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PS2Answers - Problem Set 2 1 Robinson is the only person in...

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Problem Set 2 1) Robinson is the only person in an island, and has an endowment of 40 units of X and 60 units of Y. His utility function is U=X 1/2 Y 1/2 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 Y and to buy X (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 = 2 1 2 1 2 1 Y X MU Y = 2 1 2 1 2 1 Y X b) 5 . 1 40 60 2 1 2 1 / / 2 1 2 1 2 1 2 1 X Y Y X Y X Y U X U MRS c) He will be willing to sell good Y and buy X only if: 5 . 1 Y X P P 2) Emma has a monthly endowment of 40 dollars that she spends buying books (B) and music cds (M). The price of each book is 10 dollars; the price of each cd is 5 dollars. Emma’s utility is given by: U=lnB+lnM.
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