses divide tasks as well. Even a relatively simple business like a restaurant divides the task of serving meals into a range of jobs like top chef, sous chefs, less-skilled kitchen help, servers to wait on the tables, a greeter at the door, janitors to clean up, and a business manager to handle paychecks and bills—not to mention the economic connections a restaurant has with suppliers of food, furniture, kitchen equipment, and the building where it is located. A complex business like a large manufacturing factory, such as the shoe factory ( Figure 1.4 ), or a hospital can have hundreds of job classifications.

Why the Division of Labor Increases Production

When we divide and subdivide the tasks involved with producing a good or service, workers and businesses can produce a greater quantity of output. In his observations of pin factories, Smith noticed that one worker alone might make 20 pins in a day, but that a small business of 10 workers (some of whom would need to complete two or three of the 18 tasks involved with pin-making), could make 48,000 pins in a day. How can a group of workers, each specializing in certain tasks, produce so much more than the same number of workers who try to produce the entire good or service by themselves? Smith offered three reasons.

First, specialization in a particular small job allows workers to focus on the parts of the production process where they have an advantage. (In later chapters, we will develop this idea by discussing comparative advantage .) People have different skills, talents, and interests, so they will be better at some jobs than at others. The particular advantages may be based on educational choices, which are in turn shaped by interests and talents. Only those with medical degrees qualify to become doctors, for instance. For some goods, geography affects specialization. For example, it is easier to be a wheat farmer in North Dakota than in Florida, but easier to run a tourist hotel in Florida than in North Dakota. If you live in or near a big city, it is easier to attract enough customers to operate a successful dry cleaning business or movie theater than if you live in a sparsely populated rural area. Whatever the reason, if people specialize in the production of what they do best, they will be more effective than if they produce a combination of things, some of which they are good at and some of which they are not.

Second, workers who specialize in certain tasks often learn to produce more quickly and with higher quality. This pattern holds true for many workers, including assembly line laborers who build cars, stylists who cut hair, and doctors who perform heart surgery. In fact, specialized workers often know their jobs well enough to suggest innovative ways to do their work faster and better.

A similar pattern often operates within businesses. In many cases, a business that focuses on one or a few products (sometimes called its “ core competency ”) is more successful than firms that try to make a wide range of products.

Third, specialization allows businesses to take advantage of economies of scale , which means that for many goods, as the level of production increases, the average cost of producing each individual unit declines. For example, if a factory produces only 100 cars per year, each car will be quite expensive to make on average. However, if a factory produces 50,000 cars each year, then it can set up an assembly line with huge machines and workers performing specialized tasks, and the average cost of production per car will be lower. The ultimate result of workers who can focus on their preferences and talents, learn to do their specialized jobs better, and work in larger organizations is that society as a whole can produce and consume far more than if each person tried to produce all of their own goods and services. The division and specialization of labor has been a force against the problem of scarcity.

Trade and Markets

Specialization only makes sense, though, if workers can use the pay they receive for doing their jobs to purchase the other goods and services that they need. In short, specialization requires trade.

You do not have to know anything about electronics or sound systems to play music—you just buy an iPod or MP3 player, download the music, and listen. You do not have to know anything about artificial fibers or the construction of sewing machines if you need a jacket—you just buy the jacket and wear it. You do not need to know anything about internal combustion engines to operate a car—you just get in and drive. Instead of trying to acquire all the knowledge and skills involved in producing all of the goods and services that you wish to consume, the market allows you to learn a specialized set of skills and then use the pay you receive to buy the goods and services you need or want. This is how our modern society has evolved into a strong economy.

Why Study Economics?

Now that you have an overview on what economics studies, let’s quickly discuss why you are right to study it. Economics is not primarily a collection of facts to memorize, although there are plenty of important concepts to learn. Instead, think of economics as a collection of questions to answer or puzzles to work. Most importantly, economics provides the tools to solve those puzzles.

Consider the complex and critical issue of education barriers on national and regional levels, which affect millions of people and result in widespread poverty and inequality. Governments, aid organizations, and wealthy individuals spend billions of dollars each year trying to address these issues. Nations announce the revitalization of their education programs; tech companies donate devices and infrastructure, and celebrities and charities build schools and sponsor students. Yet the problems remain, sometimes almost as pronounced as they were before the intervention. Why is that the case? In 2019, three economists—Esther Duflo, Abhijit Banerjee, and Michael Kremer—were awarded the Nobel Prize for their work to answer those questions. They worked diligently to break the widespread problems into smaller pieces, and experimented with small interventions to test success. The award citation credited their work with giving the world better tools and information to address poverty and improve education. Esther Duflo, who is the youngest person and second woman to win the Nobel Prize in Economics, said, "We believed that like the war on cancer, the war on poverty was not going to be won in one major battle, but in a series of small triumphs. . . . This work and the culture of learning that it fostered in governments has led to real improvement in the lives of hundreds of millions of poor people.”

As you can see, economics affects far more than business. For example:

• Virtually every major problem facing the world today, from global warming, to world poverty, to the conflicts in Syria, Afghanistan, and Somalia, has an economic dimension. If you are going to be part of solving those problems, you need to be able to understand them. Economics is crucial.
• It is hard to overstate the importance of economics to good citizenship. You need to be able to vote intelligently on budgets, regulations, and laws in general. When the U.S. government came close to a standstill at the end of 2012 due to the “fiscal cliff,” what were the issues? Did you know?
• A basic understanding of economics makes you a well-rounded thinker. When you read articles about economic issues, you will understand and be able to evaluate the writer’s argument. When you hear classmates, co-workers, or political candidates talking about economics, you will be able to distinguish between common sense and nonsense. You will find new ways of thinking about current events and about personal and business decisions, as well as current events and politics.

The study of economics does not dictate the answers, but it can illuminate the different choices.

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2.1: Market Equilibrium Problems

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• Page ID 83917

• Mike May, S.J. & Anneke Bart
• Saint Louis University

As we mentioned in the previous chapter, many functions are locally linear, so if we restrict the domain the function will appear linear. Thus we often start with linear models when trying to understand a situation. In this section we look at the concepts of supply and demand and market equilibrium. For our examples in this section we will assume that the functions are linear in the range we care about.

Supply and Demand and Market Equilibrium.

The normal laws of supply and demand assume we are in a market with many producers and consumers, operating independently, all of them looking out for their own best interests. We expect that when the price goes up, more producers are willing to sell but fewer consumers are willing to buy. Conversely, when the price goes down, fewer producers are willing to sell but more consumers are willing to buy.

Consider the example of gasoline prices. Different prices will make some areas of exploration and production profitable or not profitable. When prices go up, new wells get drilled. If prices go down too far, stripper wells cease being profitable and are shut down. From the consumer side, when prices go up, more people look at mass transit or getting a more fuel-efficient vehicle. When prices go down, it is easier to think about a road trip.

The law of supply looks at the economy from the supplier’s point of view. Price and quantity available for sale always move in the same direction. If the price goes up we can assume that all the old suppliers are still willing to sell at the higher price, but some more suppliers may enter the market. If the price goes down, no new suppliers will enter the market, and some old suppliers may leave the market. For a linear model:

\[ \text{slope of supply curve} = \frac{\text{change in price}}{\text{change in quantity supplied}} = \frac{\Delta p}{\Delta q} \gt 0\text{.} \nonumber \]

The law of demand looks at the economy from the consumer’s point of view. Price and quantity available for sale always move in the opposite direction. If the price goes down we can assume that all the old consumers are still willing to buy at the lower price, but some more consumers may enter the market. If the price goes up, no new consumers will enter the market, and some old consumers may leave the market. For a linear model:

\[ \text{slope of demand curve} = \frac{\text{change in price}}{\text{change in quantity demanded}}= \frac{\Delta p}{\Delta q} \lt 0\text{.} \nonumber \]

When we look at a graph of the supply price graph and the demand price graph on the same graph, we know the supply curve goes up as we go left to right, while the demand curve goes down. From the properties of lines we know there is a single point where such a pair of lines can intersect. It is at the point where the amount of goods offered for a price equals the amount of goods desired for the same price.

• This intersection of the supply and the demand functions is called the point of market equilibrium , or equilibrium point .
• The price at this point is referred to as the equilibrium price .
• The standard economic theory says that a free and open market will naturally settle on the equilibrium price.

Example 2.1.1: Starting With Formulas.

Figure \(2.1.2.\) Video presentation of this example

Suppose \(q\) denotes quantity, and the supply price for widgets is given by

\[ \text{Supply price} =\$6+\frac{q}{100}\text{.} \nonumber \]

We are also told the demand price is given by

\[ Demand \ price=\$18-\frac{2q}{100}\text{.} \nonumber \]

Find the equilibrium price and quantity.

Solution. 1 (a)

We have started with an example that we can do by basic algebra without any technology. Subtracting the two equations, we see that

\[ 0=\$12-\frac{3q}{100}\text{.} \nonumber \]

Some straightforward algebra shows that the equilibrium quantity is 400. Substituting back into either equation gives an equilibrium price of $10.

Solution. 2 (b)

While we can do this example by hand, we also want to use it to set up a solution with Excel, since we may want help on problems where the numbers are not as nice. Our plan is to use Goal Seek to find the intersection. We need a cell where we can solve the problem by forcing the cell to have a value of zero.

When cell D2 is zero, the supply price will be the same as the demand price. We now invoke Goal Seek.

As expected, it finds equilibrium when \(q=400\text{.}\)

We need to do a bit more work when we are simply given data points and need to find the supply and demand curves.

Example 2.1.3: Starting With Data.

Figure \(2.1.4.\) Video presentation of this example

My market data indicates customers will buy 700 gizmos if they are priced at $13 each. If the price rises to $15, they will only buy 500. If the price is $12 a unit, the producers will make 400 gizmos. If the price rises to $13, they will produce 600 gizmos. Assume that the supply and demand curves are linear for between 300 and 1000 gizmos. Find the equilibrium point for the gizmo market.

We start by making a chart for the values given. We add a scatterplot so that we can see the values.

Next we add linear trendlines for both the supply and demand. We select the option to show the equations.

The projected equations are:

\begin{align*} \text{supply price}\amp =0.005*\text{quantity}+10\\ \text{demand price}\amp =-0.01*\text{quantity}+20\text{.} \end{align*}

We set up columns for the projected supply and demand curves. We also add a column for the difference so that we can use Goal seek to find the equilibrium point.

It is then straightforward to see that the equilibrium quantity is 666.67 and the equilibrium price is $13.33.

There is one more detail worth noting from this last example. Depending on the units used, the slope can be very close to zero. If we are selling tens of millions of units for a price under a dollar, the change in price of a penny may correspond to a change in quantity of several thousand. Make sure to include enough digits for your equation to be meaningful.

Example 2.1.5: Computing Sales.

Figure \(2.1.6.\) Video presentation of this example

We have obtained the following data for sales of gizmos in our location.

Assume the supply and demand curves are linear for quantities between 600 and 1300. Find the best fitting lines for the supply and demand functions. Find the equilibrium point. Make a chart listing how many we can sell for $6.40 and $6.60. Remember that sales will be the minimum of the supply and the demand.

We start by putting the data into a spreadsheet and finding the best fitting lines. We select the option to show the equations in the chart.

The supply and demand functions are:

\begin{align*} \text{supply price}\amp =.0032*\text{quantity}+3.44\\ demand\ price\amp =-0.0010*quantity+7.46\text{.} \end{align*}

We add columns for the projected supply and demand prices, using the equations obtained from the best fitting lines. We also add a column, and compute the difference of the supply and demand functions. We can now use goal seek to solve the problem.

We now use Goal Seek to find the equilibrium point.

At equilibrium we sell 956 gizmos at $6.50. To find sales at $6.40 and $6.60, we use Goal Seek to get those values at both supply and demand prices.

We see that we can sell 1055 gizmos at $6.40, but can only obtain 925. Thus our sales at $6.40 will be 925. At $6.60 we can obtain 987 gizmos, but can only sell 855. Thus our sales at $6.60 will be 855. We can eliminate a step in this process if we recall that below equilibrium price the constraint is supply, while above equilibrium price the constraint will be demand.

Exercises 2.1 Equilibrium Problems

• For problems 1-4, given the equations of the supply and demand curves:
• Evaluate the curves at \(q_0\text{.}\)
• Find the market equilibrium.

Exercise 1:

Given \(supply\ price=3 quantity+10\) and \(demand\ price=-2 quantity+30\text{,}\) with \(q_0=6\text{.}\)

Entries in the cells before quick fill

Table with quantities ranging from 0 to 10

From the table we see that at \(q_0=6\) the supply price is $28 and the demand price is $18.

Applications of the Derivative

Optimization problems in economics.

In business and economics there are many applied problems that require optimization. For example, in any manufacturing business it is usually possible to express profit as function of the number of units sold. Finding a maximum for this function represents a straightforward way of maximizing profits.

The problems of such kind can be solved using differential calculus.

Solved Problems

A game console manufacturer determines that in order to sell \(x\) units, the price per one unit (in dollars) must decrease by the linear law ( the demand function ) \[{p\left( x \right) = 500 - 0.1x \;\left( {\frac{\$ }{\text{device}}} \right)}.\] The manufacturer also determines that the cost depends on the volume of production and includes a fixed part \(100,000 \left( {\$} \right)\) and a variable part \(100x\), that is \[C\left( x \right) = {100000} + {100x}.\] What price per unit must be charged to get the maximum profit?

The total revenue is given by

The profit is determined by the formula

Find the derivative of \(P\left( x \right):\)

There is one critical value:

We use the Second Derivative Test to classify the critical point.

Since \(P^{\prime\prime}\left( x \right)\) is negative, \(x = 2000\) is a point of maximum.

Hence, the profit is maximized when \(2000\) game consoles are sold.

In this case, the price per unit is equal to

The demand function for a certain commodity is \[p\left( x \right) = 10 - 0.001x,\] where \(p\) is measured in dollars and \(x\) is the number of units produced and sold. The total cost of producing \(x\) items is \[C\left( x \right) = 50 + 5x.\] Determine the level of production that maximizes the profit.

The profit function is given by

Take the derivative of \(P\left( x \right):\)

so the critical point is

Since the second derivative of \(P\left( x \right)\) is negative, \(x = 2500\) is a point of maximum.

Hence, the company has the largest profit when \(x = 2500.\)

The demand function for a certain product is linear and defined by the equation \[p\left( x \right) = 10 - \frac{x}{2},\] where \(x\) is the total output. Find the level of production at which the company has the maximum revenue.

The revenue is defined by the formula

We see that \(R\left( x \right)\) is a parabola curved downward. It has a maximum at the following point:

As the second derivative of the function \(R\left( x \right)\) is negative, the point \(x = 10\) is a point of maximum.

Thus, the maximum revenue is attained at the production rate \(x = 10.\)

A plant produces and sells semiconductor devices. The cost per one unit (also known as the unit cost) depends on the volume of production and includes a fixed part \(1000\) ($/ device ) and a variable part \(2n\) ($/ device ), where \(n\) is the number of units produced per month. The price of the device, in turn, depends on the volume of production according to the law \[p\left( n \right) = 10000 - n\; \left(\$/device\right).\] Determine at what volume of production the profit will be highest?

The income from the sale of units manufactured during a month is

The monthly expenses are given by

Then the profit is determined by the formula

Investigate extreme values of the profit function. Assuming that \(n\) is a real number and differentiating with respect to \(n,\) we get:

Calculate also the second derivative:

Since the second derivative is negative everywhere, the solution \(n = 1500\) is a maximum point. Thus, production of \(1500\) devices per month provides the highest profit for the company.

