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Handout3 - University of Minnesota Department of Economics...

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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 ll do this in two di/erent routes: following 1 Competitive equilibrium In class we gave the de±nition of competitive equilibrium, now we can do it mathsmatically: Def: A competitive equilibrium is a set of ( C;N s ;N d ;T;Y;w ) such that given ( G;z;K;h ) : 1. The representative consumer chooses C;‘ to solve max C;‘ U ( C;‘ ) s.t. C = w ( h ) + T C ± 0 0 ² ² h where N s = h . 2. The representative ±rm chooses N d to solve max N d zF ( K;N d ) wN d s.t. N d ± 0 where Y = zF ( K;N d ) , = Y wN d = zF ( K;N d ) wN d . 1
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3. All markets clear: N d = N s : G = T: 2 Characterizing the competitive equilibrium U ( C;‘ ) wU C ( C;‘ ) = 0 (1) wN s + T C = 0 : (2) zF N ( K;N d ) = w; (3) and ±nally, we need the market clearing condition, plus the government budget constraint: N d = N s (4) G = T: (5) N d = N s = N , and substitute in (2), (3). Then we get: wN + T C = 0 (6) zF N ( K;N ) = w: (7) 2
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Handout3 - University of Minnesota Department of Economics...

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