2/19/2009 ProblemSetsW09.doc 5:28 PM 1 Robert DeaconEcon. 210CWinter 2009 Problem Set #1 (Where the problem setup is one of partial equilibrium, you may assume that the underlying preferences make it legitimate to use partial equilibrium analysis.) 1.An economy consists of two consumers,2,1=i, who have preferences given byiiimxU+=212where ixis i'’s consumption of an ordinary consumption good andimis i'’s consumption of the numeraire. The economy’s production technology requires that producing qunits of the consumption good requires using 2qunits of numeraire as input. Consumers are endowed withiϖunits of the numeraire and their consumptions of the two goods must satisfy0,0≥≥iimx. a.Find the utility possibility frontier ()(21UFU=) for this economy. b.Suppose a tax of tper unit is imposed on consumption of xand the economy reaches a competitive equilibrium. What is the Marshallian surplus for this economy and what is the deadweight loss from the tax? 2. A city-owned golf course charges different prices for residents and nonresidents, with the nonresident price being exactly twice as high as the resident price. The golf course operates at zero marginal cost and has a fixed capacity of Qrounds of golf per day. The mayor, who does not play golf, keeps any profits from golf course operation. All golfers, residents and nonresidents, have identical quasilinear utility functions, all demand functions are linear over the relevant range, and there are equal numbers of golfers in each group. a.Characterize the prices the city will charge if it wishes to have zero excess demand. a.Do golfers (residents and nonresidents), considered as a group, gain or lose from this pricing policy, relative to a policy of charging the same (competitive equilibrium) price to all? How does the mayor fare under the discriminatory pricing policy, relative to charging a homogeneous price. 3. A perfectly competitive industryis composed of numerous identical firms, each of which has the cost function 21)(jjqqcα+=, where qjis the output of the jthfirm. Aggregate demand is perfectly inelastic in the relevant range, at X=200. a.What is the long run (allowing for entry) equilibrium price and number of firms? (Don’t worry if the number of firms is not an integer.) b.Suppose the industry is in long run equilibrium with α=1. If αincreases to 2, how will industry profits be affected in the short run situation where the number of firms cannot adjust? c.What number of firms will operate in the new long run equilibrium?
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