Econ 301 - Problem Set #2 - Due on Friday, Jun 25, 2010 1. Constrained Consumer Choice . Steve’s utility function is U = BC , where B = veggie burgers per week, and C = packs of cigarettes per week. Here MU B = C and MU C = B . (a) What is his marginal rate of substitution if veggie burgers on the vertical axis and cigarettes are on the horizontal axis? (b) Steve’s income is $120, the price of a veggie burger is $2, and that of a pack of cigarettes is $1. How many burgers and how many packs of cigarettes does Steve consumer to maximize his utility? (c) When a new tax raises the price of a burger to $3, what is his new optimal bundle? Illustrate your answer in a graph. 2. Constrained Consumer Choice . A consumer has the following utility function for goods X and Y: U ( X,Y ) = 5 XY 3 + 10 The consumer faces prices of goods X and Y given by p x and p y and has an income given by I . a. Write out the Lagrangian expression for the consumer’s utility maximization problem.
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