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Unformatted text preview: Intermediate Microeconomics, 2008 Problem Set No 6 due: Thursday, Jan 31; Wed, Jan 30 Problems 1) We considered preferences represented by the following utility function in the last homework: U ( q 1 ;q 2 ) = q 1 q 2 . Income is &xed at Y = 2 and the price of good two is &xed at p 2 = 1 . a) Suppose p 1 increases. Illustrate graphically how the change in demand can be decomposed into a substitution e/ect and an income e/ect. b) Suppose p 1 increases from 1 4 to 1 2 . Derive the total change of the demand for good one. Decompose that change into the change due to the substitution e/ect and the change due to the income e/ect. Note: The total change in demand is D 1 & 1 2 ;Y & D 1 & 1 4 ;Y at Y = 2 . The change due to the substitution e/ect is H 1 & 1 2 ; & U & H 1 & 1 4 ; & U . The change due to the income e/ect is the change in demand D 1 & 1 2 ;Y when income changes from the hypothetical level Y = E & 1 2 ; & U to Y = E & 1 2 ; & U N = 2 . & U and & U N are the utility levels at the old and the new price, p 1 = 1 4 and p N 1 = 1 2 , respectively. c) Suppose p 1 increases from 1 4 to 4 . Again, decompose the change of demand into the change that is due to the substitution e/ect and the change that is due to the income e/ect. d) Calculate the elasticity of demand at p 1 = 1 4 . Decompose this elasticity into the Hicks elasticity " & and the weighted income elasticity & . 3) Let p 2 = 1 . Consider the following utility functions: U ( q 1 ;q 2 ) = min f q 1 ;q 2 g U ( q 1 ;q 2 ) = q 1 + q 2 U ( q 1 ;q 2 ) = q 2 + p q 1 a) Illustrate the indi/erence curves graphically and illustrate how a price change a/ects demand. Carefully illustrating the indi/erence curves will be helpful. You might want to check earlier problem sets when graphing the indif- ference curves. b) Illustrate how a change in income changes demand. 1 c) Derive the expenditure function E ( p 1 ;U ) and the Hicks demand curve for good one, H 1 ( p 1 ;U ) for U = 4 and for general U ....
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This note was uploaded on 06/18/2008 for the course ECON 401 taught by Professor Kuhn during the Winter '08 term at University of Michigan.
- Winter '08