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Unformatted text preview: UCLA Economics 11 - Fall 2010 Professor Mazzocco Problem Set 2 Due by October 14 before 9:00am in the box located outside room 2221E, Bunche Hall Question 1 Tom Hanks is the only person on an island, and he has an endowment of 120 units of x and 60 units of y. His utility function is U ( x,y ) = x 1 3 y 2 3 a) Find Tom’s marginal utility with respect to x and y. U x = 1 3 x- 2 3 y 2 3 U y = 2 3 x 1 3 y- 1 3 b) Find Tom’s marginal rate of substitution with respect to the 2 goods. MRS = U x U y = y 2 x c) Suppose a ship arrives and offers to trade x and y at the prices, p x = 2 and p y = 3 . What would Tom do in order to maximize his utility? (You do not need to solve this, just set up the maximization problem and the Lagrangian) max x,y x 1 3 y 2 3 s.t 120(2) + 60(3) = 2 x + 3 y Question 2 Megan is a big fan of peanuts and cookies. She has a budget for peanuts and cookies worth 40. The price of peanuts is $3 per can and the price of a box of cookies is $1. Her utility function is U ( p,c ) = ln( p ) + ln( c )....
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- Fall '08
- Economics, Tom Hanks