Exam 1 Review Problems

Transcription

1 Exam 1 Review Problems 1.) Consider a section of freeway that is uncongested during off-peak hours, but congested during rush hour. Suppose the trip to and from work takes 4 min. when the freeway is uncongested. Also, supposed that taking the side streets to and from work always takes 6 min. On the freeway, assume congestion effects occur only after the 3 rd car. After the 3 rd car, each additional car that enters the freeway adds 5 minutes of travel time to all freeway commuters. Lastly, assume that all commuters value their time at $12/hour (or, equivalently $.2/min). a.) Given the open access to the freeway, how many cars will travel on the freeway? Cars ave. time total time marginal time Cars will enter to the point that average time on the freeway is equal to the trip time on the side streets. As a result, 7 cars will enter when there is open access to the freeway. b.) Suppose the freeway is now privately owned. What toll would be charged by the owner and how many cars would now travel on the freeway? The owner would charge a toll such that cars would enter the freeway to the point where marginal time is equal to the trip time on the side streets. As a result, 4 cars will travel on the freeway when it is privately owned. And, the owner will charge a toll of $3. c.) Which situation is efficient (i.e. open access freeway vs. privately owned freeway)? WHY? The open access freeway is inefficient because cars 5, 6, and 7 could be allocated to different routes (i.e. the side streets) to decrease total commute time of all commuters. The privately owned freeway is efficient because cars 1 through 4 could not be reallocated in any other manner to decrease the total trip time of all commuters.

2 2.) Assume a city of 1,, people, 6% of whom are willing to pay $1 maximum (each) to clean up pollution. The rest of the population is better off and is willing to pay $1 each to clean up pollution. Pollution clean-up costs $2,,. It has been proposed that each person be taxed equally to pay for the pollution clean-up. Will that pass a majority-rule vote? Is it desirable from the point of view of the Pareto criterion? Is it desirable from the point of view of the compensation principle? Explain each of your answers briefly. Taxing each person equally means a $2 tax to all residents. A vote on this proposition would fail to gain a majority, since 6% of the population is willing to pay only $1 to reduce pollution, and would therefore be expected to vote against it. By the same logic, this proposition as it stands is not a Pareto improvement: the 6% would be made worse off by paying $2 for pollution control when their willingness-to-pay is $1. The proposal is desirable, however, using the compensation principle. The 4% willing to pay $1 could compensate the 6% sufficiently to gain their support. $1 to each of these 6, residents requires $6,. The other 4, residents have a surplus of (1-2)*4, = $39,2,. That is, we should say they could easily compensate the 6%. The compensation principle states that this proposition is desirable because this possibility exists, even if the compensation doesn t actually take place. 3.) The initial cost of constructing a temporary dam that is expected to last for 5 years is $1 million. The annual net benefits will depend on the amount of rainfall: $18 million in a dry year, $29 million in a wet year, and $52 million in a flood year. Meteorological records indicate that over the last 1 years there have been 86 dry years, 12 wet years, and 2 flood years. Assume the annual benefits, measured in real dollars, begin to accrue at the end of the first year. Using the meteorological records as a basis for prediction, what are the net benefits of the dam if the real discount rate is 5 percent? The first step is to calculate the expected value of the annual net benefits: (.86)($18 million) + (.12)($29 million) + (.2)($52 million) = $2 million The second step is to find the present value of the stream of annual net benefits: ($2 million)/ ($2 million)/1.5 5 $87 million Lastly, subtract the cost of construction from the present value of the annual expected benefit stream to obtain the overall present value of expected net benefits: $87 million - $1 million = -$13 million. Thus, the dam is not built.