A shop sells pies for \(\$5\) each. The daily cost function has the form \[C\left( x \right) = x + 10 + 0.01{x^2},\] where \(x\) is the number of pies sold on a typical day. Find the value of \(x\) that will maximize the daily profit.

The profit function is written as

where the revenue \(R\left( x \right)\) is given by \(R\left( x \right) = xp\) (\(p\) is the price per one pie). Then

The derivative of \(P\left( x \right)\) is

Determine the point at which the derivative is zero:

Notice that the second derivative is negative:

herefore, \(x = 200\) is a point of maximum, so the largest profit is attained at \(x = 200.\)

To produce \(x\) units of some product a company spends \[C\left( x \right) = a{x^2} + bx\;\left(\$\right),\] where \(a\) and \(b\) are real numbers. The product is sold at price \(p\,\$\) per unit. Determine the sales volume at which profit reaches its maximum.

When selling \(x\) units of the product, the company has income equal to

Hence, the profit of the company is

Find the derivative of the function \(P\left( x \right):\)

The derivative is zero at the point

Consider the second derivative:

Since the second derivative is negative, then the point \(x = {\frac{{p - b}}{{2a}}}\) is the maximum point, i.e. the company will have the maximum profit at the given sales volume.

The revenue for a certain product is given by the equation \[R\left( x \right) = 100 - \frac{{400}}{{x + 5}} - x,\] where \(x\) is the number of produced items. Find the value of \(x\) that results in maximum revenue.

We differentiate the function \(R\left( x \right)\) to determine its critical point.

Using the First Derivative Test, we can verify that \(x = 15\) is a point of maximum.

Hence, the maximum revenue occurs when \(x = 15.\)

The production cost per a period of time is given by the quadratic function \[C\left( x \right) = a + b{x^2},\] where \(a,b\) are some positive real numbers and \(x\) represents the number of units. Find the minimal average cost. (The average cost is the total cost divided by the number of units produced.)

By definition, the average cost \({\overline C}\) is written in the form

Take the derivative and set it equal to zero to find the critical points:

By the First Derivative Test, we identify that this point is a point of minimum.

Calculate the minimal average cost:

See more problems on Page 2.

Engineering Economic Analysis Practices for Highway Investment (2012)

Chapter: chapter three - case examples.

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32 chapter three Case examples ImpaCt of CrItICal Interstate transportatIon faCIlItIes Introduction The Port Authority of New York and New Jersey (PANYNJ) is a regional public authority established by bi-state charter that operates a number of multimodal transportation facili- ties within its defined Port District. It has responsibility for major interstate transportation facilities, including six highway crossings between New York and New Jersey and transporta- tion stations and centers in both states. It operates three major metropolitan airports and two regional airports, several marine facilities, and transit lines with ferry connections to Manhattan. The PANYNJ also oversees reconstruction of the World Trade Center in Lower Manhattan (“The Port Authority . . .” n.d.; “Overview of Facilities and Services” 2010). Despite the signif- icance of its existing transportation infrastructure and resulting impacts to the movement of people and goods throughout the metropolitan region, PANYNJ before 2000 had not attempted to quantify comprehensively the economic benefits conferred by its transportation infrastructure. This case describes the first step in that quantification: the estimation of the economic ben- efits of PANYNJ’s interstate transportation facilities. Although the Port Authority’s own study considered several categories of infrastructure outlined previously, this case example focuses specifically on the six bridges and tunnels between New York and New Jersey; facilities that can be regarded as critical infra- structure in terms of the impact of highway investment on local and regional economic conditions. The data and methodology used in this effort form part of a proposed regional cost–benefit capability described here. The case is unique given the network- level significance and criticality of the transportation facilities involved. Within the framework of this synthesis, it provides an example of planning information developed at a corridor and network level. The documentary source for this critical facilities case is the economic impact study performed for the Port Authority by a consulting firm (The Economic Impact . . . 2000). Other sources relating to a specific issue regarding the Bayonne Bridge will be presented at that point later in the case example. role of economic analysis in Highway Investment Facilities The Port Authority’s transportation facilities are located in the New York–New Jersey metropolitan region as illustrated in Figure 1. The Port Authority Interstate Transportation Facili- ties (PAITF), which is the focus of this case example, is a sub- set of the facilities in Figure 1 comprising the following: • Highway Bridges and Tunnels – George Washington Bridge, Goethals Bridge, Outer- bridge Crossing, Bayonne Bridge – Lincoln Tunnel, Holland Tunnel. • Interstate Transit Links – Port Authority Trans-Hudson (known as PATH) tran- sit service – Coordination of transit service with ferry services to downtown and midtown Manhattan that are provided by other operators. • Transportation Stations and Centers – Port Authority Bus Terminal – George Washington Bridge Bus Station – Journal Square Transportation Center. Daily use of these facilities is shown in Table 7, which orga- nizes the facilities into four major corridors. This traffic repre- sents the major share of commuter and freight flows between New York and New Jersey. The PAITF are critical links within the highway, transit, and rail networks that serve the New York–New Jersey metropolitan region shown in Figure 1. These networks connect New York City, Long Island, the northern suburbs of New York, other points north, other points east of the Hudson River, the northern suburbs of New Jersey, and other points west of the Hudson River. The Midtown Cor- ridor shows substantial road traffic in the Lincoln Tunnel. This tunnel, which provides an exclusive bus lane, is a major transit corridor into midtown Manhattan. The Port Authority’s report includes a separate estimate of the benefits of this bus traffic. In addition to the PAITF, rail and transit services to midtown are provided by Amtrak, New Jersey Transit, the Metro–North Railroad, the Long Island Rail Road, New York City Transit, and private commuter bus and ferry services. Components of the Analysis Three components of economic benefit were considered in the Port Authority study of the PAITF: 1. Transportation benefits, comprising savings in travel time and VOC resulting from the existence of a PAITF facility.

33 FIGURE 1 Locations of PANYNJ transportation facilities. Source: Port Authority of New York and New Jersey, http://www.panynj.gov/about/facilities-services.html. Corridor/Facility Weekday Use Weekend Use Measure of Use Northern Corridor George Washington Bridge 151,700 149,000 Vehicles Midtown Corridor Lincoln Tunnel 62,200 57,400 Vehicles PATH Service to 33rd Street 41,300 21,600 Passenger trips Midtown Ferry Service 11,500 6,100 Passenger trips Downtown Corridor Holland Tunnel 49,700 49,500 Vehicles PATH to World Trade Center 60,400 13,400 Passenger trips Downtown Ferry Service 12,500 1,500 Passenger trips Southern Corridor Goethals Bridge 36,000 38,000 Vehicles Outerbridge Crossing 40,900 45,900 Vehicles Ba yo nne Bridge 9,700 7,000 Vehicles Source: The Economic Impact… (2000). TABLe 7 DAILY USe OF PAITF, 1999

34 2. Operating and capital impacts, the result of expendi- tures on the Interstate Facilities by the Port Authority, its tenants, and other transportation providers. These expenditures purchase goods and services from regional businesses that support the maintenance, operation, and enhancement of the facilities. The result is not only an improved level of transportation service, but also an improved economic welfare of the region resulting from direct purchases and subsequent indirect purchases owing to PAITF expenditures. 3. Competitive impacts, which result from more efficient access to, and movement within, the region served by PAITF. This benefit reflects the improved economic competitiveness and stimulation of growth owing to services provided by the Interstate Facilities in several categories; for example, commuter trips between New Jersey and New York, tourist travel, intra-regional and longer-distance trucking shipments, and direct eco- nomic development occurring around and surrounding PAITF locations. This synthesis focuses on the first of these benefits cate- gories, direct transportation benefits, and on the bridges and tunnels specifically, because these tend to be the most preva- lent for consideration in LCCAs for highway investment. methods and measures Analytic Principle A methodology was needed to address the quantification of benefits resulting from facilities of different modes, character- istics, and usages, located within an extensive metropolitan, multimodal transportation network. The principle that was adopted was that the benefits of an existing facility would be equal to the additional costs to all travelers if that facility were removed from the network. Worded more formally in the Port Authority report: The transportation benefits of a facility are defined in this [Port Authority] study as the value of increased travel costs, consist- ing of travel time and vehicle operating costs, that displaced users would incur if that facility were no longer available, and all other network facilities remained open. Source: The Economic Impact . . . 2000, p. 5. The Port Authority believed that this estimate was con- servative in the following sense: If two or more Interstate Facilities were closed down simultaneously, the overall cost impacts would likely exceed the sum of the costs of individu- ally removing each of these facilities from the network. The Port Authority also realized that highway-user costs would differ among facilities for several reasons, including wide variations in origin–destination points among respective road users, the convenience of the preferred river crossings perceived by users, the convenience and travel cost of avail- able alternate routes, and existing levels of congestion. The Port Authority’s study offered the following examples to illustrate these points. . . . closing the George Washington Bridge imposes a high increase in travel time on its users principally because alterna- tive river crossings (primarily the Holland and Lincoln Tunnels) are relatively distant and the sheer volume of present users at the George Washington Bridge would cause grave congestion prob- lems at these alternative crossings. On the other hand, closing the Holland Tunnel would lead to significantly smaller increases in travel costs because the existing traffic at the Holland Tunnel is much lower . . . and alternative facilities are both relatively near and capable of absorbing the increase in traffic. Similarly, while the Goethals Bridge and Outerbridge Crossing serve over- lapping markets and have similar traffic levels, the analysis mag- nifies the impact of the latter bridge because it does not have as many nearby alternatives as the former. Source: The Economic Impact . . . 2000, p. 5. Methodology With this guiding principle established, the calculation of benefits was organized within a methodology that entailed four basic assumptions governing the determination of needed input values. These assumptions involved value of road users’ time, value of VOC, the degree of diversion to transit, and projection of traffic volumes to year 2000, the base year of the analysis. • Value of road users’ time. Value of time was estimated based on relationship to wage rates and variations based on trip purpose. The assumed values of time were as fol- lows: working time during transportation (e.g., truck and bus drivers) is equal to the gross wage; commuting time is equal to 50% of the gross wage; and leisure time (or personal travel) is equal to 25% of the gross wage. Val- ues of the gross wage were estimated based on the aver- age wage in the vehicles’ destination county in the a.m. travel period (from origin–destination data), because the destination would be an indication of work location for commuters. Destination county was also used to estimate the wages of those in heavy-goods vehicles, factored at 100% of the county’s average wage. The value of travel time associated with each vehicle also accounted for aver- age vehicle occupancy. • Value of VOC. VOC include the costs of fuel, oil, tire wear, and vehicle maintenance, plus an allowance for the capital cost of the vehicle. A literature review was con- ducted to estimate the following composite values for the New York metropolitan area: $0.29 per mile for autos, $1.20 per mile for trucks, and $0.91 per mile for buses. • Diversion to transit. Some of the road users displaced by bridge or tunnel closure were expected to divert to mass transit. An elasticity factor was assumed based on locally available transportation alternatives at each PAITF. This elasticity of transit use to auto travel time was estimated to be 0.15 to 0.3, with the study assump- tions leaning toward the higher end of this range. For example, an elasticity of 0.25 would mean that for every 10% increase in auto travel time, transit use

35 would increase by 2.5%. This range of 0.15 to 0.3 was somewhat lower than values appearing in the literature at the time of the study (extending to 0.8). The lower values were believed to be more realistic for this par- ticular study; however, because other studies had found relatively inelastic behavior of auto travelers on trans- Hudson crossings with respect to diversion to transit. • Projected traffic volume. Available traffic data were projected to the study year (2000) to arrive at 24-hour weekday distributions, which served as a basis for assum- ing traffic volume inputs. Other data were applied to complete the estimate. For example, survey results were available to enable estimates of average vehicle occupancy on certain of these bridges and tunnels, as well as trip purpose. The Interstate Network Analysis (INA) model was used to simulate the closing of individual bridges and tunnels and the resulting “shock” impacts throughout the network. These impacts consisted of rerouting the displaced vehicles to the “best” available alternative based on their origin–destination data, and then rerunning the INA model to compute a new net- work equilibrium. The model did not assume any peak shift- ing as the result of these diversions, regardless of the level of congestion and increased travel time to the road users. More- over, the focus of the calculations was on the change in travel costs to the former users of the closed facility, not to the users of other facilities in the network. (This assumption is another indication that the estimate of transportation benefit conferred by each Interstate Facility was conservative.) The INA model then reported the net increases in travel time and distance for road users, which were converted to costs using the travel time and VOC inputs discussed earlier. The results of this analysis show that the George Washing- ton Bridge has greater benefits than the other crossings, for the reasons cited earlier: heavy travel demand and the lack of alternate crossings nearby. Results for each bridge and tunnel are also available disaggregated into three line items that respond to the imposed closure of a facility: the cost of increased travel time experienced by former users of the facil- ity who must now divert to alternate routes; the increased time for former facility users who are now diverting to transit; and the increased cost of vehicle operation by former users of the closed facility. Decision support Background Information The economic analysis described earlier provides a point of departure for more comprehensive and detailed analyses of the roles that these critical interstate transportation facilities serve at a regional and national level. As an example, the fol- lowing paragraphs frame a transportation issue that PANYNJ is now dealing with that involves significant investment needs as well as significant impacts to regional highway transporta- tion and, potentially, to national and international maritime shipping. The issue is multimodal and multijurisdictional: it involves benefit–cost applications in both a regional and a national context. The issue concerns the Bayonne Bridge, which is shown at the lower-left-hand area of Figure 1. The bridge carries a high- way link between Bayonne, New Jersey and Staten Island, New York. The body of water that it crosses, the Kill Van Kull, is the entrance westward to the Port Authority’s mari- time facilities, also shown in Figure 1. The current height of the bridge over the water (151 ft), referred to as its air draft, is becoming a limiting factor on shipping entering the port because of the increasing size of cargo ships worldwide. This growth in the dimensions of large container ships is expected to increase when the capacity expansion of the Panama Canal is completed by 2015. The Port Authority recognizes a dual set of objectives and needs regarding issues such as this air- draft constraint: to continue providing a world-class port with navigable channels and clearances that can accommodate large cargo vessels and continue to provide the landside infrastruc- ture needed to move cargo (“Next Steps to Address . . .” n.d.). USACE Air Draft Analysis In 2008, the Port Authority commissioned the New York District of the U.S. Army Corps of engineers (USACe) to study “the commercial consequences of and the national economic ben- efits that could be generated by a potential remedy of the Bay- onne Bridge’s air draft restriction” (“Next Steps to Address . . .” n.d.). The USACe approached the problem by addressing when and to what extent the Bayonne Bridge would present an obstacle to larger ships, what are the economic consequences, and would further planning and environmental analyses of pos- sible solutions be warranted. The report was conducted in the nature of a Corps reconnaissance study, rather than a feasibility study, in that it did not recommend a specific project or cost- sharing plan. However, it did provide technical and economic data responsive to the Port Authority’s planning and decision- making needs. The primary findings of this study included the following (Bayonne Bridge Air Draft Analysis Sep. 2009): • The current height of the Bayonne Bridge is and will be an obstruction to larger container vessels within a 50-year analysis horizon. • Based on preliminary estimates addressing a range of engineering solutions to the air-draft problem, all have favorable benefit–cost ratios as summarized in Table 8. • Further planning and environmental analyses by the Port Authority are warranted to identify a preferred solution to the air-draft restriction. The current Bayonne Bridge structure is a steel arch with cables suspended from the arch to support the roadbed. The

