Problem set 91.Consider the lemons model with variable quality discussed in class. Quality of sellers is denoted by v, and the buyer is willing to pay a price equal to the average quality of a car. The buyer does not know the quality of the car he buys: he only knows that the quality is uniformly distributed in [0,1].Suppose the cost of quality v to a seller is c(v). Find the market price if (i) c(v) = v/4 and(ii) c(v) = 2v3. 2.Consider case (ii)of the above problem. Interpret the quality of a car as the utility that a buyer receives from a car. Suppose the only change is that the buyer is risk averse. Will the market price go up or down compared to the above problem? Will the highest quality available in the market increase or decrease compared to the above problem? (No math necessary)3.While self-employed workers have the option to purchase private health insurance, many do not, due to adverse selection. Suppose half the population is healthy and half is unhealthy. The cost of getting sick is $1000 for healthy people and $10000. In a year, any
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