3 4.) Suppose we have an efficiently operating market for good X. Also, suppose the government adds a sufficiently large quantity of good X to the market such that the price of good X decreases (as shown in the graph below). Use the graph below to answer the following: a.) (3 points) The gain in consumer surplus is given by what area on the graph? P abp 1 b.) (2 points) Which supply curve do private sector suppliers operate on, S or S? S c.) (3 points) The loss in producer surplus is given by what area on the graph? P acp 1 d.) (2 points) What area on the graph represents the net surplus among producers and consumers? Is this net surplus positive or negative? abc, and this amount is positive e.) (3 points) Government surplus is given by what area on the graph? Q 2 cbq 1 -Government sells (Q 2 Q 1 ) units at price of P 1 f.) (2 points) The overall gain in social surplus is given by what area on the graph? Q 2 cabq 1 Q. What have we ignored? Costs to government of supplying additional units. Px S f S a P P 1 c b e d D Q 2 Q Q 1 Qx

4 5.) Consider the following extended form game ( : decision node. : random selection of state of nature) C flood dam P 1 C flood dam 1 st year 2 nd year P 2 Build dam 1-P 2 1-P 1 C dam 1-P 2 P 2 Do not build dam 1-P 1 C dam C flood dam 1-P 2 P 1 P 2 C flood no dam C flood no dam

5 This is a two period game where a town faces the decision of whether or not to build a dam to protect against flooding. The dam will cost C dam. The town faces this decision over a two year span. If the town builds the dam in the first year, then it does not face the choice of building the dam in the second year (because it is already built). If the town does not build the dam in the first year, then it has the option of building the dam in the second year. Regardless of whether the dam is built in the first year, the town faces the chance that a flood occurs (with probability P 1 ). If the town builds the dam and the flood occurs, then the town incurs costs of C flood dam. If the town does not build the dam and the flood occurs, then the town incurs costs of C flood no dam. The probability of the flood occurring in the second year is P 2. a.) Suppose the dam is not built in the first year (i.e. consider the bottom half of the decision tree). What is required for building the dam in the second year to be the dominant strategy? C dam + P 2 C flood dam < P 2 C flood no dam b.) Suppose your answer to part a.) holds (i.e. if the dam is not built in the first year, then the dominant strategy is to build the dam in the second year). What are the expected costs of building the dam? What are the expected costs of not building the dam? (These will be present value estimates because the expected costs cover two time periods.) E[costs of building] = C dam + P 1 C flood dam + [{P 2 C flood dam }/(1+d)](1-P 1 ) E[costs of not building] = P 1 C flood no dam + [{C dam + P 2 C flood dam }/(1+d)](1-P 1 ) where d is a discount rate c.) Suppose that C flood no dam = 2*C flood dam. What is required for the town to build the dam in the first year? If [d/(1+d)]*c dam P 1 C flood dam >, then the town will build the dam in the first year.

6 6.) Assume a country imposes an import fee on the crude oil it imports. Assume that prior to the imposition of the import fee, the country annually consumed 9 million short tons of coal, all domestically mined, at a price of $66 per short ton. How would the CBA of the import fee change if, after imposition of the import fee, the following circumstances are assumed to result from energy consumers switching from crude oil to coal? a. Annual consumption of coal rises by 4 million short tons, but the price of coal remains unchanged. As long as the secondary market for coal is undistorted and its price does not change, the increased consumption of coal is irrelevant to estimation of changes in social surplus in the primary (crude oil) market. b. Annual consumption of coal rises by 4 million short tons and the price of coal rises to $69 per short ton. In answering this question, assume that the prices of other goods, including coal, were not held constant in estimating the demand schedule for crude oil. Since it was assumed that the price of other goods, including coal, were not held constant in estimating the primary market (crude oil) demand schedule, the crude oil demand curve can be viewed as an equilibrium demand curve. Consequently, there is no need to consider changes in the secondary market for coal. c. The market price of coal underestimates its marginal social cost by $15 per short ton because the coal mined in the country has a high sulphur content that produces smog when burned. In answering this question, assume that, as in question 2.a, the annual consumption of coal rises by 4 million short tons, but the price of coal remains unchanged. If the market for coal is distorted with an externality, then a relevant social surplus change occurs even if price does not change. In this case, the social surplus loss in this secondary market would be (4 million short tons)($15 externality per short ton) = $.6 billion/per year. Note that all of the analyses in the answers to question 3 in Chapter 4 and to this question assume that there are no externalities in the primary (crude oil) market. If there were an externality in this market, then the import fee would generate additional benefits because total crude oil consumption falls. Of course, the switch to coal might very well involve an even larger social surplus loss due to environmental externalities.