36 USACe considered the following engineering alternatives to remove the bridge air-draft restriction: • Jack the existing steel arch and roadbed to a new height providing an air draft of 215 ft. • Build a new bridge structure with an air draft of 215 ft. • Bore a tunnel under the Kill Van Kull to replace the existing bridge. • Construct an immersed tunnel under the Kill Van Kull to replace the existing bridge. The benefit–cost results for each of these alternatives are shown in Table 8. Costs were estimated using data provided by PANYNJ’s Tunnels, Bridges & Terminals Department, based on the start of detailed engineering and design in 2010. Facility operation and maintenance (O&M) costs were esti- mated for each alternative, using the 50-year analysis period with O&M costs commencing at the completion of construc- tion. Benefits were estimated according to National economic Development (NeD) guidance, discussed here. Benefits were assumed to commence at the completion of construction of each alternative as shown in Table 8, including removal of the constraining roadbed from the channel. Net present value, benefit–cost ratio, and IRR of the cost and benefit streams were computed using a discount rate of 4.625% over a 50-year analysis period. The USACe also projected 50-year forecasts on the characteristics of shipping to the Port of New York and New Jersey (PONYNJ) in the absence of alteration or replacement of the Bayonne Bridge (i.e., the No-Build option) (Bayonne Bridge Air Draft Analysis Sep. 2009, pp. 32–36, Appendix B). Federal objectives and guidelines regarding studies of water and related land/resources development are spelled out in a document prepared by the U.S. Water Resources Coun- cil (Economic and Environmental Principles . . . Mar. 1983). The federal objective in project planning involving these resources is “to contribute to national economic devel- opment consistent with protecting the Nation’s environ- ment,” and to do so in compliance with relevant federal statutes, executive orders, and other planning requirements (Economic and Environmental Principles . . . Mar. 1983, p. iv). Project plans might address problems and explore opportunities to meet this objective, including identification of project benefits that contribute to NeD. Contributions to NeD are defined as “increases in the net value of the national output of goods and services, expressed in monetary units” (p. iv). Contributions to NeD may occur within the study region, or elsewhere in the nation as the result of the proj- ect. That NeD reflects a net increase in total output implies real gains attributable to the project on a nationwide basis, not simply a transfer of benefits from one region of the country to another. Benefits of the proposed Bayonne Bridge project were analyzed in terms of the reduced costs of maritime shipping owing to economies of scale in using larger vessels. To com- pute this cost reduction, USACe formulated two future pos- sibilities: (1) the Without-Project (or No-Build) condition, in which maritime commerce entering PONYNJ would be car- ried in smaller, less economically efficient vessels that could operate with the restricted air draft of the Bayonne Bridge; and (2) the With-Project condition, in which the existing air- draft constraint is removed by bridge alteration or replacement, allowing larger, taller vessels to be added to New York-bound routes. The USACe analysis forecast the amount of freight commerce through PONYNJ over a 50-year analysis period. It also forecast changes in the worldwide shipping fleet with the addition of the larger container vessels, contrasting the fleets to be used in Conditions 1 and 2. The USACe analysis then in effect “loaded” the two fleets with the projected cargo volumes, estimated the number of trips and container-miles required for the With-Project and Without-Project assumptions, and com- puted the respective vessel operating costs in each case. The difference between these two shipping-cost totals was taken as the NeD benefit attributable to the project (Bayonne Bridge Air Draft Analysis Sep. 2009, pp. 12, 13, 32, 33). USACe dealt with a number of issues in formulating this economic benefits study (Bayonne Bridge Air Draft Analysis Sep. 2009, pp. 13–32): • The trends in several inputs to the benefits computation had to be estimated through the 50-year analysis period. Alternative Year the Im provem ent Is in Place Break-Even Year Benefit– Cost Ratio Internal Rate of Return Net Benefit, $Billions Jack Structure to 215 ft 2019 2033 3.0 10.7% $3.271 New Structure at 215 ft 2022 2039 2.1 8.4% $2.822 Bored Tunnel 2024 2042 1.9 7.7% $2.585 Immersed Tunnel 2024 2051 1.4 6.1% $1.517 Source: Bayonne Bridge Air Draft… Sep. 2009, Tables 4 and 6. TABLe 8 SUMMARY OF BeNeFIT–COST ReSULTS, USACe AIR-DRAFT STUDY

37 These trends included a forecast of commerce through PONYNJ, the characteristics of the future maritime fleet, likely patterns of fleet use on routes bound for U.S. east Coast ports, loading patterns in accommodating cargo on different types of vessels while conforming to the opera- tional needs of regularly scheduled service worldwide (i.e., ships depart ports on a schedule, whether or not fully loaded), how the vessel fleets should be deployed in the analysis to handle growth in cargo volume for the With-Project and Without-Project conditions respec- tively, and estimation of the costs of operating vessels in the With-Project and Without-Project fleets. • USACe also had to address other potential restrictions on shipping that might negate the benefits of the Bayonne Bridge project. For example, if PONYNJ harbor chan- nels were not deep enough to handle large vessels, the prospective benefits of increasing the air draft on the Bayonne Bridge might never be realized. On this par- ticular point, an earlier Harbor Navigation Study (HNS) had been performed in 1999, recommending deepening of several channels in PONYNJ; construction funding for this project was authorized by the U.S. Congress in 2000. For a number of positive reasons, USACe applied the NeD methodology used in the Harbor Navigation Study to its air-draft study. This consistency of method made it possible for the Corps to ensure that the benefits of the air-draft project were separate and distinct from the benefits of the harbor deepening work, avoiding double-counting or overstating of benefits. • Other external factors and constraints could also limit the actual benefits to be realized from the Bayonne Bridge project, along the lines suggested in the preced- ing item. For example, possible limitations in rail and highway capacity, port crane capacity, berthing space, and yard capacity could themselves limit the volume of cargo handled by PONYNJ, apart from restrictions imposed by the bridge air draft. Also note that the Bay- onne Bridge is not an obstacle to port facilities located eastward, so greater use of these port facilities could increase benefits regardless of whether or not the air- draft constraint were removed. (This is not to say that such capacity constraints actually existed. USACe was just pointing out that a valid evaluation of benefits needed to consider these other factors, which was done in a broad context in developing the findings of the air-draft study.) • A similar point related to more global constraints—the USACe further considered whether these might limit the benefits that could be realized by altering or replacing the Bayonne Bridge. A key global constraint was the existence of air-draft restrictions in other parts of the world, which might themselves constrain the heights of future maritime fleet additions. The Corps investi- gated these and found that although certain height lim- its did exist, the air draft of the Bayonne Bridge was the most constraining among those affecting 12 major ports worldwide. USACe further considered other factors that might influ- ence future decisions on the project, and conducted scenario analyses to investigate the effects of differing assumptions underlying the study. • The Corps recognized factors that were outside the scope of its study, but that could inform and affect PANYNJ’s decisions on how to proceed on this project. These included regional and local economic benefits and impacts (as compared with the national benefits com- puted in the air-draft study); the possibility that not all NeD benefits were accounted for in the study (maritime transportation cost savings tend to be used as a NeD benefit measure because they are relatively conserva- tive and easier to compute than other categories of ben- efits); and that although the study referred generally to “the Port of New York and New Jersey,” the Port com- prises a number of stakeholders to whom benefits will accrue; for example, ocean carriers, terminal operators, labor interests, land-side transportation providers, and regional consumers (Bayonne Bridge Air Draft Analysis Sep. 2009, pp. 37–38). • The Corps recognized several areas of potential uncer- tainty in the analysis, and subjected each to scenario testing in which key parameters or assumptions were varied to assess their impact on the economic results. Nine categories of scenario analyses were addressed in all, covering diverse aspects such as the projections of maritime commerce, shifts in the location of man- ufacturing in Asia and their effect on shipping to the east Coast, project cost estimates, different engineer- ing options in the height to which the bridge roadway might be raised, and delays in the start of design and construction, among others. For a given category, the scenarios comprised several repetitions of the analysis, each repetition testing a different parameter value or assumption. Results of each repetition provided infor- mation comparable to that shown in Table 8. Coming PANYNJ Analyses The USACe analysis demonstrated that the Bayonne Bridge project was justified economically from a national perspec- tive. This result opened the door for the Port Authority to con- duct its own technical and economic analyses of the project and how it might proceed. As the contact representative of the PANYNJ has pointed out, the roles of the respective eco- nomic analyses can be understood essentially as follows: the USACe analysis indicated that the project is justified at a national level, whereas the PANYNJ analysis will indicate whether the regional benefits exceed the costs. The coming PANYNJ regional analysis will examine issues not addressed in detail in the national study; for example, a more comprehen- sive assessment of highway-user benefits addressing the land- side facilities of PONYNJ (including traffic over the Bayonne Bridge during and after construction), and changes in maritime

38 air pollution emissions because of the anticipated shift in ves- sel fleet characteristics calling on PONYNJ as the result of the modified air draft. In December 2010, the Port Authority announced that its preferred engineering option for the Bayonne Bridge would be a reconstruction of the main-span roadbed and bridge approaches and ramps, to raise the roadbed as it crosses the channel through its supporting steel arch. As of March 2011, PANYNJ was proceeding to identify and select an engineer- ing consultant to provide design services for this project. resources needed and other Information Resources The PANYNJ’s study of the economic impacts of its trans- portation infrastructure has been accomplished with the assis- tance of a consulting firm working with Port Authority staff. Although USACe personnel performed the cost and benefit analysis for the Bayonne Bridge Air Draft study and developed a portion of the input data, it obtained other data from PANYNJ. Corps personnel also met with PANYNJ consultants who were performing comparable analyses on other studies, to compare trend projections and check their consistency. plannIng anD programmIng: mobIlIty anD safety projeCts Introduction This section presents the methodology now used by WSDOT for highway capital programming, currently being extended to highway system planning. WSDOT’s programming pro- cess has been in place for almost two decades, and has bene- fited from continual updating, improvement, and integration within broader statewide performance-accountability initia- tives. This case example describes work that is comprehen- sive, innovative, and unique in the thorough integration of economic thinking from the top-level guidance of enabling state legislation through detailed analysis of the estimated costs, benefits, and technical performance of project alter- natives. An extensive information infrastructure has been built to support these procedures in headquarters and region (district) offices. WSDOT’s Capital Program Development and Management Office (CPDM) provides overall guidance to this effort in its conception, implementation, and applica- tion. Although WSDOT manages programs across several modes and types of work, the processes and economic analy- ses described here apply only to the highway construction program. It would normally be more natural to explain the planning process first, followed by capital programming. However, given the history of program-development pro- cesses at WSDOT, the following description will reflect the chronological order of their implementation: highway capi- tal programming first, followed by the extension to highway system planning. role of economic analyses in Highway Investment Background In 1990, WSDOT began working on a new, performance- based capital programming process under a project sponsored by the (then Joint) Legislative Transportation Committee. It had become apparent by that time that an emerging set of policy issues at the federal and state levels would confront WSDOT and Washington’s Transportation Commission, and changes to the highway capital construction programming process would be needed. Key objectives to be met included: (1) a strong, clear connection between the programming pro- cess and the emerging policy concerns; (2) a strengthened abil- ity to highlight and evaluate key tradeoffs in funding projects; (3) a more rational, understandable basis for prioritization rooted in economic as well as engineering performance; and (4) incorporation of greater flexibility and accountability in rec- ommending projects. The study was concluded in 1991, and its recommendations were accepted by WSDOT for future imple- mentation. Since that time, the programming process has been continually refined to meet new transportation program needs, accommodate the terms of new legislative requirements and funding sources, update analytic methods and decision criteria, contribute to statewide initiatives in performance-based man- agement and accountability, and incorporate new technology. Statutory Program Guidance The Revised Code of Washington (RCW) compiles all per- manent laws of the state of Washington; Title 47 deals with public highways and transportation. RCW 47.05, Priority Programming for Highway Development, was rewritten in 1993 as the result of the capital programming study men- tioned earlier and enabled WSDOT implementation of the new programming process to be fully implemented. The new statute restructured Washington’s highway investment program, introduced new capital construction programming processes that considered least-cost and benefit–cost evalu- ations of proposed solutions to transportation problems, and responded to new policy initiatives at the state and federal levels. The law has been revised since then to be coordinated with other chapters of Title 47 (e.g., defining legislatively mandated transportation goals) and to fit within an expand- ing application of performance-based management through- out Washington state government. The declaration of purpose of RCW 47.05 is as follows, with specific reference to use of economic methods: The legislature finds that solutions to state highway deficiencies have become increasingly complex . . . Difficult investment trade-offs will be required. It is the intent of the legislature that investment of state trans- portation funds to address deficiencies on the state highway system be based on a policy of priority programming having as its basis the rational selection of projects and services according to factual need and an evaluation of life cycle costs and benefits that are system- atically scheduled to carry out defined objectives within available

39 revenue. The state must develop analytic tools to use a common methodology to measure benefits and costs for all modes. The priority programming system must ensure preservation of the existing state highway system, relieve congestion, provide mobility for people and goods, support the state’s economy, and promote environmental protection and energy conservation. . . . The priority programming system for improvements must incorporate a broad range of solutions that are identified in the statewide transportation plan as appropriate to address state highway system deficiencies, including but not limited to high- way expansion, efficiency improvements, nonmotorized trans- portation facilities, high occupancy vehicle facilities, transit facilities and services, rail facilities and services, and transpor- tation demand management programs. Source: http://apps.leg. wa.gov/rcw/default.aspx?cite=47.05.010. Legislatively mandated goals for the transportation pro- gram are as follows (RCW 47.04.280): • Economic vitality: To promote and develop transpor- tation systems that stimulate, support, and enhance the movement of people and goods to ensure a prosperous economy; • Preservation: To maintain, preserve, and extend the life and utility of prior investments in transportation systems and services; • Safety: To provide for and improve the safety and security of transportation customers and the transpor- tation system; • Mobility: To improve the predictable movement of goods and people throughout Washington state; • Environment: To enhance Washington’s quality of life through transportation investments that promote energy conservation, enhance healthy communities, and protect the environment; and • Stewardship: To continuously improve the quality, effectiveness, and efficiency of the transportation system. programming mobility projects WSDOT’s highway capital construction program is divided into two major components, Preservation (P) and Improve- ment (I). Specific types of projects are organized within pro- gram categories under Programs P and I, respectively. Both major programs employ economic analyses to assist in project ranking and selection, program development, and recommen- dation of a biennial budget. The Preservation Program gener- ally considers the criterion of lowest life-cycle cost, whereas the Improvement Program is based typically on benefit– cost considerations. Other, nonmonetary factors are also considered in final decisions on P and I projects. The P and I programs are further subdivided into subprograms that contain specific types of projects. This case example addresses one of the Improvement Program subprograms, Mobility. The Mobility subprogram includes projects addressing urban congestion, rural mobility, urban bicycle connectiv- ity, and high-occupancy vehicle (HOV) lanes. Projects are grouped in this way to enable “peer group” or “apples-to- apples” comparisons among candidates when prioritizing and selecting the best solutions to identified needs or prob- lems. each program receives an investment target from the legislature; this target anticipates monies from a number of state and federal funding sources, each with separate require- ments (“2009–2011 Scoping . . .” Aug. 2007). Recommen- dation of those high-ranking projects to be constructed within the budget target is the task of the programming process. The process encompasses the following steps (MacDonald Feb. 2004; “WSDOT Projects . . . Prioritization” 2008): • To identify a problem or need (typically based on find- ings in the Highway System Plan), based on an identi- fied performance objective or goal. • To explore possible solutions and advance the most cost-effective and least capital-intensive alternative. • To develop a project scope that—in addition to esti- mated effects on transportation system performance— takes into account potential issues in environmental impact, roadway design, and stakeholder reaction, including community acceptance. • To estimate project costs based on information in the scope and develop a basis of estimate to document all assumptions. • To estimate project benefits based on information in the scope. • To compare the benefits and costs of this project with those of its peers to determine project rank and priority. As part of the Highway System Plan updating process, WSDOT uses multiple tools in screening and evaluating proj- ect candidates. CPDM uses the Highway Segment Analysis Program as a screening tool to identify all congested highway segments on the network, complemented by other WSDOT analytic tools (e.g., to identify bottlenecks). Resulting state highway needs are consolidated with road needs identified by MPOs, RTPOs, and tribal nations. Cost-effective solutions are then developed and analyzed using traffic analysis tools to make sure the projects improve performance. Next, the Mobil- ity Project Prioritization Process (MP3) tool is used to analyze the benefits and costs of each Mobility project as affected by its engineering and performance characteristics, to prioritize and rank projects within each subprogram, and to evaluate program tradeoffs in the face of budget constraints. • Screening criteria – Candidate projects that are not listed in the Highway System Plan are ineligible for further consideration. – To meet air quality conformity requirements, candidate projects that would degrade air quality in non attainment areas are ineligible for further consideration. – Given budget limitations, candidate projects might favor near-term to mid-term needs, rather than solely long-term needs, to warrant further consideration. • Evaluation criteria – BCA (discussed in the following section). – environmental impact: wetlands, water quality and permitting, and noise; evaluated on a nonmonetary

