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Unformatted text preview: University of Minnesota Department of Economics Econ 3102: Intermediate Macroeconomics Handout 3 This handout presents how we can use all the results obtained in handouts 1 and 2 in order to characterize our competitive equilibrium. Well do this in two different routes: following the definition of a competitive equilibrium, and then using the social planners equivalence. 1 Competitive equilibrium In class we gave the following definition: Definition 1.1. A competitive equilibrium is a set of ( C,N s ,N d ,T,Y,w ) such that given ( G,z,K ): 1. The representative consumer chooses C, to solve max C, U ( C, ) subject to C = w ( h- ) + - T C h, here N s = h- . 2. The representative firm chooses N d to solve max N d zF ( K,N d )- wN d subject to N d , where Y = zF ( K,N d ), = Y- wN d = zF ( K,N d )- wN d . 3. All markets clear: N d = N s . 4. The governments budget constraint is satisfied: G = T. 1 2 Characterizing the competitive equilibrium To characterize the competitive equilibrium, note that from the consumers problem we get: U ( C, )- wU C ( C, ) = 0 (2.1) wN s + - T- C = 0 . (2.2) From the firms problem we get zF N ( K,N d ) = w, (2.3) and finally, we need the market clearing condition, plus the government budget constraint: N d = N s (2.4) G = T. (2.5) Now lets try to simplify (2.1) (2.5). From (2.4), let N d = N s = N , and substitute in (2.2), (2.3). Then we get: wN + - T- C = 0...
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This note was uploaded on 02/07/2011 for the course ECON 3102 taught by Professor Mingyi during the Spring '08 term at Minnesota.
- Spring '08