PS2AllenQs

PS2AllenQs - b Set up the Lagrangian and ﬁnd her optimal consumption c How does her consumption of cookies change if her income doubles 1

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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. b) Find Tom’s marginal rate of substitution with respect to the 2 goods. 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) 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 ). a) Set up the budget constraint.

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Unformatted text preview: b) Set up the Lagrangian and ﬁnd her optimal consumption. c) How does her consumption of cookies change if her income doubles? 1 Question 4 For each of the following expressions, state the formal assumption that is being made about the individual’s utility function: a) Gouda cheese can be used whenever you need Mozzarella cheese and vice versa b) Eggs and bacon taste better together. c) Traﬃc jams are horrible. Question 5 Avon Barksdale enjoys the health beneﬁts of running but ﬁnds it painful. His utility function is u ( r ) = 50 ln( r )-r 2 a) Which part of the utility captures the beneﬁts and which part the costs of running? b) What is Avon’s marginal beneﬁt of running and the marginal cost? c) Solve for Avon’s optimal run. What happens to the optimal r if the 50 is replaced by 100 in the utility function? 2...
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This note was uploaded on 10/18/2010 for the course ECON 11 taught by Professor Cunningham during the Spring '08 term at UCLA.

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PS2AllenQs - b Set up the Lagrangian and ﬁnd her optimal consumption c How does her consumption of cookies change if her income doubles 1

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