2010-Problem-Session-2

2010-Problem-Session-2 - h ( p,U ) and her expenditure e (...

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Stanford University Department of Management Science and Engineering Optional Problem Session 2 Winter 2010 Friday, January 22, 2010 Practice Problem 2.1 (Quasilinear Utility and Welfare Measures) Laura likes to consume two goods, 1 and 2. She has a positive income of w , and her utility is given by the function u ( x ) = ln( x 1 ) + k x 2 , for x = ( x 1 ,x 2 ) ± 0, where k > 0 is a constant. We assume that the price vector p = ( p 1 ,p 2 ) ± 0 with the prices for the two goods is given. (i) Explain why we can, without loss of generality, assume that k = 1 and that p 2 = 1. Why can good 2 be interpreted as “money”? In the following parts of the problem we assume that k = p 2 = 1. (ii) Compute Laura’s marginal rate of substitution MRS 12 ( x ) between goods 1 and 2 at the consumption bundle x and interpret your result. Could Laura’s friend Jane have a different marginal rate of substitution between the two goods? (iii) Compute Laura’s Hicksian demand
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Unformatted text preview: h ( p,U ) and her expenditure e ( p,U ) for a given utility level U . (iv) What are Lauras compensating variation C and her equivalent variation E for a change of p 1 to p 1 > 0? (v) Determine the change in Lauras consumer surplus CS for the price change in part (iv). (vi) Compare your results for the three welfare measures in parts (iv) and (v). In light of the inter-pretation of good 2 as money, provide an intuitive explanation for the dierence (or lack thereof) between the three measures. (vii) Would the ordinal comparison in part (vi) be dierent for Lauras friend Jody, whose utility function is u ( x ) = 1-e-x 1 + x 2 , all else equal? (viii) [ Bonus ] Discuss the dependence of the welfare measures C , E , and CS on wealth w , for Laura, Jody, and . .. Jane. 1...
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