Econ 422 Problem Set 2 - Optimal Consumption and Investment in a Two-Period Economy - Prof, Assignments of Economics

Download Econ 422 Problem Set 2 - Optimal Consumption and Investment in a Two-Period Economy - Prof and more Assignments Economics in PDF only on Docsity! Econ 422 E. Zivot Summer 2008 Problem Set 2 Due Monday 7/31/08 Make sure that you can do BM Chapter 3 problems with ease. Sample on your own some of the quiz problems with answers in the back of the book. Hand in the following textbook problems (it looks like a lot of problems but they are mostly pretty short): 1. Suppose Tom Jones lives in a one-good (say corn), two-period world. Tom's preferences for current and future consumption can be represented by a utility function of the form U= log(C0) + (2/3)log(C1) where C0 and C1 are current and future consumption. With this utility function the marginal rate of substitution between current and future consumption is MRS = -3C1/(2C0). Tom begins the current period with an endowment of 500 units of corn; no endowment is received in the future. Tom has two ways of reallocating corn over time. (i) He can borrow or lend at an interest rate of 20% (r = .20). (ii) He also has the option of planting corn in the current period which will ready for harvest in the future period. The production relationship is Q = 48·I0.5 I is the amount of corn planted in the current period and Q is the amount of corn harvested in the future period. The marginal product (i.e., the MRT) of planted corn is MP = 24·I-0.5 (This expression for the marginal product gives the slope of the production function.) (a) How much corn will Tom plant? How much corn is harvested in the future period? [Hint: What are the conditions that determine the optimal level of investment? If you can determine the right investment level, then you can find the combination of present and future resources that produces maximum wealth.] (b) With his preferences, Tom's consumption function for the initial period is 0 0 3 5 C W=