课程名称︰个体经济学一 课程性质︰经济系大二必修 课程教师︰黄贞颖 开课学院：社会科学院 开课系所︰经济学系 考试日期（年月日）︰106年1月9日 考试时限（分钟）：180分钟 试题 : 1. Tom has an initial wealth of 100. His car may be stolen so he runs a risk of a loss of 40 dollars. The probability of loss is 0.2. It is possible, however, for Tom to buy insurance. One unit of insurance costs γ dollars and pays 1 dollar if the loss occurs. Thus, if α units of insurance are brought, the wealth of Tom will be 100-γα if there is no loss (a good state) and 100-γα-40+α if the loss occurs (a bad state). Tom is an expected utility maximizer with Bernoulli utility function u(x)=ln(x) where x is his wealth in a state. (a)(10%) Write down Tom's expected utility if he buys α units of insurance. Different- iate it with respect to α to derive the first order condition which will be useful later. (b)(10%) Suppose in 2016 insurance is actuarially fair in the sense that the insurance company breaks even on average. What should γ be? How much insurance (α) will Tom buy? What is his wealth in the good state? What is his wealth in the bad state? Does Tom face any risk after being insured? (c)(10%) In 2017 insurance company decides to change the premium so now γ becomes 0.25 How much insurance (α) will Tom buy now? What is his wealth in good state? What is his wealth in the bad state? (d)(10%) Facing the premium change from 2016 to 2017, what is the Slutsky substitution effect of Tom's wealth in the good state? 2. Consider a consumer who lives for two periods. The consumer gets utility from consumption in each period. The consumer also gets an endowment of time in each period, L hours, which the consumer can use to work or consume as leisure . The consumer gets NO utility from leisure, however. There is no borrowing or lending. (a)(10%) Let w1 and w2 be the wage rates per hour in periods 1 and periods 2 respect- ively. In period 1, the consumer can spend some of the time endowment of obtaining education. Call this amount of time h. This time provides neither utility nor disutility, but it reduces the time available for working. The benefit of spending time on education is that this raises the wage the consumer can earn in period 2. In particular, assume w2=h．w1 Under these assumptions, draw the intertemporal budget set of the consumer. (b)(10%) The consumer's utility function is u(c1,c2)=lnc1+βlnc2 where c1 is the consumption of period 1, c2 that of period 2 and β>0 a constant. Write down the optimization problem this consumer faces and solve for the optimal h of this consumer. (c)(10%) What effect does an increase in β have on the decision to invest in eduction? Interpret. 3. True or False: You need to explain briefly your answers. (a)(10%) In the CAPM model, if stock A has the same standard deviation of return as stock B, and has lower expected return than stock B, then no one would want to hold stock A because all money invested in stock A should go to stock B. (b)(10%) If apples are normal good for a net supplier of apples, then it is possible that when the price of apples increases, his demand for apples increases as well. (c)(10%) Suppose there are two states of nature. State 1 occurs with probability p1 and state 2 with p2 = 1-p1. A consumer has the utility function of the following U(c1,c2,p1,p2) = c1^p1．c2^p2 where c1 is his consumption at state 1 and c2 is that at state 2. Since the consumer is behaving exactly like an expected utility maximizer who has the utility p1．ln(c1)+p2．ln(c2), we claim that the consumer's utility function takes the expected utility form. Enjoy the winter break! --

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