# PS5Answers - UCLA Economics 11 Fall 2010 Professor Mazzocco...

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UCLA Economics 11 – Fall 2010 Professor Mazzocco Problem Set 5 Due by November 4 before 9:00am in the box located outside room 2221E, Bunche Hall 1. Alex eats only apples (X) and oranges (Y) . His utility function is U(X,Y) = (x .5 + y .5 ) 2 . a. Find the Marshallian and Hicksian demand functions. L = (x .5 + y .5 ) 2 + λ(I-p x x-p y y) L x = 2 (x .5 + y .5 )x -.5 - λp x =0 L y = 2 (x .5 + y .5 )y -.5 – λp y =0 L λ = I- p x x- p y y = 0 Combining the first two equations gives us y .5 /x .5 = p x /p y . Then, y = x*(p x /p y ) 2 Plugging into the budget constraint and rearranging yields * () y x x y pI x p p p . Plugging x back into the last equation, we get * x y x y y p p p . To find Hicksian demand functions, we can plug y = x*(p x /p y ) 2 into the new constraint (x .5 + y .5 ) 2 = u. Solving, we get 2 y x xy p hU pp and 2 x y p . b. Find the indirect utility and expenditure functions. Plugging x and y into the utility function yields I p p V . Then we can set V=U and solve for I to get the expenditure function. Therefore EU

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## This note was uploaded on 11/09/2011 for the course ECON 11 taught by Professor Cunningham during the Fall '08 term at UCLA.

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PS5Answers - UCLA Economics 11 Fall 2010 Professor Mazzocco...

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