solutionproblemset3

# solutionproblemset3 - UCLA Economics 11 Fall 2006 Problem...

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UCLA Economics 11 – Fall 2006 Problem Set 3, Answer Key 1) Suppose that an individual with income I cares about two goods, X and Y. The Price of the two goods is Px and Py. The individual has the following utility function: U(X,Y) = X (1 + Y) a) Find the Marshallian (uncompensated) demand for X and Y. Are X and Y normal or inferior goods? b) Find the Hicksian (compensated) demand for X and Y. c) What is the minimum expenditure necessary to achieve a utility level of U= 72 with Px=4 and P Y =2?. a) L(x,y, λ ) = X(1+Y) + λ [I- P x x – P z y] L X = 1 + Y - λ P x = 0 (1) L Y = X – λ P y = 0 (2) L = I- P x x – P y y = 0 (3) With equations (1) and (2) we get: P X /P y = (1+Y)/X (4) X * =(I+P Y )/ 2p x , Y * =(I-P Y )/ 2p y , a) L(x,y, λ ) = P x x + P z y + λ [U- X – XY] L X = Px – λ (1+Y) = 0 (1) L Y = Py – λ (X) = 0 (2) L = U- X – XY = 0 (3) With equations (1) and (2) we get: P X /P y = (1+Y)/X (4)

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Replacing back in (3) we get: Y=(UPx/Py) 1/2 -1 X=U(Py/Px) 1/2 c) We can obtain the indirect utility function replacing the demand functions in U=X+XY V=((I+Py) 2 )/4PxPy And from that we can obtain the expenditure function (solving for I, check page 153 in Nicholson book): E= (4PxPyU) 1/2 -Py
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• Winter '08
• cunningham
• Utility, indirect utility function

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