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Unformatted text preview: Public Goods Chapter 20 1. Suppose that the demand for a good by person A is Q A =176-4P and the demand for the same good by person B is Q B =245-20P. The good is produced in a perfectly competitive industry and sold at 6 dollars per unit. a) Graph the aggregate market demand for the good under the assumption that the good is public and alternatively under the assumption that the good is private. Explain why the market demand curves are different under the two scenarios. b) How much of the good would consumers purchase in a private market where consumers do not take account of each others behavior? Now suppose that person A and person B recognize that they can enjoy the benefits from others purchases of the good. If each individual assumes (naively) that the other will continue to purchase the same quantity of the good as before, how much will person A and person B choose to purchase? Explain. c) Find the socially optimal amount of output of the good if it is a public good. d) What is the cost of providing the optimal amount of the public good? How could this cost be allocated between the two individuals if they share the costs in proportion to their economic benefits? Answer: Quantity 5 10 15 20 25 30 35 40 45 200 400 600 Demand P(A) Demand P(B) AC=MC=P Quantity 10 20 30 40 50 60 200 400 600 Demand P (pri) Demand P (pub) AC=MC=P a) For a private good, the individual demand curves are summed horizonally to get the market demand, because consumption of a good by one person precludes consumption of the same good by the other. For a public good, consumption is nonrival and nonexclusive, so when either party purchases some of a public good, it is available to the other as well. Hence, demands for a public good are summed vertically. b) Demand for A is 152 and for B is 125, if the good is private. If consumers recognize that it is a public good and expect the quantities to remain the same then they will both try to free ride. A will expect that B will purchase 125, so he will purchase an additional 27, because his marginal benefit will exceed his marginal cost until this point. B will not purchase anything, because he expects A to purchage 152 and B will have marginal costs greater than marginal benefits at this point. The result is that only 27 units are purchased and the good is underproduced. c) The optimal amount for a public good is 167.5. d) The price is 2.125 for A and 3.875 for B. 2. Amy and Bill just got married and rented an apartment. They both work and are planning to hire somebody to clean their apartment. The price of housecleaning is $5 per hour. Suppose that Amys demand for housecleaning services is Q A =16-2P, and Bills demand is Q B =24- 3P....
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