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HW2key - Econ 3102 Intermediate Macroeconomics Homework#2...

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Econ 3102: Intermediate Macroeconomics Homework #2 Answer Key 1 Problems (55 points) Exercise 1 (20 points) Consider a simple one-period, closed-economy model where the representative consumer has utility function U ( C; ‘ ) = C 1 = 2 1 = 2 and has ° h available hours to divide between work and leisure. The representative °rm has technology given by Y = zK 1 = 3 N 2 = 3 . There is a government that sets its expenditure level at a value G ° 0 . (a) Carefully de°ne a CE for this economy. (b) Find the CE allocation ( C ° ; ‘ ° ; N ° ; T ° ; ° ° ; w ° ) given parameters ° h = 1 , z = 1 , K = 8 , and G = 0 . Verify that the global maximum is, in fact, an interior one. Answer: You can do this in a variety of ways; most likely you°ll get full credit unless you are not careful enough to get the de±nition pretty much correct. (a) Given ±scal policy G ° 0 , a CE in this economy is a household allocation ( C ° ; ‘ ° ) , a ±rm°s allocation N ° , pro±ts ° ° , lump-sum taxes T ° , and prices w ° such that: ± Given prices, pro±ts, and taxes, the household allocation solves the representative consumer°s problem: max C;‘ C 1 = 2 1 = 2 s.t. C + w ° = w ° h + ° ° ² T ° ± Given prices, the ±rm°s allocation solves: ° ° = max N ± 0 n zK 1 = 3 N 2 = 3 ² wN o K > 0 given ± The government°s BC is satis±ed: G = T ° ±
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