ps3_key - EEP 101/ECON 125 Prof Zilberman GSIs Alix McKim...

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EEP 101/ECON 125 Prof. Zilberman GSIs: Alix, McKim, Schoengold Answer Key for Problem Set # 3 1. (Public Goods) You have just received an important assignment as a consultant to the Prime Minister of a small country called Zilbermania. The Prime Minister is seeking advice on how to best manage a long- neglected but beautiful wildlife reserve called Giannini Park. Giannini Park has a total area of 100 acres, and the annual marginal maintenance cost (MC) is: MC=$2A where A is the number of acres maintained. Using the valuation tools acquired in EEP101/ECON125, you have estimated the willingness to pay for acres of maintained park by the country's 5 citizens to be: mb 1 =20 - .4A (for each citizen, where A is the number of maintained acres). Assume that mb 1 =0 (i.e. citizens never dislike the park being maintained). a) The Prime Minister would like to see a report of the following (including your calculations) : i. What is the aggregate demand for acreage in Giannini Park and the optimal amount of maintained acres? Graph the aggregate demand and marginal cost curves as well as the optimal level of acreage . The following graph corresponds to all parts of question 1.a: 10 20 30 40 50 20 40 60 80 100 A F A* Maintained Acres (A) $ MC1 MC2 Aggregate Demand C B D Ac E
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Since Giannini Park is a public good, we determine aggregate demand by vertically summing each consumer’s demand. Adding up the 5 individual mb 1 demand curves gives us: MB 1 = 100 – 2A. The socially optimal supply of Park acres is where aggregate demand (marginal benefit) is equal to marginal cost: 100 – 2A = 2A 100 = 4A A* = 25 ii. How much would the annual budget expenditure be if the optimal level of acreage in Giannini Park were maintained through the use of the central government's tax revenues? How much would each citizen pay in taxes for the park? Please label the area corresponding to budget expenditures and total consumer surplus (total consumer surplus for all citizens) on your graph. The total cost (TC) of supplying the optimal number of maintained acres is equal to the area under the MC curve up to A=25. TC = ½(b*h) (area of triangle) TC(A*) = .5(25)(2*25) TC(A*) = $625 The governmental expenditure would be $625. Assuming each citizen pays the same amount in taxes, they would each pay: Per person tax= (625)/N Tax = (625)/5 = $125 On the graph, budget expenditures corresponds to the triangle, FA*C. Total consumer surplus is the area ACF. iii. The Prime Minister is considering granting a concession to a private firm to operate the park (and the right to charge a "fair" admission fee equal to the shadow value of park acres to society). Suppose the firm were able to operate the park more efficiently than the government ( MC=$1.8A ). What would be the number of maintained acres in Giannini Park, how much would the per-person entrance fee be, what is the firm’s profit and consumer surplus for society? Please label the number of maintained acres, shadow value of acres, consumer surplus, and firm profits (producer surplus) on your graph (or
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This note was uploaded on 08/01/2008 for the course ECON 101 taught by Professor Wood during the Spring '07 term at Berkeley.

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ps3_key - EEP 101/ECON 125 Prof Zilberman GSIs Alix McKim...

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