微观经济理论测试：ch19

1、CHAPTER 19THE ECONOMICS OF INFORMATION The problems in this chapter stress the economic value of information and illustrate some of the consequences of imperfect information. Only a few of the problems involve complex calculations or utilize calculus maximization techniques. Rather, the problems are

2、 intended primarily to help clarify the conceptual material in the chapter. Comments on Problems19.1This problem illustrates the economic value of information and how that value is reduced if information is imperfect. 19.2This is a continuation of Problem 18.5 that illustrates moral hazard and why i

3、ts existence may prompt individuals to forego insurance.19.3Another illustration of moral hazard and how it might be controlled through cost-sharing provisions in insurance contracts. 19.4This is an illustration of adverse selection in insurance markets. It can serve as a nice introduction to the to

4、pic of optimal risk classifications and to some of the economic and ethical problems involved in developing such classifications.19.5This is a simple illustration of signaling in labor markets. It shows that differential signaling costs are essential to maintaining a separating equilibrium.19.6An il

5、lustration of the economic value of price information. Notice that the utility of owning the TV is already incorporated into the function U(Y) so all Molly wants to do is minimize the TVs cost.19.7A continuation of Problem 19.6 which uses material from the extensions to calculate the optimal number

6、of stores to search.19.8A further continuation of Problems 19.6 and 19.7 that involves computation of an optimal reservation price.19.9This problem illustrates that principal-agent distortions may occur in medical care even when the physician is a “perfect” altruist.19.10Introduces the notion of “re

7、solution-seeking” behavior. Here the notation is rather cumbersome (see the solutions for clarification).Solutions19.1a.Expected profits with no watering are .5(1,000) + .5(500) = $750. With watering, profits are $900 with certainty. The farmer should water.b.If the farmer knew the weather with cert

8、ainty, profits would be $1,000 with rain, $900 with no rain. Expected profits are $950. The farmer would pay up to $50 for the information.c.There are four possible outcomes with the following probabilities:ForecastWeatherRainNo RainRain37.512.5No Rain12.537.5Profits in each case are (assuming farme

9、r follows forecasters advice):ForecastRainNo RainWeatherRain1000900No Rain500900Expected profits, therefore, are.375(1000) + .125(900) + .125(500) + .375(900) = 887.5.The forecasters advice is therefore of negative value to the farmer relative to the strategy of planning on no rain.19.2Premium is no

10、w $300. If she buys insurance, spending is 9700, utility = ln(9700) = 9.1799. This falls short of utility without insurance (9.1840), so here it is better to forego insurance in the presence of moral hazard.19.3A cost-sharing policy would now cost $1,750. Wealth when sick would be 20,000 1,750 3,500

11、 = 14,750. Wealth when well would be 20,000 1,750 = 18,250. Utility from this combination may exceed utility of a certain $15,000.19.4a.Premium = (.8)(.5)(1,000) + (.2)(.5)(1,000) = 500b.For blue without insuranceE(U) = .8 ln9,000 + .2 ln10,000 = 9.1261.With insuranceE(U) = ln(9,500) = 9.1590.Will b

12、uy insurance.For brown without insuranceE(U) = .2 ln(9,000) + .8 ln(10,000) = 9.1893.Better off without insurance.c.Since only blue buy insurance, fair premium is 800. Still pays this group to buy insurance.E(U) = 9.1269Brown will still opt for no insurance.d.Blue premium = 800 E(U) = 9.1269Brown pr

13、emium = 200 E(U) = 9.1901So Brown is better off under a policy that allows separate rate setting.19.5a.No separating equilibrium is possible since low-ability workers would always opt to purchase the educational signal identifying them as high-ability workers providing education costs less than $20,

14、000. If education costs more than $20,000, no one would buy it.b.A high-ability worker would pay up to $20,000 for a diploma. It must cost a low-ability worker more than that to provide no incentive for him or her to buy it too.19.6a.U (18,000) = 9.7981b.U (18,300) = 9.8147c.Utility of Trip = .5U (1

15、8,200) + .5U (17,900) = 9.8009. So since expected utility from the trip exceeds the utility of buying from the known location, she will make the trip.19.7a.Here otherwise.Cumulative function is For F(p) = 0 for P 400.Expected minimum price (see footnote 1 of extension) isb. clearly diminishes with n

16、:.c.Set n = 6.07 (i.e., 7 calls)An intuitive analysis is:With n = 6 With n = 7 With n = 8 So should stop at the 7th call.19.8According to the Extensions, the searcher should choose so that 19.9Patient utility maximization requires: . Doctor Optimization requires: . If (which I interpret as meaning t

17、hat the physician is a perfect altruist), this requires . Relative to patient maximization, this requires a smaller . Hence, the doctor chooses more medical care than would a fully informed consumer.19.10a.Expected value of utility = .5(10) + .5(5) = 7.5 regardless of when coin is flipped.b.If coin is flipped before day 1, there is no uncertainty at day 2. From the perspective of day 1, utility = 10 or 5 with p = 0.5 so E1(U) = .5(10) + .5(5) = 7.5.If the coin is flipped at day two, E