40 basis using either responses to yes–no questions (e.g., regarding permitting requirements) or penalty points and risk-factor points for adverse environ- mental consequences. – Stakeholder response: degree of community support, views of other stakeholders, potential disruption of neighborhoods; evaluated on a nonmonetary basis using responses to yes–no questions. – Project design: projected relationship of project to, or expected impact on, matters such as land use, efficient use of existing capacity, network/system connec- tivity, use of alternative modes including bicycling and walking, and modal integration (both inter- modal and packaged multimodal solutions); evalu- ated on a nonmonetary basis using responses to yes–no questions. These criteria are weighted, with the benefit–cost criterion having the heaviest weight. The mathematical prioritization considers both economic and nonmonetary criteria. Projects closer to the ideal-best result are higher in ranking; those closer to the theoretically worst result are lower in ranking. • Analytic tool – The MP3 analytic tool and its results are described in the following section. – To focus the technical discussion of this methodol- ogy, the case example considers a particular group of Mobility projects: those that improve highway capac- ity and operational performance to provide congestion relief. mobility methods and measures Engineering Economic Methodology The BCA of WSDOT Mobility projects is conducted using the Mobility Project Prioritization Process (MPPP or MP3). MP3 is a spreadsheet workbook that evolved from model develop- ment by WSDOT through the 1990s, which was improved with additions and modifications by a consultant team in 2000. The MP3 workbook accepts inputs on the type, location, and engineering characteristics of the project; traffic forecasting data; data to estimate benefits in travel-time reductions and collision reductions; and project cost data. MP3 users may also specify changes in key parameters [e.g., discount rate, project life cycle, benefit-days per year, hourly average annual daily traffic (AADT) distribution curves] and the internal representation of speed-flow curves to allow choice between the WSDOT default speed-flow relationship and that in the Highway Capacity Manual (HCM 2000). In most of the anal- yses, the benefit of travel-time savings is computed based on the difference in vehicle-hours of travel time with and with- out the project. For intersection improvements, the benefit of travel-time savings is based on the change in overall delay comparing the build and no-build options (Dowling Associ- ates, Inc. et al. May 2000, p. 9). eeAs of project benefits are structured individually for each type of Mobility improvement (Dowling Associates, Inc. et al. May 2000, supplemented by review of the current MP3 workbook provided by WSDOT): • Mainline lane addition/access management benefits: addition of general purpose lanes, addition of truck- climbing lanes, addition of a two-way left-turn lane on two-lane highways, and modification of type of median on four- to seven-lane highways. • HOV lane benefits: adding an HOV 2+ lane to an urban multilane highway/freeway, either or both direc- tions; converting a general purpose lane of an urban multilane highway/freeway to an HOV 2+ lane, either or both directions; and conversion of an HOV 2+ lane to an HOV 3+ lane when the HOV-lane volume reaches HOV-lane capacity. • Intersection improvement benefits: originally, improve ment of existing signalized intersections based on intersection control; later allowance for improve- ment of Stop-controlled intersections; later addition of roundabouts as a new type of intersection improvement. • New interchange benefits: new interchange at a new access point. • Park-and-ride lot benefits: road user benefits result- ing from constructing a park-and-ride lot adjacent to a state highway; the workbook provides several options on type and location of the parking lot. • Safety benefits: benefits of expected accident reduc- tions owing to the highway improvement; benefits assigned to collision reductions in five categories: fatal- ity, disabling injury, evident injury, possible injury, and property damage only. Consider the example of the addition of a general purpose lane: • Input data or internal global values on the proposed lane- addition project, traffic volume and composition, traffic growth rate, and 24-hour distribution of daily traffic are used to estimate the effects on speed and travel time under the build and no-build options, in the analysis base year and the analysis future year. Standard engineering cal- culations such as those used with the Highway Capacity Manual are applied to compute volume–capacity ratios, resulting operating speeds, implied travel times, and travel-time savings resulting from the proposed project. • Benefits in each of the 24 daily hours are computed using a number of default values within MP3, which can be changed from time to time with appropriate documen- tation of source and CPDM concurrence. These values include a factor that specifies the number of days per year for which benefits are assumed (i.e., the number of days per year for which the 24-hour distribution of traf- fic applies; e.g., 260 days per year); wage rates appli- cable to drivers of general-purpose vehicles and trucks, respectively; together with a multiplicative factor identi-

41 fying the percentage of wage rate to be used in the ben- efits calculation (e.g., 50% for general vehicles, 100% for trucks), average vehicle occupancy during peak and off-peak periods, and the travel-time savings computed earlier. • Benefits are tallied for each of the 24 daily hours and expanded to annual totals for each year of the analysis period using the specified days-per-year figure discussed earlier (e.g., 260 days per year). The value of the discount rate (an MP3 global variable with default value of 4%; deviation from this figure requires WSDOT approval) is used to compute the present value of the benefits stream. • Project costs are input using data from the project scop- ing estimate or planning-level cost estimate. Construction cost inputs cover preliminary engineering, right-of- way, and construction of structures, drainage, grading, and other items. Total construction costs are reduced by the amount of cost sharing by agencies other than WSDOT. Operation and maintenance costs are input on an annual basis; a workbook calculation applies these to each year of the analysis period, and computes the pres- ent value using the present-value-of-annual-series fac- tor for the specified discount rate and length of analysis period (e.g., 4%, 20 years). The present value of total costs equals the sum of WSDOT construction costs and the present value of operation and maintenance costs. • The workbook computes the net present value (present value of benefits minus present value of costs) and the benefit–cost ratio (present value of benefits divided by present value of costs). Results of Analyses A corresponding approach is used for other types of Mobility projects addressed by the MP3 workbook. A summary of the analytic elements on each workbook tab, including the tabs (or worksheets) for the respective project types, is shown in Table 9. Results for all of these analyses are expressed as net present values and benefit–cost ratios. mobility Decision support The benefit–cost results for Mobility projects, together with results of corresponding economic analyses for other I and P subprograms, provide the economic input to project prioriti- zation that is critical to WSDOT’s development of its capital construction program and biennial budget. The recommended project rankings produced by the analytic programming procedures such as MP3 are helpful in understanding the economic value-to-cost of projects and programs, as well as their relative strengths in other, nonmonetary criteria; how- ever, they do not determine the final budget. Flexibility in the process allows WSDOT to respond to other influences such as community interest and need. Individual projects may be raised in priority and others deferred to compensate within the constrained budget. The legislature may also direct fund- ing to specific projects regardless of their computed priority (“WSDOT Projects . . . Prioritization” 2008). These results of the programming process are reviewed internally by department executives and other senior manag- ers. externally, the resulting program and budget recommen- dations are forwarded to the legislature and communicated to the appropriate executive agencies, other stakeholders, and the public. Budget recommendations are reviewed by the Washington State Legislature, including confirmation of revenue forecasts to fund the transportation programs. Separate reviews and hearings are conducted by the House and the Senate Trans- portation Committees, respectively. either committee may adjust the proposed list of projects or the amount of funding requested in any of the programs. One or both committees may file a budget bill, which proceeds through the legislative process to final passage and submittal to the governor for sig- nature. The governor may sign the bill as is, veto selected line items, or veto the entire bill, returning it to the legislature for further action. After the transportation budget is passed and signed, CPDM works with WSDOT’s Budget Services Office to communicate legislative authorizations and funded items internally to WSDOT regional managers and modal system managers, enabling final adjustments to lists of projects and related tracking-system data. Baselines are established for monitoring subsequent project delivery at the regional and headquarters levels. These baseline data are also incorporated within the legislature’s computerized tracking system and WSDOT’s Transportation executive Information System, enabling the legislature and department executives to moni- tor progress in delivering WSDOT’s transportation programs (“Building the Capital Program” Feb. 2008). programming safety projects In May 2005, AASHTO presented WSDOT with its newly established Safety Leadership Award, recognizing the depart- ment’s “proactive approach to safety”: This approach involved [a] local, corridor, and system-wide perspective. Working with other safety agencies, WSDOT adopted a strategic safety plan, called Target Zero. As an out- come, the state has had a 56% decrease in fatal and disabling crash rates since 1990 even though vehicle miles traveled over that period have increased by 35%. Source: Measures, Markers, and Mileposts: The Gray Notebook, Quarter ending June 30, 2005, p. 52. Washington State has continued to apply its management, planning, engineering, data collection, and analytic resources to identify and apply cost-effective measures that reduce the societal costs of fatal and disabling crashes. The approach is holistic in that a number of Washington’s highway programs and subprograms have measurable safety-related objectives. These objectives consider historical experience; for exam- ple, highway locations/sections that have a serious accident

42 Worksheet Description Required Inputs/Actions Optional Inputs Notes/Comments Software Notes Provides software’s purpose, structure, color coding scheme. Describes each of the worksheets. None None None Project Description Project description Project description, including route, posted speed, title, beginning and ending mileposts, no build and build num ber of lanes, and terrain None The default population density is taken from the Global Variables worksheet. Posted speeds are rounded to 50, 60, or 70 mp h. Global Variables Benefit–cost analysis assum ptions and default values that are used throughout the workbook. Discount rate ( i ), project life cycle ( n ), benefit days per year, select or define ADT 24- h distribution curve, identify start and end of a.m . and p.m . peak periods, value of tim e and operating costs, population density (urban or rural) Project-specific peak and/or off-peak AVOs. Can provide ratio of benefits to new users (default assumes economic “rule of half”) Defaults should be used unless there is a co mp elling reason to do otherwise. Any m odifications to the default values need to be docum ented. 24-Hour Volume Distribution Chart Graphically displays the selected Year 1 directional and total volume distribution by hour of the day Select or define the ADT 24-h distribution curve in the Global Variables worksheet. The selected curve will automatically be displayed in the 24 Hour Volume Distribution chart None Graph only displays the selected Year 1 curve. Estimate and B-C Ratio Cost estimates for preliminary engineering, environmental retrofit, right-of-way, construction, operation & maintenance. Incorporates present value of user benefits for each particular im provem ent. Estimates the benefit/cost ratio. Quantities needed for cost calculations, non-WSDOT cost share, and operation & maintenance costs, or total WSDOT present value costs (PVc) User has the option of entering general cost per m ile estimates, or a resultant to tal WSDOT present value cost (PVc) estim ated outside of the worksheet. Can use general cost per mile calculations or detailed cost calculations Output from this worksheet is used as inputs to TOPSIS to pr io ritize highway mobility projects. 4-Step M odel Benefits Estim ates annual 24-h user benefits based on output from an accepted 4-step m odel. Model description, truck percent, peak period AVOs, and 24-h vehicle-hours traveled on state facilities 24-h vehicle-hours traveled on entire system , not just state system. Can estim ate user benefits for entire system if data are provided, but only benefits for state system users will be incorporated into overall project B/C rat io. Two-Way Left-Turn Lane (TWLTL) and Multilane Acces s Management Benefits Estim ates annual 24-h user benefits for converting a 2-lane undivided facility to a 3-lane TWLTL facility (Harwood/St. John method), or for median treatm ents and/or access spacing changes for 4–7 lane facilities ( NCHRP 395 method). Peak direction of selected ADT hourly distribution curve, median type, average access spacing, access control class, daily and peak hour traffic data, and truck % Peak and nonpeak turns per access, if evaluating benefits using the NCHRP 395 meth od. Uses ADT hourly distribution curve selected in Global Variables to estimate peak and off-peak percents and to convert working peak hour user benefits to 24-h benefits. General Purpose Lane Benefits Estim ates annual 24-h user benefits for adding a general purpose lane. Facilities that can be analyzed include: a 2- lane highway, an arterial, a rural/sm all urban freeway, or a mu ltilane highway or freeway. No build and build posted speeds, direction(s) of added lane, ADT and K factor or working peak hour volum es, truck percent, grade and length of grade, volume growth rate, and roadway type ADT and K factor or working peak hour volume is required, but either can be input. Can input data for one or two directions. Benefits are estimated by each hour of the day for the selected direction(s) of the facility. Climbing Lane Benefits Estimates the annual 24-h user benefits for adding a truck clim bing lane to a 2-lane highway or to an arterial. Sam e as above Sam e as above This worksheet has not been updated to look up values from the WSDOT speed-flow curve worksheet. WSDOT curves are em bedded in worksheet. TABLe 9 MP3 WORKSHeeT DeSCRIPTIONS

43 role of economic analysis in Highway safety Investment The computation of the societal costs of accidents (or the benefits of avoiding these costs) is based on the following (Median Treatment Study . . . Mar. 2002): • Identification of the societal costs of different severities of accident: cost per fatal collision, cost per disabling (or serious) injury collision, cost per evident injury col- lision, cost per possible injury collision, and cost per property-damage-only collision. • Identification of the frequency of occurrence of each cat- egory of accident severity, before and after a particular history—as well as proactive analyses of highway character- istics and traffic volumes and behaviors that point to a poten- tial for accidents in the future (“Safety Management System” Oct. 2009). WSDOT’s highway system Preservation (P), Improvement (I), and Maintenance (M) programs all play a role in promoting highway safety. However, this case exam- ple will focus specifically on projects included in the Safety improvement (I2) subprogram. Although a number of state DOTs use economic dollar values in analyzing accident costs and conduct safety-related benefit–cost studies, WSDOT’s approach is unique in the way it has organized the leadership of statewide highway safety initiatives, including coordina- tion with other agencies and stakeholders. Worksheet Description Required Inputs/Actions Optional Inputs Notes/Comments Intersection Benefits Estimates the annual 24-h user benefits for improving an existing intersection No build and build total approach volumes, number of lanes, average intersection delays, and in tersectio n v/c ratios, existing approach volum es by hour for 24-h, and build scenari o percent reduction by approach Most recent counts of hourly approach volumes that can be converted to existing hourly approach volumes Benefits are estimated by each hour of the day. Since Year 20 VHT can be higher than Year 1 VHT, there is a potential for negative benefits. When negative benefits are estim ated, they are assum ed to be zero benefits. New Interchange Benefits Estimates the annual 24-h user benefits for adding a new interchange to an existing facility Year 1 and Year 20 working peak hour volumes, distances and speeds or travel tim es for no build and build or ig in– destination (O-D) pa th s Model travel times can be input for specific O-D paths instead of being calculated based on distances and speeds. Working peak hour user benefits are converted to 24-h benefits using ADT hourly distribution curve selected in Global Variables. HOV Lane Benefits Estimates the directional annual 24-h user benefits for addi ng an HOV lane Directional num ber of lanes with and without project, ADT or directional working peak hour volum es, HOV and GP growth rates, truck percentages, and traffic composition Can select the HCM 2000 speed-flow curve instead of using the WSDOT default curves. Can change default GP/HOV capacities per lane, but mu st document. Benefits are estimated by each hour of the day for the selected direction(s) of the facility. Worksheet assu me s that HOV lane can be used by GP traffic outside of the peak period. Park & Ride Lot Benefits Estimates the bi-directional annual 24-h user benefits for constructing a park & ride lot. Nu mb er of parking spaces, percent of lo t capacity used, various destination data, user distribution (t ransit riders/carpoolers), and AVOs None 24-h benefits are assum ed to be equal to working peak hour or peak period benefits. Safety Benefits Estimates the annual 24-h user benefits of im proving the safety of a facility. Selection of safety im provem ents, identification of the num ber of accidents by type of accident None None WSDOT Default Curves Contains WSDOT default speed-flow curves for 50, 60, and 70 mph facilities. Speeds are dependent on v/c ratio and the number of lanes. HOV lane speeds are dependent upon volumes. None None The lowest allowed congested speed for general purpose lane speeds is 15.2 mph (for v/c ± 1.2). Allowable HOV lane speeds are 55 mph at free-flow down to 40 mph at capacity. HOV lane speeds are solely dependent on lane volumes and an assumed capacity HCM 2000 Curves Contains the HCM 2000 speed-flow curves for freeways. Speeds are dependent on free-flow speeds, length of segment, and v/c ratio. Posted speed and length of section must be provided in the Project Description worksheet. These values are used to estimate speed-flow relationship. None Freeway speeds for GP and HOV lanes can range from free-flow speeds down to about 12 mph at a v/c of 2.0. Source: WSDOT MP3 workbook, “Software Notes” tab (2009). TABLe 9 (continued)

