Econ 301 - Problem Set #2 - Due on Friday, Jun 25, 20101.Constrained Consumer Choice. Steve’s utility function isU=BC, whereB= veggie burgers perweek, andC= packs of cigarettes per week. HereMUB=CandMUC=B.(a) What is his marginal rate of substitution if veggie burgers on the vertical axis and cigarettes areon 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 hisutility?(c) When a new tax raises the price of a burger to $3, what is his new optimal bundle? Illustrateyour answer in a graph.2.Constrained Consumer Choice. A consumer has the following utility function for goods X and Y:U(X, Y) = 5XY3+ 10The consumer faces prices of goods X and Y given bypxandpyand has an income given byI.a. Write out the Lagrangian expression for the consumer’s utility maximization problem.
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