課程名稱︰個體經濟學上 課程性質︰必修 課程教師︰黃貞穎 開課學院：社會科學院 開課系所︰經濟學系 考試日期（年月日）︰101/01/07 考試時限（分鐘）：160 是否需發放獎勵金：是，麻煩了 （如未明確表示，則不予發放） 試題 : 1.Consider a consumer who lives for two periods. The consumer gets utility from consumption in each period. The consumer also gets an endownment 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 2 respectively. In period 1, the consumer can spend some of the time endownment 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 raise 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) = ln(c1) + β * ln(c2) 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 education? Interpret. 2.Evan Evader earns $5000 in income. Income is taxed at 20%. Evan can underreport his income to the tax collecting ministry and pay taxed only on the amount that he reports, but should he be audited, the ministry will impose a surcharge of 100% on the unpaid taxes; that is, he will have to pay 40% of any unreported income if he is audited. Evan realizes that the probability is 0.4 that he will be audited. His Bernoulli utility function is u(x) = ln x and he is an expected utility maximizer. Assume that Evan can never overreport. (a)(10%) Draw Evan's budget set in a diagram where on the x-axis, label Evan's final income when he is audited, while on the y-axis, label his final income when he is not audited. What i s the slope of the budget line? (b)(10%) Is Evan's indifference curve convex to the origin? Explain. (c)(10%) How much will Evan report to ministry? 3.There are two stocks in the world, A and B. In one year, the expected return of a share of A is 10% and that of B is 20%. The standard deviation of the return of a share of A and that of B is 0. There is a risk free asset which yields the return of 5%. (a)(10%) In a diagram where the standard deviation of the return is on the X axis and the expected return is on the Y, clerk mark where A, B and the risk free asset locate. (b)(10%) An investor invests 1 dollar in which proportion p ∈ [0, 1] is invested in A and proportion 1-p in B. What is the expected return of this investment? What is the standard deviation of the return of this investment? (c)(10%) Suppose all investors have mean-variance perference. Draw a typical indifference curve in a diagram where the standard deviation of the return on the return on the X axis and the expected return is on the Y. Explain why the indifference curve has the shape you draw. (d)(10%) Derive the market portfolio. That is, for a typical investor, for every dollar, what proportion p ∈ [0, 1] will he invest in A? --

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