Economics+395+Fall+2008+PS4 - Question Thirteen 45 A EUH...

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45° ω A EU H EU L 1 EU L 0 EU H Y 1 Y 2 -(1-π L )/ π L -(1-π H )/ π H Economics 395 Risk and Uncertainty Problem Set 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? (b) What is the most Amy would pay a painter picked at random from the population? (Assume Amy is risk-neutral). (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. (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). (e) If Amy is risk-neutral, what price do you think she will offer a painter? Which type or types of painter will accept such an offer? Is this outcome efficient? (f) If Amy is risk-averse, would your earlier answers change at all? If your answers change, would you expect the outcome to be more or less efficient than the outcome when Amy is risk-neutral?
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Question Fourteen Jack manufactures snowboards. Jill manufactures skateboards. During the winter, each faces uncertainty over income. If the snowfalls are significant, then there is high demand for Jack’s products, but low demand for Jill’s. On the other hand, if the snows are light, demand for Jill’s products remain relatively high and demand for Jack’s product is low. Jack and Jill are both risk-averse expected utility maximizers. Suppose the chance of light snowfall is 1/3, and the chance for heavy snowfall is 2/3. In the event of heavy snowfall, Jack’s income is $1100/week while Jill’s income is $500/week. In the event of light snowfall, Jack’s income is $200/week and Jill’s income is $1100/week. (a) If Jack can insure against poor snowfalls, what would be the “fair” price of
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Economics+395+Fall+2008+PS4 - Question Thirteen 45 A EUH...

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