44 safety action (e.g., a safety project, enforcement activ- ity, or educational campaign). • Computation of benefits in terms of the reduction in accident societal costs resulting from the safety action (whether a reduction in accident frequency, accident severity, or both), comparing the “before” and “after” cases with the yearly benefits discounted through an analysis period. • Computation of costs of performing the safety action (typically construction plus maintenance) with the annual costs discounted through the analysis period. • Computation of the benefit–cost ratio, using the dis- counted values. Although the B/C ratio is computationally straightforward, predicting accident frequency and severity that result from a safety investment can be difficult. Technical studies such as those described here provide a basis for estimation. Similarly, valuing the societal costs of an accident involves a number of assumptions; cost- and benefit-related issues and a synthesis of state DOT practices are discussed by Hanley (2004). In its safety analyses, WSDOT uses societal costs recommended by FHWA (2007–2026 Highway System Plan . . . Dec. 2007). Legislative Guidance and Agency Goals WSDOT’s highway-safety approach responds to the provi- sions of the federal SAFeTeA-LU legislation (P.L. 109-59, Aug. 10, 2005). SAFeTeA-LU establishes and funds the Highway Safety Improvement Program as a core program, giv- ing states flexibility to address their most critical safety needs with a focus on demonstrating performance. It calls for states to develop Strategic Highway Safety Plans (SHSPs), approved by the governor or a responsible state agency, to identify safety needs and opportunities, propose ways to address them through prioritized actions, and evaluate the quality of data. To conform to the provisions of SAFeTeA-LU, the SHSP is developed in consultation with others involved in high- way safety. It specifies performance-based goals for meet- ing highway safety needs in both the infrastructural and the driver behavioral categories on all public roads, proposes ways to assess resulting improvement in safety performance, and applies these lessons to prioritizing future safety actions (SAFeTeA-LU Aug. 10, 2005). WSDOT’s SHSP is embodied in the Target Zero document mentioned earlier, currently updated to 2010 [(Target Zero) Washington State’s Strategic Highway Safety Plan . . . Aug. 27, 2010]. This strategic safety plan sets the important aspirational goal of zero traffic deaths and serious injuries on Washington State’s roads by 2030. Consultation in developing this SHSP has included a number of state agencies: WSDOT; State Patrol; Departments of Health, Licensing, and Social and Health Services; Washington Traffic Safety Commission; Washington Transportation Commission and a host of others; several federal agencies; tribal nations and organizations; private and nonprofit groups; and community, local, and regional agencies and organizations. The plan encompasses the “four es” commonly associated with highway safety programs: engineering, education, emergency services, and enforcement. Key elements of Target Zero are incorporated within WSDOT’s 20-year Highway System Plan. The SHSP indicates that fatal highway accidents have declined in Washington State from a rate of 4.91 deaths per 100 million vehicle-miles traveled (MVMT) in 1966 to 0.94 per 100 MVMT in 2008, the state’s lowest traffic fatality rate on record and below the 1.27 per 100 MVMT national rate computed by NHTSA (Target Zero, p. 7). Several likely reasons for this decline in fatal crashes are cited, including decreased levels of driving resulting from escalating gaso- line prices and the economic recession in 2008; investments in cost-effective, performance-enhancing safety projects; improvements in roadway engineering, specific roadside safety features (discussed in greater detail later), vehicle design, and safety equipment; and the beneficial effects of safety education, tougher impaired-driver and seat-belt-use laws, faster emergency response, and law enforcement. Not- withstanding these improvements, challenges to meeting the Target Zero goals remain. For example, motorcycle deaths are increasing, countering the otherwise favorable motorist fatality trend. Although impaired-driver-related fatalities are decreasing, they are not dropping fast enough to meet the 2030 zero-level target. WSDOT has adjusted its proposed safety countermeasures to address these issues. Target Zero organizes the factors involved in traffic fatali- ties, related safety analyses, and resulting recommendations within four priority levels. For the 2010 update, these priority levels are based on recorded percentages of total highway fatal- ities during 2006–2008, as follows (Target Zero, pp. 11–14): • Priority One consists of factors implicated in 40% or more of traffic fatalities between 2006 and 2008. It includes accidents involving alcohol- or drug-impaired drivers, speeding, and run-off-the-road crashes. each of these factors was identified as a contributing circum- stance in accidents accounting for 40% or more of total highway fatalities. (Author’s note: in structuring these priority levels, the number of fatalities, not the number of fatal crashes, is used.) • Priority Two consists of factors implicated in 21% to 39% of traffic fatalities in 2006–2008. It includes acci- dents involving young drivers (ages 16–20 and 21–25), unrestrained passenger vehicle occupants, distracted drivers, and accidents at intersections. • Priority Three consists of factors implicated in 11% to 20% of traffic fatalities in 2006–2008. It includes acci- dents involving unlicensed drivers; opposite-direction, multi-vehicle collisions; motorcyclists; pedestrians; and heavy trucks. • Priority Four consists of factors implicated in less than 10% of traffic fatalities in 2006–2008. It includes accidents involving older drivers, drowsy drivers, nonmotorized cyclists, road work zones, wildlife, vehicle–train collisions, school buses, and aggressive drivers.

45 Target Zero notes that many fatalities are associated with more than one of these factors. These traffic deaths are there- fore represented more than once in the fatality data associated with the four priority levels. Technical and Organizational Approach WSDOT, like several other state DOTs, has found that a partic- ularly cost-effective approach to reducing fatal and disabling- injury accidents is to invest in low-cost, systematic safety improvements. WSDOT has focused on centerline rumble strips and cable median barriers on its mainline state high- ways as successful ways to manage vehicular departures from the road. Other cost-effective, performance-enhancing safety measures include improvements in (or greater use of) the fol- lowing: pavement markings (including wider markings, chev- rons, and route decals or “horizontal signing”), directional signage, fluorescent yellow sign sheeting (e.g., on curve- warning signs), addition of left-turn lanes, active-warning sys- tems (e.g., for “crossing traffic ahead” and advanced-warning “end-of-green” flashers), roadway lighting, shoulder and edge- line rumble strips, access management (e.g., raised medi- ans), speed-feedback signs, vehicle recovery areas, guardrail end treatments, roadside or guardrail delineators, and features at intersections (e.g., improved vehicular and pedestrian traffic signals, transverse rumble strips, improved signage, and round- abouts). Several state DOT presentations on these types of traf- fic engineering countermeasures were given at a traffic safety summit (“everyOne Counts” Feb. 2009). WSDOT’s organizational approach to highway safety improvement differs from models used in some other DOTs. In lieu of a designated safety office or safety engineer, WSDOT organized a Highway Safety Issues Group (HSIG) in the 1990s. Co-chaired by the heads of traffic operations and highway design, the HSIG core membership consists of representatives of WSDOT planning, program management, traffic operations, WSDOT regional traffic and design engineers, and the FHWA division office. By its nature, it promotes a team approach and brings multidisciplinary expertise to safety issues. The HSIG undertakes a number of activities, among them identifying areas of potential safety improvement and coordinating the development of safety policies and initiatives on behalf of the department. It may undertake studies such as safety BCAs, recommend applications of departmental safety resources, and review proposed actions submitted by WSDOT management. It acts as a champion for safety. It also can interact effectively with outside groups through the Washington Traffic Safety Commission (WTSC) (Mercer Consulting Group June 2007, pp. 6–7; State of Alaska . . . Sep. 2007, p. e-15). safety program methods and measures WSDOT’s assignment of Priority One to run-off-the-road crashes and its emphasis on centerline rumble strips and cable median barriers as technically and economically feasible solutions resulted from nationwide data and analyses that were conducted in the 1990s and early 2000s. A key influ- ence on WSDOT’s thinking was a study by the Insurance Institute for Highway Safety, or IIHS (Persaud et al. 2003). The IIHS report compiled available data and research find- ings from several sources, including FHWA, NHTSA, state DOTs, and academic and consultant researchers, all within the 1990s–early 2000s time frame. These research results collectively indicated the following (Persaud et al. 2003, pp. 1–3): • Although urban areas experience the highest rates of motor vehicle accidents overall, fatal accidents are more likely to occur in rural areas (2.3 fatal crashes per 100 MVMT on rural highways versus 1.0 fatal crash per 100 MVMT on urban highways nationally). • Reasons for the higher average rate of severe accidents on rural roads include generally higher traffic speeds, lower seat belt use, longer response times for emergency medical assistance, and road design characteristics, particularly on rural two-lane roads. • Nationally, rural two-lane roads account for approxi- mately 90% of all fatal crashes on rural highways. The characteristically undivided configuration of two-lane highways, and the absence of wide medians or centerline barriers to physically separate opposing-traffic flows, are factors in vehicles crossing the centerline. • The result of vehicles departing from their correct direc- tional lanes can be head-on collisions or the sideswiping of vehicles traveling in the opposite direction. Although these collisions are not the result of a single cause, fac- tors typically cited by police include failure to keep in the proper lane, driver inattention, driver fatigue, and speeding. • Roadway widening and installation of centerline barri- ers are possible highway engineering solutions to reduce opposing-traffic collisions; however, they are expensive and therefore tend to be limited to specific, high-priority locations. Such spot-location fixes do not solve the more general problem of opposing-traffic collisions that can occur virtually anywhere along the length of a two-lane, undivided highway. • A more economical and practical potential solution is the installation of centerline rumble strips along the length of undivided two-lane highways. By providing an audible vibration under vehicles encroaching on the centerline, rumble strips can alert inattentive, fatigued, distracted, or speeding drivers that they are drifting into the opposite lane. • Rumble strips had already proven themselves on the right-hand shoulders of limited access highways in reducing run-off-the-road-to-the-right incidents, which did not involve collisions with opposing traffic. How- ever, at the time of the IIHS study (2003), there was relatively little research or field experience on how these rumble strips would perform on the centerlines of two-lane rural highways. The limited informa- tion that was available, however, comprising simple before–after comparisons of crash rates in studies

46 by two state DOTs, indicated that centerline rumble strips did reduce the rates of both head-on collisions and opposing-direction sideswipes. • The purpose of the IIHS study was to update these findings on the value of centerline rumble strips in improving rural highway safety. It did this by expand- ing the available data to a larger pool of state DOT experience, and refining the analysis of crash reduc- tions resulting from centerline rumble strips to cor- rect for certain mathematical algorithms and biases in earlier works. • The results of the 2003 IIHS study indicated that center- line rumble strips did indeed result in significant crash reductions on two-lane rural highways. All injury crashes combined (i.e., disabling injury, evident injury, and possible injury) were reduced by an average of 15%, or a range of 5% to 25% at the 95% confidence inter- val. Head-on (frontal) crashes and opposing-direction sideswipe crashes were reduced by an average 25% (5% to 45% at a 95% confidence interval). The study concluded: In light of their effectiveness and relatively low installation costs, consideration should be given to installing centerline rumble strips more widely on rural two-lane roads to reduce the risk of frontal and opposing-direction sideswipe crashes. Source: Persaud et al. 2003. The evaluation of candidate safety project sites entails a technical diagnosis of problems and potential solutions, plus a BCA to assist in prioritization. safety program Decision support Decision-Making Approach The objective of this study is to identify cost-effective solu- tions that yield a high rate of return in terms of reducing fatal and serious (or disabling) injury crashes. For a valid analy- sis, however, the locations, frequencies, and circumstances of fatal and serious-injury accidents must be known. WSDOT relies on a GIS-based safety management reporting system, supported by descriptive accident data provided by the State Patrol, which enables WSDOT managers to identify where serious safety problems exist, what factors are influenc- ing crashes (particularly those of high severity), and what options might provide the best solution. (WSDOT’s Trans- portation Data Office heads a Collision Report Commit- tee that, with the cooperation of the State Patrol, provides for uniform accident reporting across the state.) The GIS- based graphical displays are packed with information that assists highway and traffic engineers in diagnosing crash locations, clusters, and situations. The highway route and the crash-location symbols employ color coding to indi- cate crash severity, density of clustering, and locations of significant Priority One events. each accident indication can be expanded to reveal detailed text descriptions of all crashes that have occurred at that location within the speci- fied time frame (which can be multi-year), based on the aforementioned State Patrol reports. Based on these data, WSDOT can pursue cost-effective solutions that provide the “biggest bang for the buck” in addressing the targeted safety goal. As an illustration for this case example, WSDOT’s analysis shows that many fatal accidents are caused by head-on collisions on undivided highways. The GIS reporting system allows WSDOT to pinpoint those highway locations having the greatest con- centration of these crashes or of vehicles leaving the road after crossing the centerline and opposing lanes. In lieu of relatively expensive centerline barriers, WSDOT has pur- sued more economical centerline rumble strips. The BCA described earlier allows WSDOT to identify high-priority segments where the installation of centerline rumble strips is recommended. It is not unusual for B/C ratios in these seg- ments to exceed 100 to 1. Legislative Review and Approval This methodology is the foundation of WSDOT’s safety pro- gram budget recommendations. The recommendations are submitted to the legislature as part of the transportation bud- get package. The legislature reviews these recommendations and proposed funding levels, and may make adjustments as described earlier in the section on Mobility before sending the approved budget to the governor for signature. Follow-Up Studies WSDOT has followed up on this benefit/cost-based prioriti- zation process to determine whether the safety performance results for centerline rumble strips has been effective. (One could also consider economic performance to be reflected in the before–after analysis of crash statistics, because changes in the frequencies of different accident severities underlay the benefit–cost calculation.) The results of this follow-up study could then inform any updates needed in WSDOT’s highway design guidance for centerline rumble strips. Find- ings and conclusions of this study were as follows (Olson et al. Mar. 2011, pp. ix–x): • The collisions of primary concern when installing cen- terline rumble strips are crashes with opposing traffic, either frontal (head-on) or sideswipes. The observed before–after results were a 44.6% reduction in All Injury Severities and a 48.6% reduction in Fatal & Serious (Disabling) Injury collisions. • In this study, this positive performance result held for all ranges of posted speed limits. No particular speed limit (or range of limits) detracted from the reduction in cross-centerline collisions. • This positive performance result held for all contributing causes to crashes except one: excess speed. An 18.5%

