Peter J Wilcoxen > PAI 723 Economics for Public Decisions

Exercise 5

Due Sunday 10/11 by 11:59 pm

Part A

Suppose a small community has a wastewater agency that charges all customers $100 per year. There are currently 10,000 customers of type L who are inexpensive to serve (they live close to the treatment plant). Those customers are also known to have a demand elasticity of -0.5. The agency’s `WTA_L` to serve them is perfectly elastic at $80. The agency also has 5,000 customers of type H who are more expensive to serve (they live further away) and who have a demand elasticity of -1. The agency’s `WTA_H` is perfectly elastic but at a price that will need to be deduced. It is also known that the agency is currently running a deficit of $100,000 in the cross subsidy program: the government is having to contribute $100,000 a year to keep the system in operation. To address the deficit, the government is considering raising the price charged to both groups to $110. Finally, in doing this problem you should assume that using the wastewater agency is not mandatory: either type of customer could switch to a septic system (home treatment) if they choose not to be customers of the agency.

  1. Determine the extra revenue the agency is currently raising in the L market at the $100 price. Then determine `WTA_H`, the cost of serving an H customer.
  2. Calculate the number of customers of each type the agency would serve at the proposed $110 price. What is the new surplus or deficit on the program? Does the price increase solve the problem?
  3. Calculate the change in consumer surplus for each type of customer, and the overall change in social surplus due to the price increase.
  4. Finally, briefly discuss how much each of the following contributes to addressing the budget problem: increased revenue in the L market and lower subsides in H.

Part B

Suppose a community usually has two suppliers of gasoline: firm A, which has a supply curve given by WTAa = 2+(1/6)*Qa, and firm B which brings in gasoline from other areas with a WTAb = $5. The demand for gasoline is given by WTP = 24 – (1/5)*Q. However, a hurricane has damaged local infrastructure and firm B can no longer bring in any gasoline. Gasoline prices have risen and there are calls for the government to impose a price control that would limit the price of gas to its usual no-hurricane level.

  1. Please determine the usual price and quantity of gasoline in the no-hurricane situation when both firms can supply the market. Draw the corresponding market diagram and indicate how much gasoline is supplied by each firm.
  2. Now determine the market equilibrium after the hurricane hits (when firm B is unable to supply) but before any price control has been imposed.
  3. Finally, determine what would happen if the price ceiling were imposed. What would the price and quantity be in the market? What changes in CS and PS would the ceiling cause relative to the post-hurricane equilibrium from part 2?
  4. Briefly discuss who would benefit and who would be hurt by imposition of the price control.

Part C

Suppose four people, person 1 (P1) through person 4 (P4), are asked to rank several hypothetical cars with different combinations of features. Each person is to assign a rank of 1 to the car they like the most, a 2 to the car they like second most, and so on. If they like two cars equally, both receive the same number (eg, there may be two cars ranked 2). The table below shows the results:

Car Horsepower MPG P1 Rank P2 Rank P3 Rank P4 Rank
170 22 1 2 4 2
200 20 1 3 3 4
140 24 1 1 5 1
200 16 2 4 3 3
230 14 2 5 2 5
260 12 2 6 1 6

Using this data, please answer the following questions:

  1. Compute the marginal rate of substitution between horsepower and fuel efficiency for person 1.
  2. Is person 4 rational? Explain.
  3. Sketch some possible indifference curves for each person for different combinations of horsepower and fuel efficiency (MPG). Please use one graph per person, and put Q MPG on the horizontal axis. Note that you won't be able to compute the MRS for some of the people, but it's still possible to sketch some appropriate curves.

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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 10/04/2020