Coursenotes_ECON301

# Py 2 py yb 12 19px 2 py 7b now that we have the

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online