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PS11_solutions

PS11_solutions - Intermediate Microeconomics 2008 Problem...

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Unformatted text preview: Intermediate Microeconomics, 2008 Problem Set No. 11: Solutions Problems (17.16) Guards patrolling a mall protect the mall’s two stores. The television store’s demand curve for guards is strictly greater at all prices than that of the ice-cream parlor. The marginal cost of a guard is \$ 10 per hour. Use a diagram to show the equilibrium, and compare that to the socially optimal equilibrium. Now suppose that the mall’s owner will provide an \$ s per hour subsidy. Show in your graph the optimal s that leads to the socially optimal outcome for the two stores. Using the information in Figure 17.6 in the text: at the market price of guard service of \$10 per hour, the TV store will hire four guards and the ice-cream store will hire none. Now with a \$2 per hour subsidy from the mall owner, the private price of the TV store will be \$8 per hour. Subse- quently, the TV store will hire 5 guards, which makes the social marginal benefit equal to social marginal cost and therefore achieves the socially optimal quantity of guards. (17.22) Suppose that the inverse demand curve for paper is p = 200- Q , the private marginal cost (unregulated competitive market supply) is MC p = 80 + Q , and the marginal harm from gunk is MC g = Q . a) What is the unregulated competitive equilibrium? The unregulated equilibrium (found where MC p = p ) is: MC p = p 80 + Q = 200- Q 2 Q = 120 Q = 60 so Q = 60 ,p = 140. b) What is the social optimum? What specific tax (per unit of output of gunk) results in the social optimum? The socially optimal equilibrium (found where MC s = MC p + MC g = p ) is: MC p + MC g = p 80 + Q + Q = 200- Q 3 Q = 120 Q = 40 1 so Q = 40 ,p = 160. A specific tax of \$40 per unit results in this outcome, because with the tax, MC p = 120 + Q . (17.25) The tenants of a mall are protected by the guard service, q . The number of guards per hour demanded by the television store is q 1 = a 1 + b 1 p , where p is the price of one hour of guard services. The ice-cream store’s demand is q 2 = a 2 + b 2 p . What is the social demand for this service? To find the social demand for the service, add the demand curves vertically (you must solve for p first). Individual inverted demands are p = (- a 1 /b 1 ) + (1 /b 1 ) q for the television store, and p = (- a 2 /b 2 ) + (1 /b 2 ) q for the ice-cream store. When added, the resulting curve will be nonlinear unless the demand curves have the same horizontal axis intercept. Note that b 1 ,b 2 < 0. For the solution below, assume that a 1 /b 1 < a 2 /b 2 . p = (- a 1 /b 1- a 2 /b 2 ) + (1 /b 1 + 1 /b 2 ) q if q < a 1 p = (- a 2 /b 2 ) + (1 /b 2 ) q if q > a 1 (10.10) Initially, Michael has 10 candy bars and 5 cookies, and Tony has 5 candy bars and 10 cookies. After trading, Michael has 12 candy bars and 3 cookies. In an Edgeworth box, label the initial allocation A and the new allocation B . Draw some indifference curves that are consistent with this trade being optimal for both Michael and Tony....
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PS11_solutions - Intermediate Microeconomics 2008 Problem...

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