Section 1. (Suggested Time: 45 Minutes) For 3 of the following 6 statements, state whether the statement is true, false, or uncertain, and give a complete and convincing explanation of your answer. Note: Such explanations typically appeal to specific macroeco- nomic models. 1. The U.S. will likely have to increase its military activities in the Middle East. This should cause output to rise. 2 Suppose that the data shows that times of high consumer and firm borrowing are also times of high economic growth We could then conclude that financial constraints are an important determinant of economic activity. 3 What Macroeconomic models miss is that consumers do not want to borrow during recessions 4 Policies used to bring us out of one recession sow the seeds of the next. 5. During a liquidity trap, it is possible that increases in money supply can cause deflation. 6. We observe that during the Great Recession, housing prices drop substantially. Mean- while, mortgage interest rate also drop. Therefore, a drop in interest rates causes declines in housing price.Part C (continued) 2. Consider the North American Auto market as represented by a U.S. and German firm, both of which are located in North America and producing for North American customers. When the NAFTA was implemented, it specified that firms purchase least y percent of their inputs from NAFTA partners (US/Mexico/Canada) to qualify for preferential NAFTA benefits, a) Consider the case of the German firm and its assembly of cars in Mexico. The firm's production process requires it to combine an engine with a specified set of parts. Show how the shadow price for Mexican and German-origin auto parts depends on the content requirement y. What is the intuition for your result? b) Now assume that the production functions for the U.S. and German firm are given by Xus = Z." Zab and X, = Zo Zan , where Zo represents inputs that are from the NAFTA block, and Zrb represents inputs that originate outside the block, and (8 0. Find the risk-free interest rate R! (d,), and R" = E( R-! (d,)), the unconditional mean of the risk-free rate. Next, suppose the flow utility function is logarithmic: u(c) = In(c,). Find the risk-free interest rate, R-(d,) and its unconditional mean: R" = E( R-' (d.)). Recalling that {d,} is i.id., show that R" is higher when preferences are logarithmic. Explain your findings. (d) Find the price of a share of stock, p (d,), and its unconditional variance, for both the linear and logarithmic specifications. (e) Let p; - EF, R"' duty denote the realized discounted dividend stream. Assum- ing that flow utility is linear, what is the unconditional variance of p;?.Is the variance of the stock price p, greater than or less than the variance of the realized sum p;? Explain. (f) Repeat the analysis in part (e) under the assumption of logarithmic flow utility.Question 1 (50 points) Consider a pure exchange economy with 2 islands. Each island consists of infinitely- lived identical agents whose measure is normalized to one. There is a single consump- tion good, or fruit, that is non-storable. The representative agent of island i values different consumption streams according to 1(c') = \\ Be), vi, with o > 0. The total endowment in this economy (i.e., in both islands) in period f is given by a deterministic sequence {}fo, with e > 0 for all t. However, due to the location of the two islands, weather conditions are different affecting the fruit yield on each island. Letting each period t denote a season, we assume that in even periods the fruit yield on island 1 is given by el = aer, a e [0, 1], and in odd periods it is given by el = (1 - a) e. Of course, by definition, the endowment of fruit on island 2 must be given by ef = e - er, in all periods. a) For this economy define an Arrow-Debreu equilibrium (ADE) and a Sequential Markets equilibrium (SME). b) Fully characterize (i.e., find a closed-form solution for) the ADE prices. c) Using any method you like, characterize the SME consumption allocation in as much detail as you can. In the remaining questions, we will assume that the total endowment in the economy (in both islands) follows the process a = ye, with y > 0. d) Given this new parametric specification, provide a closed-form solution for the SME consumption allocation. e) What happens to the consumption allocation you calculated in part (d) when y = 1 (no growth in the endowment)? What if (y = 1 and) a = 1? f) Back to the model with general a, 7; can you specify parameter values for which agents on island 1 consume more than agents on island 2 in a typical period ? g) For what parameter values do the ADE prices you calculated in part (b) increase as a function of t? Provide some intuition for your result. Hint: Notice that I am asking you to find only the equilibrium consumption allocation. This has important consequences for which method is the most convenient to use here