47 increase in Fatal & Serious Injury crashes occurred when speeding was a contributing cause. For all other contrib- uting causes, rates of both Fatal & Serious Injury crashes and All Injury Severities crashes declined following the installation of centerline rumble strips. • With respect to horizontal alignment: Cross-centerline collisions decreased by 59.0% on tangent sections and by 26.8% on curves after installing centerline rumble strips. On the curved sections that were studied, the Fatal & Serious Injury crashes that did occur were pri- marily the result of excess speed or to drivers impaired by alcohol or drugs. Also, there were differences in the resulting accident rates depending on whether the cross-centerline collisions occurred on the inside or the outside of the highway curve. • Centerline rumble strips were not anticipated to reduce the collision rates for run-off-the-road-to-the-right events, but they did: a 6.9% decline in All Injury Sever- ities crashes and a 19.5% reduction in Fatal & Serious Injury crashes. Although the research team found this result interesting, further investigation as to why this result occurred and how to explain it was judged to be beyond the scope of that study. • Conclusions: Centerline rumble strips “are an effective, low-cost, low-maintenance countermeasure that sig- nificantly reduces the frequency of collisions, regard- less of lane/shoulder width, posted speed limit, or any of the other geometric conditions examined.” To fur- ther the applications of this successful countermeasure, WSDOT planned to conduct a further study of noise aspects to determine where centerline rumble strips could be installed acceptably in residential areas. Based on the findings of this study, the research team rec- ommended that (1) WSDOT maintain its current guidance on reducing cross-centerline collisions; (2) WSDOT continue installing centerline rumble strips conforming to this guid- ance; and (3) from the analytic results, future priority might be given to locations with AADT less than 8,000, combined (one-directional) lane plus shoulder widths of 12 to 17 ft, and posted speeds of 45 to 55 mph (Olson et al. 2011). extension to Highway system planning Strategic View Reducing congestion is critical to Washington State’s people, economy, environment, and quality of life. “Moving Wash- ington” has been formulated as a strategic initiative compris- ing actions in three broad areas, all of which are needed to improve mobility in major transportation corridors (“Conges- tion” and “Moving Washington . . .” 2010). WSDOT execu- tives issue guidance to the planning process in terms of these focus areas: • Managing demand entails commuter travel options that promote greater efficiency by reducing the need to drive, particularly to drive alone. There are many possibili- ties, such as access to convenient bus service, carpool- ing and vanpooling, telecommuting, and flextime. Other measures include real-time traffic information displayed on variable message signs, which can influence traffic demand to shift to less congested routes. • Operating the highway system more efficiently by improving the functioning of existing roads. This approach includes measures that smooth traffic flow and remove impediments to flow more efficiently, as in responding to accidents. • Adding capacity strategically through informed invest- ment choices by focusing on the worst bottleneck loca- tions. WSDOT notes that such an approach can improve traffic flow on longer segments of highway while remain- ing within budget constraints. These strategies are part of the process incorporated in the production of the Highway System Plan. Identifying the most cost-effective options within these strategies and pro- ducing a balanced approach to congestion reduction require additional considerations before BCAs are addressed. The WSDOT office of CPDM introduces these additional con- siderations as screening criteria and by structuring a tiered, incremental approach to defining candidate solutions for fur- ther evaluation in the planning process. Screening and Structuring Potential Solutions The screening process recognizes that there is insufficient annual funding to achieve free-flow conditions on highways statewide. The goal is therefore to achieve maximum through- put on congested state highways: approximately 2,000 vehicles per hour, at speeds of 42–51 mph, or about 70% to 85% of the posted speed. At speeds below this threshold, the throughput decreases and the highway no longer operates efficiently. A key screen used by WSDOT for assessing mainline high- way congestion is to identify locations where peak-hour speed is less than 70% of the posted limit. This is the pri- mary criterion; others, related to bottlenecks, chokepoints, and congested corridors, are described in WSDOT’s High- way System Plan (2007–2026 Highway System Plan . . . Dec. 2007). Needs identification is accomplished in coor- dination with the appropriate MPOs or RTPOs. Proposed projects that meet these criteria are advanced to the next step in the planning process. Those that do not yet meet these screening criteria are held in the Highway System Plan database for future consideration should traffic condi- tions change on these segments or locations. Another mechanism used by WSDOT to guide project development toward effective and efficient solutions is to apply a tiered, incremental approach in defining projects. In this way, solutions that do not entail large capital expendi- tures are investigated first; and, new projects build on the improvements accomplished by previous projects, avoiding

48 wasted effort. The project tiers are at three levels (2007–2026 Highway System Plan . . . Dec. 2007, p. 70): • Tier I—low-cost projects with high return on capital investment and short delivery schedules; for example, incident management, ITS, access management, ramp modifications, turn lanes, and intersection improvements. • Tier II—moderate- to higher-cost improvements that reduce congestion on both highways and affected local roads; for example, improvements to parallel corri- dors (including local roads), auxiliary lanes, and direct- access ramps. • Tier III—highest-cost projects that yield corridor-wide benefits; for example, commuter rail, HOV/HOT lanes, additional general-purpose lanes, and interchange modifications. The incremental aspect of WSDOT’s planning process means that proposed mobility solutions in Tier I must be evaluated (unless they already exist on the highway segment under study) before Tier II solutions can be recommended. Proposed mobility solutions in Tier I and Tier II must be eval- uated (unless they already exist on the highway segment under study) before Tier III solutions can be recommended. evalua- tion of tiered solutions at this step entails an analysis of traffic impacts and performance improvement over 10 or 20 years. Further Evaluations for Inclusion in System Plan Once solutions at the appropriate tiers have been identified as candidates they are subjected to a BCA using the MP3 tool. Solutions with favorable benefit–cost results receive further review under additional criteria; for example, impact on cur- rent and future needs projections, the degree of improvement in traffic throughput, and the estimated number of years that the solution will last (in terms of throughput speed meet- ing or exceeding 70% of posted speed). Proposed solutions, refinements of concepts, and the BCA are conducted in coop- eration with cognizant MPOs and RTPOs. Those projects judged most favorable are entered in the Highway System Plan database and forwarded to headquarters executives for review and approval. Projects that are judged as not yet meet- ing criteria for selection are held in the Highway System Plan database for further future analysis (“2011–2030 Highway System Plan . . .” n.d.). Analytic Tools The MP3 workbook that was described for project program- ming is also used to evaluate Mobility solution benefits at the planning stage. Because projects have not yet been scoped, however, prepared cost estimates are not available. WSDOT has therefore developed a Planning Level Cost estimation tool to estimate costs for projects still at a conceptual level of development. It is based on historical unit price data for key highway construction cost factors, accounting for regional variations and differences in land use and development den- sity within a region. Input data describe the project in terms of characteristics and features of its right-of-way, mainline roadway, intersections and interchanges, crossroads, bridges, retaining walls, noise walls, wetlands, ITS features, and other items. Unit prices are applied to the quantity estimates for these items; assigned prices also account for regional location (Central Puget Sound, Vancouver, Spokane, other parts of the state) and density of local development (rural, suburban, urban, dense urban). Adjustments can be included for preliminary engineering, mobilization, construction engi- neering, traffic control, and other implementation items, as well as a separate adjustment for uncertainty (Murshed and McCorkhill 2008). resources needed and other Information The MP3 workbook and the Planning Level Cost estima- tion tool are the primary analytic tools for the BCA at the planning stage. The MP3 workbook and project scoping estimates provide benefit–cost data for project programming. IDAS (ITS Deployment Analysis System) software is used for ITS cost and benefit estimates. WSDOT also applies a number of other software packages for different types of traf- fic analyses depending on the complexity of the proposed solution (“Requirements for Proposed . . .” n.d.). WSDOT staff is conversant with economic methods, and apply the information and tools discussed throughout this summary for long-range and biennial planning updates, capi- tal programming, and budget development. The department makes use of academic and consulting experts for tasks such as research, business-process renewal, model/system devel- opment, and implementation assistance. For the most part, however, the department assumes responsibility for using these products once completed. brIDge projeCt programmIng anD permIttIng Introduction This case describes the methodology applied by Caltrans for bridge project programming, with significant influence on deci- sions exerted by permitting requirements. Caltrans applies the Pontis™ bridge management system (BMS) for conventional analyses of bridge preservation and mobility improvement, and for decision support in project prioritization. However, a number of critical, risk-related bridge needs are not addressed by a BMS and must be analyzed separately. Moreover, bridge projects in California are potentially subject to permitting requirements or right-of-way negotiations that, experience has shown, can extend several years beyond the time needed for project plan development. The Caltrans Bridge Manage- ment Office has therefore developed a unique and innovative

49 approach to evaluating bridge projects for inclusion in its State Highway Operation and Protection Program (SHOPP). This procedure entails the use of utility theory to capture the benefits of reducing risks of degraded bridge performance regarding scour, seismic events, and bridge-railing safety, in addition to benefits associated with meeting the preserva- tion and mobility needs. This computed value of utility is applied as the measure of benefit in a “benefit–cost analysis” (or, perhaps more accurately, a cost-effectiveness analysis structured as a B/C ratio). Cost-effectiveness is not, how- ever, the only decision variable to be considered. The time to obtain permit approval for these bridge projects, particu- larly in coastal regions and certain other situations, means that the programming decision must consider those projects that realistically can be expected to be ready for construction within a manageable time period. The following descriptions describe Caltrans’ analytic procedures for programming of bridge needs, and use of these results in decisions on bridge project recommendations. role of economic analysis in Highway Investment Background With an inventory of just under 13,000 state highway bridges and with bridge needs exceeding annual funding, Caltrans looks to make informed decisions in selecting the “best” projects for its bridge program. The California SHOPP identifies bridge preservation needs in five areas: (1) reha- bilitation and replacement owing to deterioration of bridge elements, (2) scour risk reduction, (3) seismic risk reduction, (4) bridge rail upgrade (a safety matter), and (5) mobility upgrades (raising and strengthening structures to accom- modate updated traffic volumes and vehicle characteristics). SHOPP lists funding commitments to selected projects through a 4-year programming period. California state law also requires a 10-year SHOPP plan that identifies uncon- strained needs across all transportation assets. Although BMS analyses, which include economic as well as technical modeling, can address needs for preservation (rehabilitation or replacement) owing to condition-based deterioration of bridge elements and for mobility upgrades, they do not deal effectively with risk-related problems: seismic, scour, and bridge-rail safety. These risk-based needs, which account for about 40% of the total SHOPP bridge-related amount, require different analytic procedures. Caltrans has turned to multi-objective utility theory to represent the benefits of addressing the five categories of bridge needs, with initial application of the procedure to the 2008 SHOPP develop- ment (Johnson 2008). Multi-Objective Utility Model A dimensionless, multi-objective, zero-to-one utility func- tion represents the contributions of several factors relevant to programming decisions. Moreover, the factors can be weighted to reflect their relative importance. The general utility relationship is given in eq. 1 (Johnson 2008). U a b X a b X a b X a b X a b X a b t i i i= = + + + + Σ 1 1 1 2 2 2 3 3 3 4 4 4 5 5X5 1( ) where: Ut = total project utility, zero to one; S = sum for all i = 1 to 5; ai = indicator that attribute i is addressed (1 = yes, 0 = no), i = 1 to 5 denoting each category of bridge needs; bi = weighting factor for attribute i; sum of all weighting factors = 1.0; Xi = value function of attribute i contributing to the utility function, where: X1 = value function for bridge rehabilitation or replacement; X2 = value function for scour risk mitigation; X3 = value function for bridge rail upgrade; X4 = value function for seismic risk mitigation; and X5 = value function for bridge mobility improve- ment (strengthening and raising clearances). Example for Scour The individual value functions Xi are themselves relation- ships containing dependent and independent variables, coef- ficients, and functions. For example, in terms of the National Bridge Inventory (NBI) rating items, the scour-related con- tribution to utility (i.e., the value function X2) is formulated using the NBI scour item (Item 113), the average daily traffic (ADT, Item 029), and detour length (DL, Item 019) (Record- ing and Coding Guide . . . Dec. 1995). Ratings of condition within the NBI are assigned on a 0 to 9 scale, where 9 denotes “undamaged” or “not subject to risk,” 3 denotes “critical,” and 0 denotes “bridge failed, out of service.” As an example, consider the scour value function X2, with a form expressed in eq. 2. This function is graphed in Figure 2 versus the NBI scour rating code SC, with values of traffic ADT and detour length DL held constant. The value-function results are inter- preted as follows (Johnson 2008, pp. 191–192): • When SC = 8, the bridge foundation is “stable” and the scour risk is essentially zero. A project that addresses scour would therefore provide no real benefit in terms of scour risk mitigation. (An NBI rating of 9 for this item would denote a bridge foundation on dry land, well above flood water elevation, and is not represented in the value function.) • As the scour risk increases (i.e., as SC moves toward the “critical” threshold where the scour rating would equal 3), the scour value function likewise increases and at SC = 3 it exceeds 0.75. Projects that mitigate scour risk now are in a range to contribute substantial potential benefit to the utility function.

