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# PS3Answers - UCLA Economics 11 Fall 2009 Professor Mazzocco...

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UCLA Economics 11 Fall 2009 Professor Mazzocco Problem Set 3 Due by October 22 before 9:00am in Room 8271 1) Suppose that an individual with income I cares about two goods, X and Y. The price of the two goods is P x and P Y . 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 - λP x = 0 (1) L Y = X λP y = 0 (2) L λ = 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 λ = U- X XY = 0 (3) With equations (1) and (2) we get:

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P X /P y = (1+Y)/X (4) 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
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PS3Answers - UCLA Economics 11 Fall 2009 Professor Mazzocco...

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