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Unformatted text preview: 1.7355608862 YA = 3.012171587 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 + _19PY__ - PX PX PY = 1 + 19 / 1.735560886 - (1.735560886) = 1 + 10.94746958 1.735560886 126 when PY = 1 The other part is irrelevant since we assume PX > 0 XA* = 10.21190869 XB = 19/2 + _PY__ 2 PX = 19/2 + 1/(2 1.735560886) = 9.5 + 1 / 3.471121772 XB* = 9.788091304 YB = 1/2 + _19PX__ 2PY = 1/2 + 19 (1.735560886) / 2 = 0.5 + 32.97565683/2 YB* = 16.98782842 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. XA + XB = 10.21190869 + 9.788091304 XA + XB = 20 XA + XB = X YA + YB = 3.012171587 + 16.98782842 YA + YB = 20 YA + YB = Y 127 So, in both the market for X and the market for Y, demands are equal to supplies and we have market clearing (equilibrium). HOMEWORK 1. Consider a pure exchange economy with two goods, Xylophones (X) and Yarn (Y), and two consumers, Anne (A) and Betty (B). Anne has a Cobb-Douglas utility function with = 0.2, = 0.8, and = 4 while Betty has a Cobb-Douglas utility function with = 0.35, = 0.65, and = 1. There are 12 Xylophones and 8 balls of Yarn allocated between the two consumers according to the following endowment distribution: Consumer A Consumer B Total GOOD X XA = 7 XB = 5 X = 7 + 5 = 12 GOOD Y YA = 2 YB = 6 Y = 2 + 6 = 8 Solve for the general equilibrium price ratio, and report the equilibrium quantities demanded for each consumer. 2. Consider a pure exchange economy with two goods, aXes (X) and knYves (Y), and two consumers, Andy (A) and Bill (B). UA = 4X1/2 + 2Y UB = X + Y A = (XA , YA) = (2,1) B = (XB , YB) = (1,2) Solve for the general equilibrium price ratio, and report the equilibrium quantities demanded for each consumer. 3. Con...
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- Spring '10