ps03_micro_s08

ps03_micro_s08 - Problem Set 3 Microeconomics Spring 2008 1...

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Problem Set 3 Microeconomics Spring 2008 1. A household consumes only apples ( X ) and bananas ( Y ). We denote a consumption bundle consisting of x bags of apples and y bags of bananas is denoted by ( x, y ) . The preferences of the household are given by the utility function U ( x, y )= Ax α y 1 α where A> 0 and 0 <α< 1 . Suppose that prices for apples and bananas are P X and P Y and let I denote the income of the household. (a) Determine the marginal rate of substitution (MRS) for any consumption bundle ( x, y ) . (b) Describe the consumer’s utility maximization problem using the information provided. (c) Illustrate graphically where the optimal consumption bundle will lie with appropriately drawn indi f erence curve and budget line. (d) Write out the Lagrangian function for the consumer’s maximization problem. (e) What are the f rst order conditions?(Hint: There are three.) (f) Use the f rst order conditions to solve for the optimal quantity of x and y. (g) If α =0 . 25 , I = 100 , and both prices are equal to 2 , f nd the optimal consumption bundle of apples and bananas.

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This note was uploaded on 02/15/2011 for the course ECON 101 taught by Professor Womer during the Spring '08 term at NYU.

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ps03_micro_s08 - Problem Set 3 Microeconomics Spring 2008 1...

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