EEP 101/ECON 125Prof. ZilbermanGSIs: Alix, McKim, SchoengoldAnswer Key for Problem Set # 31. (Public Goods) You have just received an important assignment as a consultant to the Prime Minister of asmall 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=$2A where A is the number of acres maintained.Using the valuation tools acquired in EEP101/ECON125, you have estimated the willingness to pay foracres of maintained park by the country's 5 citizens to be: mb1=20 - .4A (for each citizen, where A is thenumber of maintained acres). Assume that mb1=0 (i.e. citizens never dislike the park being maintained).a) The Prime Minister would like to see a report of the following (including your calculations): i. What is the aggregate demand for acreage in Giannini Park and the optimal amount of maintained acres?Graph the aggregate demand and marginal cost curves as well as the optimal level of acreage.The following graph corresponds to all parts of question 1.a:10 20 30 40 5020406080100AFA*Maintained Acres (A)$MC1MC2AggregateDemandCBDAcESince Giannini Park is a public good, we determine aggregate demand by vertically summing each consumer’sdemand. Adding up the 5 individual mb1 demand curves gives us: MB1= 100 – 2A. The socially optimalsupply of Park acres is where aggregate demand (marginal benefit) is equal to marginal cost:100 – 2A = 2A100 = 4AA* = 25 ii. How much would the annual budget expenditure be if the optimal level of acreage in Giannini Parkwere maintained through the use of the central government's tax revenues? How much would eachcitizen pay in taxes for the park? Please label the area corresponding to budget expenditures and totalconsumer 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 curveup to A=25.TC = ½(b*h) (area of triangle)TC(A*) = .5(25)(2*25)TC(A*) = $625The governmental expenditure would be $625. Assuming each citizen pays the same amount in taxes, theywould each pay:Per person tax= (625)/NTax = (625)/5 = $125On 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 theright to charge a "fair" admission fee equal to the shadow value of park acres to society). Suppose thefirm were able to operate the park more efficiently than the government (MC=$1.8A). What would bethe 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 maintainedacres, shadow value of acres, consumer surplus, and firm profits (producer surplus) on your graph (ora new one if you wish)..The government allows the concessionaire to charge a per-acre fee equal to the shadow value of park acres tosociety (value or price of an additional acre when marginal social cost equals marginal social benefit). First, setaggregate demand equal to marginal cost, to get the optimal number of acres:100 – 2A = 1.8A100 = 3.8AAC* = 26.3The shadow value (lambda) of an additional acre is just the value to society of one acre at AC* or aggregatedemand at AC*:AD(AC*) = 100 – 2A*AD(AC*) = 47.4The total revenue that the concessionaire will receive is just 47.4 (price per acre) times the total number of acresor: (47.4)(26.3)= 1246.6The concessionaire will set the per-person entry fee equal to total revenue divided by the number of consumers:1246.6/5 = 249.3Before calculating the firm’s profits, we need to calculate the total costs incurred by the concessionaire. This isthe area under the concessionaire’s marginal cost curve:TC = ½(b*h) (area of triangle)TC(AC*) = .5(26.3)(1.8*26.3)TC(AC*) = $623.3Firm profits are total revenues minus total costs:? = 1246.6 – 623.3 = 623.3Total consumer surplus is the area below the aggregate demand curve but above the price (shadow price in thiscase) line:CS = ½(b*h) (area of triangle)CS = .5(26.3)(100 – 47.4)CS = 691.7On the graph, the number of maintained acres is Ac and the shadow value of acres is where point D is located.Total consumer surplus is AED and firm profits are FED. iv. If the Prime Minister were to give the park over to his (greedy) brother to run, how much of the parkwould his brother decide to maintain (at MC=$2A)? What would be the per-visitor entry fee, consumersurplus, and firm profits? Please label consumer and producer surplus on your graph.Since the brother is “greedy” and there was no mention of regulation, we can assume he would operate as amonopolist and operate until his marginal revenue equals his marginal cost. Thus, AM*=A*=25 (monopolistprovides same number of acres as under the social optimum).The monopolist would extract all of the willingness to pay of the visitors. The area of this parallelogram (areaunder MB1 curve up to AM*) is:WTP = ½ (h1 + h2)b (area of parallelogram)WTP = .5(100 + 50)(25)WTP = 1875Total revenue received by the monopolist is thus 1875. The per-visitor entry fee is simply:Entry Fee = 1875/5 = 375Consumer surplus is equal to 0 (all willingness to pay is extracted by monopolist).Producer surplus is equal to total revenue minus total costs:? = 1875 – 625 = 1250On the graph, producer surplus is the area ADA*F, and there is no consumer surplus.b) You have just met with the Minister of Tourism and he says that you can expect 5 foreign tourists to visitZilbermania each year. The willingness to pay (by each foreign tourist) for visiting Giannini Park isestimated at: mb2 = 40 - .5A. Assume that mb2=0 (i.e. foreign tourists never dislike additional park acresbeing maintained). Please show your calculations (the Prime Minister wants to be able to easily double-check your work) for the following questions: i. What is the new aggregate demand for acreage in Giannini Park, the optimal amount of maintainedacres, and the new levels of government expenditures required to maintain the park? Graph theaggregate demand and marginal cost curves, government expenditures, and optimal level of acreage.The graph for 1.b is as follows:20 40 60 80 10050100150200250CFMaintained Acres