CE_definition - about the parameters or functional forms of...

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Econ 3102 - Competitive Equilibrium in the One-period Macroeconomy John Seliski 6/23/11 1 Competitive Equilibrium G & 0 , a competitive equilibrium in this economy is a household allocation ( C ;‘ ;n ) , a N , lump-sum taxes T , and wages w such that: 1. Given taxes T ; dividends ; and wages w , the household allocation ( C ;l ;n ) is the solution to the representative consumer ±s problem: max C;‘;n U ( C;‘ ) s.t. C ± w n + ( ² T ) + n ± h C & 0 ;‘ & 0 ;n & 0 (Non-negativity constraints) 2. Given wages w N solves the ±s problem: = max N ± 0 zF ± K;N ² ² w N ³ K > 0 given 3. The government G = T 4. Markets clear (supply = demand): N = n C + G = zF ± K;N ² 2 Comments about the CE Above is the of a CE, NOT the solution to the CE. There is a big di²erence between the
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Unformatted text preview: about the parameters or functional forms of the utility and production functions U and F . In fact, a CE allocation may not even exist! For example, I can de&ne what a unicorn is, but simply because I de&ne something doesn±t mean it exists! I make assumptions on parameters and the functional forms to guarantee the existence and uniqeness of a CE allocation. Once I know the solution exists, I can begin to characterize its solution. I then derive a system of equations that any CE allocation must satisfy, pinning down all the CE allocations. Therefore, the unique allocation satisfying our usual system of equations characterizes our CE. This system solves all of our economic agents±optimization problems simultaneously and clears all markets simultaneously 1...
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