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INTERMEDIATE MICROECONOMIC THEORY ECONOMICS 301 FALL 2010 SECOND HOMEWORK PROBLEM SET (Answers) 1. Assume that poor people who accept lump-sum transfer payments of $L must also agree to pay a tax on their wages of 50%. They do not pay a tax on the lump-sum payment. a. Use a labor-leisure choice analysis (Chapter 5) to show what effect the lump- sum payment and wage tax combination has on an eligible consumer’s budget constraint. b. Use your answer to the first part of this question to help explain why some individuals with the same wages and non-work income as others would not be willing to participate in this program. Hint: consumer preferences will play an important role in the decision to participate. Be explicit in showing why this is the case. Answer: a. The lump-sum increase shifts the budget line out parallel. The 50% tax, though, is equivalent to a 50% decrease in the wage. As a result, the new budget line shows that at the maximum amount of leisure, the consumer purchases L units of the consumption good. However, the C intercept (that is, at zero hours of leisure) equals L plus one-half of the old intercept. Assuming that L is not too large relative to the previous intercept, the new budget line and old budget line will cross at some combination of hours of leisure and the consumption good. b. To answer this question you need to show that a consumer’s preferences are such that the consumer maximizes utility at a point on the old budget line that yields a level of utility that is higher than that obtainable at any point on the new budget line. I will draw an example in class. 2. Assume that Ricky wins in the state lottery $500 a day for life. Use the analysis of the choice between labor and leisure to answer the following questions: a. Show how his lottery earnings affect the position of his budget line. b. Assume that Ricky continues to work the same number of hours per day after winning the lottery. Show on a graph the effect of the lottery winnings on his hours of leisure. Note: be sure to include indifference curves in addition to the new budget constraint. c. Suppose that Ricky’s boss also increases his hourly wage. Using the information from part b of this question, determine what effect the increase in wage will have on Ricky’s daily hours of work. Be sure to draw a graph 1
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showing his indifference curves and the effect that the increase in his wage has on his budget line and choice of hours of work. Answer:
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This note was uploaded on 02/20/2011 for the course ECON 301 taught by Professor Arnold during the Fall '08 term at University of Delaware.

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