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# ps2_solutions_adjusted - Microeconomics-Spring 2008 Problem...

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Microeconomics-Spring 2008 Problem Set 2 1. Consider a high school student, Freddy, whose preferences for entertainment activities- watching movies (m) and playing squash (s) - are represented by the utility function 3 / 1 3 / 2 ) , ( s m s m U = Freddy’s allocated monthly budget for entertainment is \$120 and the prices of the two goods he cares about are given by \$20 for movies and \$10 for squash. a. Write down Freddy’s utility maximization problem. 3 / 1 3 / 2 ) , ( max s m s m U = s.t 120 10 20 = + s m b. Calculate Freddy’s MRS (of m for s ). How do you interpret this number? The MRS tells us the rate at which Freddy is willing to sacrifice one squash game in exchange for a movie. In particular, it says that Freddy is willing to give up 2 squash games in exchange for one movie. Plug in the different numbers (m=2, s=4); MRS =8/2=4 (m=3, s= 5); MRS= 10/3 (m=4, S=2)=4/4=1 c. If Freddy plays 6 squash games and goes to 3 movies per month, is this an optimal consumption choice for him? (Hint; think in terms of the condition under which utility is maximized)

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