# PS2 - 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 a Find Emma’s

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UCLA Economics 11 – Fall 2009 Professor Mazzocco Problem Set 2 Due by October 15 before 9:00am in Room 8271 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. 2) Emma has a monthly endowment of 40 dollars that she spends buying books (B)
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Unformatted text preview: 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. a) Find Emma’s Budget constraint. b) Set up the Lagrangian and find her optimal consumption. c) How does her consumption change when the price of music cds goes up to 10 dollars? 3) John’s utility function is U=X 1/4 Y 3/4 . He has a monthly income I, and the prices of the goods are P X and P Y . a) Write down the optimality conditions associated with utility maximization. b) Find John’s demand equations for X and Y (consumption of X and Y as a function of prices and income). c) Explain how the demand functions for this utility function compare with those for U= . ln 4 3 ln 4 1 Y X...
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## This note was uploaded on 04/19/2010 for the course ECON Econ 11 taught by Professor Mcdevitt during the Fall '07 term at UCLA.

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