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Unformatted text preview: mand for good X must be equal to the aggregate supply of good X. X(PX, PY) = X Graphically, the market equilibrium is defined as the intersection of the aggregate demand and supply curves. On the supply side, we already know that the market supply of good Y is fixed at Y. supply = Y At market equilibrium, the aggregate demand for good Y must be equal to the aggregate supply of good Y. Y(PX, PY) = Y Graphically, the market equilibrium is defined as the intersection of the aggregate demand and supply curves.
PY "SY" PX "SX" PY* Market Equilibrium Market Equilibrium PX* X(PX , PY) X X Y Y(PX , PY) Y 98 To get the equilibrium price vector, we solve the market equilibrium equations: X(PX, PY) = X Y(PX, PY) = Y We denote these equilibrium price solutions as (PX*, PY*) to emphasize the fact that they are the prices that give rise to both the individual and market equilibria at the same time. Once these equilibrium prices are known, all other variables can be calculated accordingly. For example, we can calculate the quantity of goods demanded by consumer A and consumer B: XA* = XA(PX*, PY*) YA* = YA(PX*, PY*) PURE EXCHANGE ECONOMY EXAMPLE Consider a simple pure exchange economy with two consumers, A and B, and two goods, X and Y. Consumer A has a square root utility function while Consumer B has a CobbDouglas utility function with = 0.25, = 0.75, and = 1. There is one unit of each good allocated between the two consumers according to the following endowment distribution: Consumer A Consumer B Total GOOD X XA = XB = X = + = 1 GOOD Y YA = YB = Y = + = 1 XB* = XB(PX*, PY*) YB* = YB(PX*, PY*) We solve this particular pure exchange economy as follows: Let's start with Consumer A. This consumer has a utility function that allows us to determine their marginal rate of substitution and an endowment income that constrains their utility as follows: UA = UA(XA,YA) = X1/2Y1/2 MA = PX XA + PY YA = PX + PY 99 We can figure out consumer A's marginal rate of substitution as: MRSA = MUXA MUYA = 0.5 X-1/2Y1/2 0.5 X1/2Y-1/2 = YA XA At the consumer equilibrium, the two equations consumer A needs to satisfy are: MRSA = YA = PX XA PY Rearranging (1) we get: PX XA + PY YA = MA XA PX = YA PY (1) (2) (3) Meaning we can get demands for XA and YA by...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.
- Spring '10