Coursenotes_ECON301

# This consumer has a utility function that allows us

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Unformatted text preview: dowment income of consumer B, so we sub this in for the MB in (4B) to get: XB = PX + PY 4PX XB = 3/16 + _PY__ 16 PX 1/3 PY YB + PY YB = MB 4/3 PY YB = MB 168 (5B) YB = 3MB 4 PY (6B) and we know that MB = PX + PY is the endowment income of consumer B, so we sub this in for the MB in (6B) to get: YB = 3 ( PX + PY) 4 PY YB = 3/16 + _9PX__ 16 PY (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 = 1/8 + _3PY__ + 3/16 + _PY__ 8 PX 16 PX = 5/16 + _7PY__ 16 PX and we know that the fixed supply of X in the economy is the total endowment of X... X = X so, 5/16 + _7PY__ = 1 16 PX and solving the market equilibrium, we get the following equilibrium price ratio... _7PY__ = 11/16 16 PX or, 7PY = 11PX _PX__ = __7__ PY 11 We can do the same thing in the market for good Y. Okay, let's do it! 169 (8) 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 = 3/8 + _PX__ + 3/16 + _9PX__ 8 PY 16 PY = 9/16 + 11PX__ 16 PY and we know that the fixed supply of Y in the economy is the total endowment of Y... Y = Y so, 9/16 + _11PX__ = 1 16 PY and solving the market equilibrium, we get the following equilibrium price ratio... _11PX__ = 7/16 16 PY or, 11PX = 7PY _PX__ = __7__ PY 11 (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 = 1/8 + _3PY__ 8 PX = 1/8 + 3/8 (11/7) XA* = 5/7 170 YA = 3/8 + _PX__ 8 PY = 3/8 + 1/8 (7/11) YA* = 5/11 XB = 3/16 + _PY__ 16 PX = 3/16 + 1/16 (11/7) XB* = 2/7 YB = 3/16 + 9PX__ 16 PY = 3/16 + 9/16 (7/11) YB* = 6/11 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 sup...
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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.

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