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Unformatted text preview: d we know that MB = 5 PX + 9 PY is the endowment income of consumer B, so we sub this in for the MB in (6B) to get: YB = 35 PX + 63 PY 20 PY YB = 63/20 + _7PX__ 4PY (7B) Now that we have the individual demands for each consumer for both goods, we can do our horizontal summation to figure out the market demand. Recall, X = XA + XB = 14/5 + _6PY__ + 13/4 + _117PY__ 5PX 20PX = 121/20 + _141PY__ 20PX 114 and we know that the fixed supply of X in the economy is the total endowment of X... X = X so, 121/20 + _141PY__ = 12 20PX and solving the market equilibrium, we get the following equilibrium price ratio... _141PY__ = 119/20 20PX or, 141PY = 119 PX _PX__ = __141__ PY 119 (8) We can do the same thing in the market for good Y. Okay, let's do it! Now that we have the individual demands for each consumer for both goods, we can do our horizontal summation to figure out the market demand. Recall, Y = YA + YB = 9/5 + _21PX__ + 63/20 + _7PX__ 5PY 4PY = 99/20 + _119PX__ 20PY and we know that the fixed supply of Y in the economy is the total endowment of Y... Y = Y so, 99/20 + _119PX__ = 12 20PY and solving the market equilibrium, we get the following equilibrium price ratio... _119PX__ = 141/20 20PY 115 or, 119 PX = 141 PY _PX__ = __141__ 119 PY (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 = 14/5 + _6PY__ 5PX = 14/5 + 6/5 (119/141) = 1974/705 + 714/705 = 2688/705 XA* = 3.8128 YA = 9/5 + _21PX__ 5PY = 9/5 + 21/5 (141/119) = 1071/595 + 2961/595 = 4032/595 YA* = 6.7765 XB = 13/4 + _117PY__ 20 PX = 13/4 + 117/20 (119/141) = 9165/2820 + 13923/2820 = 23088/2820 or 5772/705 XB* = 8.1872 116 YB = 63/20 + _7PX__ 4 PY = 63/20 + 7/4 (141/119) = 7497/2380 + 4935/2380 = 12432/2380 or 3108 / 595 YB* = 5.2235 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 good...
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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