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Unformatted text preview: Microeconomics ECON 100A Problem Set 4 Solutions [THIS MATERIAL IS NOT ON THE MIDTERM] Due October 20, 2010 (Solutions Posted October 22, 2010) 1. Now, lets see if you can do the general perfect complements problem. Matt gets utility from X and Z. Matt always consumes X with Z. a. What type of utility function represents Matts preferences? Write down an expression for Matts utility. U=min{( 1 / ) X, ( 1 / ) Z} b. What is Matts utility maximizing combination of X*(P x , P z , Y) and Z*(P x , P z , Y)? Use the facts that (1) that there will be no excess X or Z (so 1 / X*= 1 / Z*) and (2) the utility maximizing bundle must be on the budget constraint (PxX*+PzZ* =Y). Substitute the expression for Z*= / X* from (1) into the budget constraint in (2) to get: Px(X*)+ Pz( / X*)=Y X*(Px+ / Pz) = Y and then solve for X*= z x p p Y + Finally, substitute this expression for X* into Z*= / X* to solve for Z*: Z*= ) ( z x p p Y + c. What is the Matts indirect utility function, i.e., V(P x , P z , Y)=U(X*(P x , P z , Y), Z*(P x , P z , Y))? U*(px, pz, Y)=min{ 1 / X*, 1 / Z* }=min{ ) ( , ) ( z x z x p p Y p p Y + + } d. Show that Roys identity holds for good x. Show that Roys identity holds for good x....
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 Fall '08
 ZAMBRANO
 Microeconomics, Utility

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