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Unformatted text preview: PY = 5/8 + _5PX__ 8 PY and we know that the fixed supply of Y in the economy is the total endowment of Y... Y = Y so, 5/8 + _5PX__ = 1 8 PY and solving the market equilibrium, we get the following equilibrium price ratio... _5PX__ = 3/8 8 PY or, 5PX = 3 PY 103 _PX__ = __3__ PY 5 (8B) So now that we have the equilibrium price ratio and the individual consumer demands (and the market demands as a result), we can find the equilibrium quantities demanded by the individuals, A and B, by subbing the price ratio into the individual demand functions. XA = + _PY__ 4 PX = + (5/3) XA* = 2/3 YA = + _PX__ 4 PY = + (3/5) YA* = 2/5 XB = 1/8 + _PY__ 8 PX = 1/8 + 1/8 (5/3) XB* = 1/3 YB = 3/8 + _3PX__ 8 PY = 3/8 + 3/8 (3/5) YB* = 3/5 As a verification (or check) of the market equilibrium condition, we add the individual consumer demands (X = XA + XB and Y = YA + YB) and they should sum to the fixed supply in terms of endowments of the goods. 104 XA + XB = 2/3 + 1/3 XA + XB = 1 XA + XB = X YA + YB = 2/5 + 3/5 YA + YB = 1 YA + YB = Y So, in both the market for X and the market for Y, demands are equal to supplies and we have market clearing (equilibrium). What if we specifically chose a particular good as the numeraire? The general equilibrium that we solved above only gives us the ratio of the two prices... _PX__ = __3__ PY 5 (8) What if we choose X as the numeraire? Then PX =1 and expression (8) above becomes... __1__ = __3__ PY 5 or, PY = 5/3 What if we choose Y as the numeraire? Then PY =1 and expression (8) above becomes... _ PX___ = __3__ 1 5 or, PX = 3/5 What if we normalized the prices? Then PX + PY = 1 and using expression (8), we get 105 and, Rearrange (9), to get... _ PX___ = __3__ PY 5 PX + PY = 1 (9) Sub (9.1) into (8) to get PX = 1 PY PY = 1 PX _ 1 PY___ = __3__ PY 5 _ 1__ = __8__ PY 5 PY = 5/8 (9.1) (9.2) Sub (9.2) into (8) to get _ PX___ = __3__ 1 PX 5 5PX = 3 3PX PX = 3/8 Are these 3 sets of prices the same or are they different? Recall, when we used X as the numeraire good, we had PX = 1, PY = 5/3. Recall,...
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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
 sning
 Economics

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