50 X SC ADT DL 2 1 1 4 8 0 000001 = + − − + −( ) + ∗ ∗    exp .     ( )2 where: X2 = the value function for scour risk mitigation; SC = the NBI scour rating code, Item 113, for a bridge; ADT = the average daily traffic, NBI rating Item 029; and DL = the detour length around the bridge, miles, rating Item 019. Generalized Value Functions for Bridges To generalize the scour example to the other utility attributes (i.e., the other categories of bridge needs), all of the value functions are expressed as a logit, or “S-shaped,” function given in general form in eq. 3 (Robert and Vlahos 2007, cited by Johnson 2008, p. 191). The specific relationships governing the value functions of all categories of bridge needs are shown in Table 10, together with explanations of parameters and the values of assigned weights. In developing these relationships and weights, Caltrans bridge engineers 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 5 6 7 8 9 NBI Scour Code Va lu e: D eg re e o f S co ur R is k M iti ga tio n FIGURE 2 Example value function for scour risk mitigation, X2. Attribute = Category of Bridge Need Key Para me ters Expression for C ( i ) in Eq. 3 Assigned Weight i = 1: Rehabilitation and replacem ent needs BHI Bridge Health Index BHI Change in BHI Due to Project TEV Total Element Value in Bridge ADT Average Daily Traffic DL Detour Length Around Bridge RU Repair Urgency 2.5 + 0.000001[(100 BHI BHI ) * TE V ]/100 + 0.00000001 * AD T * DL + 0.5 * (10 RU) 25% i = 2: Scour needs SC NBI Scour Code ADT Average Daily Traffic DL Detour Length Around Bridge 4 + (8 SC ) + 0.000001 * ADT * DL 20% i = 3: Bridge-rail upgrade needs RS Caltrans Bridge–Rail Upgrade Score 2 + RS 10% i = 4: Seismic retrofit needs Sv Caltrans Seismic Priority ADT Average Daily Traffic DL Detour Length Around Bridge 1.5 + Sv + 0.000001 * ADT * DL 25% i = 5: Mobility needs (raising/ strengthening) PIB Pontis Improvement Benefit 4.5 + 0.00015 * PIB 20% Source: Johnson (2008), Tables 1 and 2. Note: Author has changed some variable names slightly to increase comprehension. TABLe 10 CALTRANS VALUe-FUNCTION eLeMeNTS FOR FIVe CATeGORIeS OF BRIDGe NeeDS

51 sought to incorporate the set of key decision variables, draw on readily available bridge condition and rating information, and predict individual bridge-needs benefit values (Xi) and overall project utility (Ut) that would reflect the judgments of experienced bridge engineers. Trial use of the methodology and sensitivity analyses confirmed that individual value func- tions and total improvements in utility correlated highly with project priorities that would have been assigned by experi- enced bridge engineers. The utility approach that is based on eq. 1 has enabled Caltrans to analyze the programming of bridge projects across the diverse categories of bridge needs simultaneously, and to reflect the overall benefit of a project within a single utility value Ut (Johnson 2008, pp. 191–194). X C ii = + − ( )( ) 1 1 3exp ( ) where: Xi = the value function for attribute i, i = 1 to 5: that is, the value function for each category of bridge needs (refer to eq. 1); exp = the exponential function; C(i) = exponent for each attribute i, given in Table 10 (note that the negative of this value must be used in eq. 3). Values of these parameters are obtained from one of the following sources: NBI bridge ratings conducted by Caltrans according to the NBI Coding Guide (Recording and Coding Guide . . . Dec. 1995); departmental calculations of factors such as the BHI (Shepard and Johnson 2001), seismic retrofit priority Sv, and bridge rail upgrade score RS; the improvement- related benefit of projects, Pontis Improvement Benefit, as analyzed by the Pontis BMS used by Caltrans (technical refer- ence: Cambridge Systematics, Inc. 2005); and the Total ele- ment Value (TeV) of a bridge as defined in Caltrans’ bridge health index (BHI) formulas (Shepard and Johnson 2001), computed by Pontis as documented in its technical reference (Cambridge Systematics, Inc. 2005). An additional use of the TeV is explained in the following section. methods and measures Adjustment for Project Scale In applying the utility concept as a generalized measure of benefit for comparison to cost Caltrans realized one other adjustment was needed. The cost of a bridge project is influ- enced by many factors, but an important one is the scale or magnitude of the project, which is related to the size or value of the existing bridge. Given this dependence of cost on bridge scale, it was necessary to compensate on the ben- efit side to provide a fair assessment of benefit (or utility) to cost, bearing in mind that the utility is a dimensionless, zero-to-one number that does not retain any information on project scale. (This discussion applies to risk mitigation, but not necessarily to bridge rehabilitation work. Although risk mitigation is blind to bridge size, bridge rehabilitation considerations by Caltrans make use of a BHI, which does account for the relative size of the structure.) Among sev- eral possibilities for accounting for bridge scale, Caltrans selected the TeV parameter described in Table 10. The final measure of “benefit–cost,” or measure of cost-effectiveness structured such as a benefit–cost ratio, is given in eq. 4. Project Utility B C ratio Project_Cost= ∗U TEVt ( )4 where all benefits variables are as defined earlier, and Project_ Cost is the cost of the proposed project developed by Caltrans’ Office of Specialty Investigations & Bridge Management as part of its SHOPP program building. Illustration of Utility as a Benefit Measure for Bridges A simple arithmetic example illustrates how the Ut benefit measure operates to distinguish relative benefits of proj- ects on different bridges, a key step in project programming (Johnson 2008, p. 193). The example includes both a condi- tion-related need (rehabilitation and replacement) and a risk- related need (mitigation of scour-related risk); a combination that Caltrans believes demonstrates the power of the util- ity concept. Consider two bridges with similar structures but with different combinations of condition and scour needs, as shown in Table 11. Assume two projects for bridges A and B, respectively that address both condition and scour needs. • Bridge A has ratings that indicate a condition-related value (X1) of 0.20. Its NBI scour rating is 8, which denotes no scour (X2 = 0; refer to Figure 2). The con- tribution of these values to the project utility computed for Bridge A is shown in the last column of Table 11 to be 0.05, using the weights for condition and scour in Table 10. Structure Condition Value, X 1 NBI Rating of Scour Risk (Item 113) Scour Value, X 2 Contribution to Utility U t (weighted sum of X 1 and X 2 ) Bridge A 0.20 8: no scour 0.0 0.25 * 0.20 + 0.20 * 0.0 = 0.05 Bridge B 0.20 3: scour is critical 0.75 0.25 * 0.20 + 0.20 * 0.75 = 0.20 TABLe 11 exAMPLe OF THe UTILITY CONCePT APPLIeD TO TWO BRIDGeS

52 • Bridge B also has ratings that indicate a condition value X1 = 0.20. Its NBI scour rating however is 3 (critical), which corresponds to a scour value X2 of 0.75 (Fig- ure 2). The contribution of these values to the utility of the project for Bridge B is 0.20, or four times the benefit value for Bridge A. The Caltrans Bridge Management Office has applied the set of value functions and weights to every state-owned bridge in the BMS, together with estimated project costs. Those bridges with the highest utility–cost ratios (eq. 4) were evaluated for possible inclusion in the SHOPP program. This exercise showed that the approach can be used successfully for an inventory of bridges of different size, material, and composition. Possible Future Modifications Caltrans noted a simplifying assumption in this initial develop- ment of a utility approach. It was assumed that the post-project condition and risk value functions would all be restored to an undamaged (“like new”) or no-risk state. This assumption was justified partly by a tenet of the SHOPP program: all needs should be addressed when a SHOPP project is undertaken. A possible future refinement is to reflect the relative effectiveness of different bridge treatments, in which the post-project value functions do not automatically assume complete correction of damage or complete removal of risk. (Although not discussed in the Caltrans paper, this refinement could also be a first step to representing a time dimension more explicitly within the total utility result.) Decision support A multi-step process is used to evaluate candidate bridge projects for SHOPP and to build a prioritized program, a process comprising the following steps: • A bridge inspection or an analysis of the bridge identi- fies bridge needs. • For bridge replacement needs or for needs that exceed a certain cost threshold, a peer review is required by internal Caltrans policy. The peer review, conducted by Structure Maintenance & Investigations personnel, documents the following: current issues with the bridge structure and materials performance, alternatives con- sidered for solving the problems, LCCAs that have been performed to compare these alternatives, and notes of remaining concerns. • The result of the peer review is a recommended strategy to deal with the identified problems on the bridge, orga- nized within a project. • A utility function is developed for each competing bridge need or proposed project, formulated as described in the previous section. A utility–cost ratio is computed (eq. 4). • The utility–cost ratios are used to create an initial order- ing of bridge priorities for purposes of planning. • More complete project data are developed in project study reports. These data are evaluated to further assess the project’s priority and its likelihood of being deliv- ered on schedule. • Depending on the result of this assessment, funds may be allocated to the project. Alternately, the project may be developed further without additional funding alloca- tion, until its likelihood of timely delivery improves. This issue of project delivery is a significant one for Cal- trans regarding bridge projects generally, and especially those projects in coastal zones or sensitive environmental areas, and those projects involving historic bridges. Internal Caltrans reviews have shown that (1) bridge projects are much more likely to require substantial environmental study than are highway projects generally; (2) the time needed to complete an environmental review for bridge projects averages 4 years for a Finding of No Significant Impact, and 8 years for an environmental Impact Study—both of which exceed the 4-year time frame of a given SHOPP pro- gram document; (3) the time needed to complete an envi- ronmental review for bridge projects is longest for bridges requiring Coastal Zone Conservation clearances, regardless of the type of environmental document required; for exam- ple, the average time to complete an environment Impact Study in this case is almost 11 years; and (4) the type of bridge work and its setting (e.g., whether over water) also affect the environmental clearance time—bridge widen- ing and bridge replacement projects are typically the most problematic. resources required and other Information Resources • Application of the utility-based approach to program- ming is performed by Caltrans staff. • Consultants assisted in developing the initial concepts and models. • The analytic tools needed are relatively simple; value- function calculations and their contributions to total utility can be handled in spreadsheet workbooks. • Data of the required currency, accuracy, and timeliness are generated through the federally mandated biennial bridge inspection program, the peer reviews that are conducted for certain bridge projects, and routine activi- ties performed as part of the programming process, such as preparation of cost estimates. • Caltrans has been a leader in promoting eeA within a wide range of departmental activities and analyses. Members of the department’s bridge unit served on the state-user advisory panel that assisted in the original development of the Pontis BMS. The agency has also developed detailed BCA products, the Cal-B/C series, for use at a project, corridor, or network level. Cal-B/C is applied in a later case example on Value Analysis (Caltrans’ implementation of Ve).

53 • Caltrans has an extensive organizational commitment and website resources dedicated to a wide range of top- ics in eeA. Among these topics are LCCA and BCA, supported by drill-down details on individual website pages to address each step of an analytic procedure and to explain the application of the correct method to par- ticular cases or situations. There is strong integration of economic concepts and methods within a number of Caltrans business processes, buttressed by comprehen- sive and detailed documentation. eConomICs-baseD traDeoff analysIs Introduction In its consideration of asset management systems for trans- portation infrastructure, the New York State DOT (NYSDOT) has sought to articulate the distinctive aspects of an “asset management approach” as compared with that of traditional infrastructure management systems. Several precepts that distinguish asset management have been identified to guide system design and development. A core capability in this approach is the conduct of tradeoff analyses among four major departmental programs or “goal areas”: pavements, bridges, safety, and mobility. To address a well-known stumbling block in analyzing such tradeoffs—the need for a common measure of benefit across different programs or projects—NYSDOT has looked to an economics-based measure, excess road user costs. Based on this concept, a prototype tradeoff analysis has been developed. Although this experimental procedure has not yet been implemented on an operational basis, it has been included in these case examples to illustrate a unique and inno- vative application of eeA. Within the framework established for this synthesis, this case example addresses programming or resource allocation at the highway corridor and network levels, affecting investments across multiple programs. role of economic analysis in Highway Investment This case example of a tradeoff analysis prototype is drawn from materials prepared by NYSDOT asset management staff: a paper published through TRB (Shufon and Adams 2003) and a slide presentation at the Fifth National Transportation Asset Management Workshop (Adams 2003). Summary informa- tion on this presentation in the context of other workshop dis- cussions is given in the workshop proceedings (Wittwer et al. 2004). Further background information on the NYSDOT trad- eoff analysis concept has been compiled by FHWA in its asset management case study series (“economics in Asset Manage- ment: The New York experience” 2003). Asset Management Framework In their consideration of the distinguishing features of asset management that could provide value-added information and insights, NYSDOT managers realized the following (Shufon and Adams 2003): • Traditional management approaches were organized vertically within each program or goal area (pavement management, bridge management, safety management, mobility or congestion management). These vertical per- spectives, often referred to as “stovepipes” or “silos,” enabled basic infrastructure data (e.g., inventory, cur- rent and historical condition, and performance) to be transformed into information useful to various business processes at different organizational levels: identification of investment needs, planning, programming, budget- ing, and so forth. • To provide additional benefits, an asset management system needed to go beyond these capabilities of exist- ing or legacy management systems; for example, an updated system architecture, advances in data collec- tion techniques, improved database design, or other advances that enabled better decisions based on bet- ter information. Lacking any beneficial contribution, “asset management systems” would simply represent the “buzzwords du jour.” • Although a vertical perspective on infrastructure man- agement processes was still needed, asset management also called for a horizontal consideration across programs or goal areas. This view would enable managers to con- sider multiple assets and the tradeoffs inherent in balanc- ing investment choices among them. A tradeoff analysis would integrate highway infrastructure decisions and provide a greater benefit to users. (Multimodal tradeoffs have also been addressed in the asset management litera- ture, but are not the focus of this synthesis.) These perspectives led NYSDOT managers to articulate the contributions of an asset management system within the following four precepts: [1] Asset management systems are decision support systems. They do not make decisions; people make decisions. The busi- ness foundation must be in place to support decision making. [2] It would be virtually impossible to cover all assets owned or administered by a transportation agency. Assets should be covered only by the umbrella asset management system in which trade-offs make sense. For example, it makes little sense to develop procedures for trade-off analysis between investment in pavement preventive maintenance and investment in specialized transit services for the handicapped. In addition, the individual or “silo” management system should be already operational for the asset to be covered by the umbrella system. Otherwise, costs for the inventory, condition assessment, and so forth, would be prohibitive. [3] Trade-off analysis can be conducted only if a common technical measure can be used to quantify benefits of diverse proj- ects: for example, a pavement project versus a mobility project. [4] Generally, these analysis methods involve an economic analysis of competing alternatives. Source: Shufon and Adams 2003, p. 38. Common Measures for Diverse Projects: Excess Road User Costs The third and fourth precepts underlay the application of eeA to tradeoff analyses. The commensurate measures selected by

54 NYSDOT managers were the excess road user costs associ- ated, respectively, with each of the department’s goal areas (or programs). These excess costs were defined as “incremental costs incurred by [highway] users . . . attributed to less than ideal operating conditions” (Shufon and Adams 2003, p. 40). excess user costs comprised three components: the cost of delays to travelers and freight, accident or crash costs, and VOC. examples of excess road user costs resulting from less than ideal conditions are the cost of additional tire wear because of rough pavement, the additional trip length (affect- ing both travel-time cost and vehicle operating expenses) imposed on truck travel owing to a posted bridge, and the cost of an accident that might have been prevented with an improved highway feature. Another way to view these costs is to regard them as “avoidable” costs, which provides the basis for treating them as the benefits of pavement, bridge, or safety-related road improvement projects. The treatment of excess user costs in each goal area is as follows (Shufon and Adams 2003, p. 40). Pavement-Related Excess User Costs Pavement-related road user costs are related by NYSDOT to the International Roughness Index (IRI). A threshold value of acceptable IRI can be established; the additional road user costs incident to higher IRI values would constitute excess user costs. The department had engaged Cornell University researchers to advise on specific analytic relationships; their recommen- dation was to adapt pavement management models that had been developed by Saskatchewan. NYSDOT’s application of these models quantified the pavement roughness effects on various components of road user costs: fuel, tire, and vehicle parts consumption; labor cost for vehicle repair; delays and diversion of traffic; and damage to cargo. Of these, NYSDOT found that the roughness-related excess user costs for fuel consumption, cargo damage, and delays or diversion were negligible and safely ignored in network analyses of the state-maintained highways. It was recognized that these results might not hold for local roads or other nonstate networks, where IRI values might be higher than on state highways. Bridge-Related Excess User Costs excess user costs related to bridges include detour costs (entailing travel time and vehicle operation) borne by truck traffic resulting from inadequate bridge and approach clearances and load postings, and acci- dent costs resulting from deficient bridge and approach geo- metry. NYSDOT staff identified sources of information on these relationships; for example, PONTIS (a software app- lication developed to assist in managing highway bridges and other structures) and research by Florida DOT (FDOT). The department adapted the FDOT models for its bridge-related excess user cost calculation. Safety-Related Excess User Costs excess user costs result- ing from accidents are derived from concentrations of crash locations, to which roadway characteristics can be a contri- buting cause. NYSDOT’s system for tracking accidents can identify High Accident Locations (HALs), which com- prise Priority Investigation Locations and Safety-Deficient Locations. • Priority Investigation Locations are highway locations at which the accident rate is more than three standard deviations higher than the mean rate for the comparable class of highway. • Safety-Deficient Locations are highway locations at which the accident rate is one to three standard deviations higher than the comparable mean rate. The excess user cost associated with HALs is computed as the product of the difference between the accident rate at each high-accident location and the comparable mean rate, and the average cost per accident obtained from NYSDOT accident data tables. Mobility-Related Excess User Costs excess user costs related to mobility—that is, congestion costs—arise from both recurring congestion problems and from individual high- way incidents. New York State defines congestion as “delay to persons and goods beyond a limit that can be tolerated”— quantitatively, the boundary between Levels of Service D and e. NYSDOT’s Congestion Needs Assessment Model can identify congested locations and calculate excess user costs as a function of vehicle hours of delay for both auto passengers and freight. However, NYSDOT has for the time being focused the tradeoff exercise on only the freight portion of these costs. (Computation of passenger values of time is beset by several analytic issues and motorist behavioral assumptions. Delays to freight are currently believed to be more clearly defined and supported analytically, and are more consistent with NYSDOT’s current priorities and decision- making practices.) methods and measures Highway System Levels for Computing Excess User Costs For each goal area of pavement, bridge, safety, and mobility, NYSDOT computes and assembles the measures of excess road user cost at three highway-system levels: 1. Individual asset: pavement segment, bridge structure, safety-deficient location, and mobility location. 2. Analysis link: length of highway between major inter- sections, comprising some portion of the individual assets discussed earlier. 3. Corridor: a highway route within a county, comprising some portion of the analysis links discussed earlier. New York State’s highway system consists of a total of 15,000 centerline-miles or 40,000 lane-miles. This system contains approximately 7,000 analysis links and 1,500 corridors.

