10fB_ps04 - Microeconomics ECON 100A Problem Set 4...

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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, let’s see if you can do the general perfect complements problem. Matt gets utility from X and Z. Matt always consumes α X with β Z. a. What type of utility function represents Matt’s preferences? Write down an expression for Matt’s utility. b. What is Matt’s utility maximizing combination of X*(P x , P z , Y) and Z*(P x , P z , Y)? c. What is the Matt’s indirect utility function, i.e., V(P x , P z , Y)=U(X*(P x , P z , Y), Z*(P x , P z , Y))? d. Show that Roy’s identity holds for good x. e. What share of his budget does Matt spend on X*? What share of his budget does Matt spend on Z*? (Note: check that these two shares sum to one.) 2. Now, let’s see if you can do the general perfect substitutes problem. Toni gets utility from X and Z. Toni thinks that
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10fB_ps04 - Microeconomics ECON 100A Problem Set 4...

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