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# Economics+395+Fall+2008+PS4+Answers - Economics 395 Risk...

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Economics 395 Risk and Uncertainty Problem Set 4 Answer Key Question Thirteen Amy wishes to hire a painter to paint her house. She knows that some painters are better than others. But she cannot tell how good a painter is until she has seen her work. And the only way she will see any painter’s work is if she hires her. There are three types of painter available in the market. Truly excellent painters will only accept work if paid at least \$50/hour. These painters are estimated to comprise around 20% of the market. Good painters constitute a further 40% of the market. These painters will not work for less than \$30/hour. The remaining 40% of painters are mediocre, and will not work for less than \$15/hour. Amy would be prepared to pay as much as \$55/hour if she knew the painter was excellent. She would pay a good painter up to \$40/ hour and would pay a mediocre painter no more than \$18/hour. (a) If the market for painters were to allocate resources efficiently, then Amy would hire a painter whose services maximize the amount of surplus that can be shared between the two contracting parties. Which type of painter provides the greatest surplus? In the socially optimal world, which painter would Amy hire? Excellent painters provide \$55 - \$50 = \$5 of surplus/hour Good painters provide \$40 - \$30 = \$10 of surplus/hour Mediocre painters provide \$18 - \$15 = \$3 of surplus/hour Good painters provide most surplus, and would be hired by Amy in the socially optimal allocation of resources. (b) What is the most Amy would pay a painter picked at random from the population? (Assume Amy is risk-neutral). If Amy picked a painter at random from the population, the most she would pay would be her expected valuation: E[v] = (0.2)\$55 + (0.4)\$40 + (0.4)\$18 = \$32.20 (c) If Amy offered the price you calculated in part (b), which types of painter would accept the job? Explain why Amy would never offer such a price. If Amy offered \$32.20/hour, no excellent painters would ever accept the job. Only good and mediocre painters would find the contract acceptable. Half of the

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painters who find the job acceptable are good, and half are mediocre. Therefore Amy’s expected value of a painter who finds the price acceptable is E[v| P = \$32.20] = (0.5)\$40 + (0.5)\$18 = \$29. The expected value of painters who find the price acceptable is less than the price she would notionally be offering. Therefore, she would never offer such a price. (d) If Amy were to select a painter randomly from the population of “good” and “mediocre” painters, what price would she be prepared to pay that painter? Which painters would accept the job at this price? (Again, assume that Amy is risk-neutral). Amy would not pay any more than \$29 (the expected value of a painter drawn from the good and mediocre painters). But at this price, the “good” painter would never accept the job.
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