55 Tradeoff Measures Measures used in the tradeoff analysis are structured as a benefit–cost ratio. • Benefits are defined as reductions in excess road user costs that are attributable to a corrective project. They are excess user costs that are now avoided. These ben- efits are computed as an annual figure. • Costs are agency expenditures for the project. To con- vert costs to an annual basis, the project expenditures are multiplied by a capital recovery factor as a function of the service life of the project and the current depart- mental discount rate. • The benefit–cost ratio is computed using the annual benefit divided by the annualized cost. This computa- tion is performed at the asset, link, and corridor levels described in the previous section. prototyping Decision support Because the NYSDOT research was confined to a prototyp- ing stage, examples of actual decision support are not avail- able. However, departmental staff developed reports that illustrate the type of information that could be made avail- able to decision makers needing a better understanding of investment tradeoffs. Two example reports for a hypothetical highway corridor are shown in Tables 12 and 13: • Table 12 displays information on excess user costs esti- mated for each goal area by link in the corridor. In addi- tion to total excess user costs among all goal areas, it includes an estimate of “base” user costs; that is, costs that are not considered “excess.” The ratio of excess to base user costs in the rightmost column is an indication of the excess-user-cost “tax” borne by each motorist because of deficiencies in key highway assets in this corridor. • Table 13 displays the corridor benefit–cost information that would be computed as described in the previous sec- tion. The benefit–cost ratios are viewed by NYSDOT as indicators suggesting potential candidates for program investments, warranting further investigation and analy- sis. It is also the view of NYSDOT staff that “the power of the [benefit–cost] approach is the capability to assess the investment potential for groups of diverse assets taken together, such as links and corridors” (Shufon and Adams 2003, p. 44). Tables 12 and 13 can be analyzed vertically or horizon- tally. Vertical comparisons consider potential investments within a program; horizontal comparisons, among programs. NYSDOT personnel also envisioned that results shown in these two tables could be displayed not only by the aggre- gations of assets shown (individual asset, link, and cor- ridor), but also by other delineations; for example, route, county, functional classification, traffic-volume groupings, or other available parameters. economic and demographic data would also accompany these analyses, allowing sum- maries to be prepared, for example, for areas suffering low economic growth, where reduction of excess transportation user costs could be targeted to improve the local economy. resources required and other Information Implementation Issues and Challenges Given its status as a prototyping exercise, this case example has not yet developed a track record of resources to be applied in conducting actual tradeoff analyses. Suffice it to say that the proposed analysis, intended as part of NYSDOT’s asset management system for its transportation infrastructure, is Analy sis Link EU C Pavement EU C Bridge EU C Safety EU C Mobility Total EUC for Link Est. Base User Cost Excess/Base User Cost L1 50 — 100 — 150 7,000 2.1% L2 40 40 — — 80 6,000 1.3% L3 — 30 — 20 50 3,000 1.7% L4 — 80 40 30 150 10,000 1.5% L5 120 100 50 100 370 10,000 3.7% L6 90 — 60 110 260 10,000 2.6% Corridor Totals 300 250 250 260 1,060 46,000 2.3% Source: Shufon and Adams (2003), Figure 6, p. 42. Notes: EUC = Excess [Highway] User Costs. — = no excess user costs assumed to occur. TABLe 12 exAMPLe exCeSS-USeR-COST OUTPUT FOR A CORRIDOR ($000S)

Pavement Bridge Safety Mobility Link Totals Analysis Link Annual EUC Avoided Annual- ized Project Cost Bene- fit– Cost Ratio Annual EUC Avoided Annual- ized Project Cost Bene- fit– Cost Ratio Annual EUC Avoided Annual- ized Project Cost Bene- fit– Cost Ratio Annual EUC Avoided Annual- ized Project Cost Bene- fit– Cost Ratio Annual EUC Avoided Annual- ized Project Cost Bene- fit– Cost Ratio L1 50 40 1.2 — — — 100 50 2.0 — — — 150 90 1.7 L2 40 60 0.7 40 20 2.0 — — — — — — 80 80 1.0 L3 — — — 30 50 0.6 — — — 20 100 0.2 50 150 0.3 L4 — — — 80 60 1.3 40 40 1.0 30 20 1.5 150 120 1.3 L5 120 200 0.6 100 80 1.3 50 50 1.0 100 200 0.5 370 530 0.7 L6 90 50 1.8 — — — 60 110 0.5 110 100 1.1 260 260 1.0 Corridor Totals 300 350 0.8 250 210 1.2 250 250 1.0 260 420 0.6 1,060 1,230 0.9 Source: Shufon and Adams (2003), Figure 7, p. 43. Notes: EUC = Excess [Highway] User Costs. — = no excess user costs assumed to occur. TABLe 13 SAMPLe BeNeFIT–COST OUTPUT FOR A CORRIDOR (COSTS ANNUALLY IN $000S)

26 Expert-Backed Problem Solving Examples – Interview Answers

Published: February 13, 2023

Interview Questions and Answers

Actionable advice from real experts:

Biron Clark

Former Recruiter

Contributor

Dr. Kyle Elliott

Career Coach

Hayley Jukes

Editor-in-Chief

Biron Clark , Former Recruiter

Kyle Elliott , Career Coach

Hayley Jukes , Editor

As a recruiter , I know employers like to hire people who can solve problems and work well under pressure.

 A job rarely goes 100% according to plan, so hiring managers are more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical.

But how do they measure this?

Hiring managers will ask you interview questions about your problem-solving skills, and they might also look for examples of problem-solving on your resume and cover letter. 

In this article, I’m going to share a list of problem-solving examples and sample interview answers to questions like, “Give an example of a time you used logic to solve a problem?” and “Describe a time when you had to solve a problem without managerial input. How did you handle it, and what was the result?”

• Problem-solving involves identifying, prioritizing, analyzing, and solving problems using a variety of skills like critical thinking, creativity, decision making, and communication.
• Describe the Situation, Task, Action, and Result ( STAR method ) when discussing your problem-solving experiences.
• Tailor your interview answer with the specific skills and qualifications outlined in the job description.
• Provide numerical data or metrics to demonstrate the tangible impact of your problem-solving efforts.

What are Problem Solving Skills? 

Problem-solving is the ability to identify a problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation. 

Problem-solving encompasses other skills that can be showcased in an interview response and your resume. Problem-solving skills examples include:

• Critical thinking
• Analytical skills
• Decision making
• Research skills
• Technical skills
• Communication skills
• Adaptability and flexibility

Why is Problem Solving Important in the Workplace?

Problem-solving is essential in the workplace because it directly impacts productivity and efficiency. Whenever you encounter a problem, tackling it head-on prevents minor issues from escalating into bigger ones that could disrupt the entire workflow. 

Beyond maintaining smooth operations, your ability to solve problems fosters innovation. It encourages you to think creatively, finding better ways to achieve goals, which keeps the business competitive and pushes the boundaries of what you can achieve. 

Effective problem-solving also contributes to a healthier work environment; it reduces stress by providing clear strategies for overcoming obstacles and builds confidence within teams. 

Examples of Problem-Solving in the Workplace

• Correcting a mistake at work, whether it was made by you or someone else
• Overcoming a delay at work through problem solving and communication
• Resolving an issue with a difficult or upset customer
• Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
• Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
• Troubleshooting and resolving technical issues
• Handling and resolving a conflict with a coworker
• Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
• Taking initiative when another team member overlooked or missed something important
• Taking initiative to meet with your superior to discuss a problem before it became potentially worse
• Solving a safety issue at work or reporting the issue to those who could solve it
• Using problem solving abilities to reduce/eliminate a company expense
• Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
• Changing how a process, team, or task is organized to make it more efficient
• Using creative thinking to come up with a solution that the company hasn’t used before
• Performing research to collect data and information to find a new solution to a problem
• Boosting a company or team’s performance by improving some aspect of communication among employees
• Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem-Solving Examples for Recent Grads/Entry-Level Job Seekers

• Coordinating work between team members in a class project
• Reassigning a missing team member’s work to other group members in a class project
• Adjusting your workflow on a project to accommodate a tight deadline
• Speaking to your professor to get help when you were struggling or unsure about a project
• Asking classmates, peers, or professors for help in an area of struggle
• Talking to your academic advisor to brainstorm solutions to a problem you were facing
• Researching solutions to an academic problem online, via Google or other methods
• Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

How To Answer “Tell Us About a Problem You Solved”

When you answer interview questions about problem-solving scenarios, or if you decide to demonstrate your problem-solving skills in a cover letter (which is a good idea any time the job description mentions problem-solving as a necessary skill), I recommend using the STAR method.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them. 

Start by briefly describing the general situation and the task at hand. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact. Finally, describe the positive result you achieved.

Note: Our sample answers below are structured following the STAR formula. Be sure to check them out!

EXPERT ADVICE

Dr. Kyle Elliott , MPA, CHES Tech & Interview Career Coach caffeinatedkyle.com

How can I communicate complex problem-solving experiences clearly and succinctly?

Before answering any interview question, it’s important to understand why the interviewer is asking the question in the first place.

When it comes to questions about your complex problem-solving experiences, for example, the interviewer likely wants to know about your leadership acumen, collaboration abilities, and communication skills, not the problem itself.

Therefore, your answer should be focused on highlighting how you excelled in each of these areas, not diving into the weeds of the problem itself, which is a common mistake less-experienced interviewees often make.

Tailoring Your Answer Based on the Skills Mentioned in the Job Description

As a recruiter, one of the top tips I can give you when responding to the prompt “Tell us about a problem you solved,” is to tailor your answer to the specific skills and qualifications outlined in the job description. 

Once you’ve pinpointed the skills and key competencies the employer is seeking, craft your response to highlight experiences where you successfully utilized or developed those particular abilities. 

For instance, if the job requires strong leadership skills, focus on a problem-solving scenario where you took charge and effectively guided a team toward resolution. 

By aligning your answer with the desired skills outlined in the job description, you demonstrate your suitability for the role and show the employer that you understand their needs.

Amanda Augustine expands on this by saying:

“Showcase the specific skills you used to solve the problem. Did it require critical thinking, analytical abilities, or strong collaboration? Highlight the relevant skills the employer is seeking.”  

Interview Answers to “Tell Me About a Time You Solved a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” or “Tell me about a time you solved a problem,” since you’re likely to hear different versions of this interview question in all sorts of industries.

The example interview responses are structured using the STAR method and are categorized into the top 5 key problem-solving skills recruiters look for in a candidate.

1. Analytical Thinking

Situation: In my previous role as a data analyst , our team encountered a significant drop in website traffic.

Task: I was tasked with identifying the root cause of the decrease.

Action: I conducted a thorough analysis of website metrics, including traffic sources, user demographics, and page performance. Through my analysis, I discovered a technical issue with our website’s loading speed, causing users to bounce. 

Result: By optimizing server response time, compressing images, and minimizing redirects, we saw a 20% increase in traffic within two weeks.

2. Critical Thinking

Situation: During a project deadline crunch, our team encountered a major technical issue that threatened to derail our progress.

Task: My task was to assess the situation and devise a solution quickly.

Action: I immediately convened a meeting with the team to brainstorm potential solutions. Instead of panicking, I encouraged everyone to think outside the box and consider unconventional approaches. We analyzed the problem from different angles and weighed the pros and cons of each solution.

Result: By devising a workaround solution, we were able to meet the project deadline, avoiding potential delays that could have cost the company $100,000 in penalties for missing contractual obligations.

3. Decision Making

Situation: As a project manager , I was faced with a dilemma when two key team members had conflicting opinions on the project direction.

Task: My task was to make a decisive choice that would align with the project goals and maintain team cohesion.

Action: I scheduled a meeting with both team members to understand their perspectives in detail. I listened actively, asked probing questions, and encouraged open dialogue. After carefully weighing the pros and cons of each approach, I made a decision that incorporated elements from both viewpoints.

Result: The decision I made not only resolved the immediate conflict but also led to a stronger sense of collaboration within the team. By valuing input from all team members and making a well-informed decision, we were able to achieve our project objectives efficiently.

4. Communication (Teamwork)

Situation: During a cross-functional project, miscommunication between departments was causing delays and misunderstandings.

Task: My task was to improve communication channels and foster better teamwork among team members.

Action: I initiated regular cross-departmental meetings to ensure that everyone was on the same page regarding project goals and timelines. I also implemented a centralized communication platform where team members could share updates, ask questions, and collaborate more effectively.

Result: Streamlining workflows and improving communication channels led to a 30% reduction in project completion time, saving the company $25,000 in operational costs.

5. Persistence 

Situation: During a challenging sales quarter, I encountered numerous rejections and setbacks while trying to close a major client deal.

Task: My task was to persistently pursue the client and overcome obstacles to secure the deal.

Action: I maintained regular communication with the client, addressing their concerns and demonstrating the value proposition of our product. Despite facing multiple rejections, I remained persistent and resilient, adjusting my approach based on feedback and market dynamics.

Result: After months of perseverance, I successfully closed the deal with the client. By closing the major client deal, I exceeded quarterly sales targets by 25%, resulting in a revenue increase of $250,000 for the company.

Tips to Improve Your Problem-Solving Skills

Throughout your career, being able to showcase and effectively communicate your problem-solving skills gives you more leverage in achieving better jobs and earning more money .

So to improve your problem-solving skills, I recommend always analyzing a problem and situation before acting.

 When discussing problem-solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Don’t just say you’re good at solving problems. Show it with specifics. How much did you boost efficiency? Did you save the company money? Adding numbers can really make your achievements stand out.

To get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t.

Think about how you can improve researching and analyzing a situation, how you can get better at communicating, and deciding on the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem-solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem-solving ability.

More Interview Resources

• 3 Answers to “How Do You Handle Stress?”
• How to Answer “How Do You Handle Conflict?” (Interview Question)
• Sample Answers to “Tell Me About a Time You Failed”

About the Author

Biron Clark is a former executive recruiter who has worked individually with hundreds of job seekers, reviewed thousands of resumes and LinkedIn profiles, and recruited for top venture-backed startups and Fortune 500 companies. He has been advising job seekers since 2012 to think differently in their job search and land high-paying, competitive positions. Follow on Twitter and LinkedIn .

Read more articles by Biron Clark

About the Contributor

Kyle Elliott , career coach and mental health advocate, transforms his side hustle into a notable practice, aiding Silicon Valley professionals in maximizing potential. Follow Kyle on LinkedIn .

About the Editor

Hayley Jukes is the Editor-in-Chief at CareerSidekick with five years of experience creating engaging articles, books, and transcripts for diverse platforms and audiences.

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