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solutionproblemset2 - UCLA Economics 11 Fall 2006 Professor...

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UCLA Economics 11 – Fall 2006 Professor Mazzocco ANSWER KEY Problem Set 2 Due by October 19 before 11:30am. 1) Robinson is the only person in an island, and has an endowment of 100 units of X and 120 units of Y. His utility function is U=lnX+lnY a) Find the marginal utility of X and Y. b) Find the marginal rate of substitution when Robinson consumes all his endowment. c) Suppose now that Robinson finds that he is not alone on the Island, so now he can trade goods with other people. Find the relative prices P X /P Y above which Robinson decides to sell X and to buy Y (Hint: think about the relative price at which if he trades a small amount he stays on the same indifference curve). Explain. Answer a) MU X =1/X MU Y =1/Y b) 2 . 1 100 120 / 1 / 1 / / = = = = = X Y Y X Y U X U MRS c) He will be willing to sell good X and buy Y only if: 2 . 1 Y X P P 2) Joe has a weekly endowment of 60 dollars that he spends buying games (G) and music cds (M). The price of each game is 20 dollars; the price of each cd is 10 dollars. Joe’s utility is given by: U=G
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