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Unformatted text preview: ECON 3102 Summer 2010 Homework 2 Answer Key 1 . Consider a oneperiod, closedeconomy model where the representative consumer has util ity function U ( C,‘ ) = C 1 / 2 ‘ 1 / 2 and has h available hours to divide between work and leisure. The representative firm has technology given by Y = zK 1 / 3 N 2 / 3 . There is a government that sets its expenditure level at a value G ≥ . a. Define a CE for this economy. b. Find the CE values ( C * ,‘ * ,N * ,T * ,Y * ,w * ) given parameters h = 14 , z = 1 , K = 15 , 625 , and G = 0 . Answer : (a) A competitive equilibrium is a set of ( C,N s ,N d ,T,Y,w ) such that given ( G ,z,K,h ): • The representative consumer chooses C,‘ to solve max C,‘ C 1 / 2 ‘ 1 / 2 subject to C = w ( h ‘ ) + π T C ≥ ≤ ‘ ≤ h, here N s = h ‘ . • The representative firm chooses N d to solve max N d zK 1 / 3 N 2 / 3 wN d subject to N d ≥ , where Y = zK 1 / 3 N 2 / 3 , π = Y wN d = zK 1 / 3 N 2 / 3 wN d . • All markets clear: N d = N s . • The government’s budget constraint is satisfied: G = T. (b) To find the competitive equilibrium, note first that the production function is given by Y = (1)(15 , 625) 1 / 3 N 2 / 3 = 25 N 2 / 3 . 1 The equations characterize the CE are: C = (50 / 3) N 1 / 3 ‘ C = 25 N 2 / 3 Considering N = h ‘ = 14 ‘ , we can equate them: (50 / 3) N 1 / 3 ‘ = 25 N 2 / 3 ‘ = 1 . 5 N ‘ = 1 . 5(14 ‘ ) ‘ + 1 . 5 ‘ = 21 2 . 5 ‘ = 21...
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 Spring '08
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 Economics, Utility, representative, representative consumer, representative firm

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