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Unformatted text preview: 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, ) = X(1+Y) + [I- P x x P z y] L X = 1 + Y - P x = 0 (1) L Y = X 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, ) = P x x + P z y + [U- X XY] L X = Px (1+Y) = 0 (1) L Y = Py (X) = 0 (2) L = U- X XY = 0 (3) With equations (1) and (2) we get: P X /P y = (1+Y)/X (4) Replacing back in (3) we get:...
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This note was uploaded on 04/19/2010 for the course ECON Econ 11 taught by Professor Mcdevitt during the Fall '07 term at UCLA.
- Fall '07