aa refer to the questions

(a) If a country is on a fixed exchange rate, how can fiscal policy be used to effectively devalue a country's real exchange rate? (b) Very briefly (no math needed), what are three possible explanations of why world long-term real interest rates have fallen in the past couple decades? What changes might take place in the next ten years that might make real interest rates rise back up to their long-term averages? (c) The gravity model of trade has been widely used to test for whether currency unions lead to an increase in trade. Explain why there might be a causality issue here, using the Euro as an example. (d) Explain two alternative rationales of why foreign creditors might be able to collect repayments from sovereign nations. Can you think of any empirical predictions that might differ across the different approaches?

Consider the following growth model: (0) = sup f+1g1=0X1 =0 ln( +1) subject to the constraint +1 2 [0 ] () Finally, note that 0 1 a. Write down the Bellman Equation. b. Solve the Bellman Equation by "guessing" a solution. Speci...cally, start by guessing that the form of the solution is () = + ln() Solve for parameters and c. Derive the optimal policy function. Problem 2 (True/False/Uncertain; 24 minutes): This question is graded on the quality of your explanation (not on the one-word answer itself). So explain each answer. When a statement is false, you'll get full credit only if you provide a counter-example. a. Assume that (i) consumers have rational expectations, and, (ii) the prod- uct of the gross interest rate and the discount factor is unity. Then marginal utility is a random walk. b. If the ow payo function is bounded, then there exists a unique bounded solution to the Bellman Equation. c. In a discrete adjustment model, the region of inaction gets larger as the variance of background noise gets smaller. d. The variance of an Ito Process monotonically increases with the forecasting horizon.

2. (24 points) Consider a one-good stochastic -country endowment economy where the representative agent in country lives for two periods and has utility function = 1 1 1 + E 1 2 1 . First-period endowment income in country is given by , and in the second period by (), where is the state of nature. Assume that there are complete state contingent markets in this global economy. (a) Characterize the Euler equation in country for a state- security - that is, a security which pays off one unit in date 2, period . Denote the price of this bond in terms of date 1 consumption () 1+ , and denote the probability state occurs (). (b) What relationship does the model predict between cross-country consumption growth rates if is the same for all countries? What if can differ across countries? You can receive full credit by directly providing the answers without derivation, but if you choose to derive them, it will be helpful to use your answer from part (a) and the fact that all countries can buy the same set of state-contingent securities. (c) Suppose differs across countries. In what sense can one think of the world riskless interest rate being determined in this model by a standard bond Euler equation of the form 0 (1) = (1 + )0 (2) where is the interest rate on a riskless bond, 1 and 2 are aggregate world measures of consumption, and () is an appropriately defined utility function over aggregate consumption? If you cannot answer this question analytically, you can get almost full credit by giving a brief intuitive discussion. Hint for analytical argument: show that the above Euler equation holds when aggregate consumption is defined using the geometric mean of country consumptions =1() 1 and () = 1 1 is CRRA with relative risk aversion that is the harmonic mean of country relative risk aversions 1 1 P =1 1 3 (d) Now suppose there are a large number of agents in each of the countries, and that within each country , everyone has an identical utility function with the same . The risk aversion parameter can still differ across countries. Very briefly, with no analytics necessary, does this change anything in part (c)?

(6) and (7) clearly define unique cutoffs, = 1 = 1(1 ) + (1 ) Does the equilibrium remain unique as we approach the common knowledge benchmark ( )? Is uniqueness guaranteed if we add a public signal of the fundamentals = + where (0 1 ) which all traders observe? No analytical work is needed to obtain full credit; a brief explanation is sufficient for this part. (d) Now suppose that instead of observing a normally distributed signal, agents observed a uniformly distributed signal. That is, suppose [ ] 2 Assuming that agents follow threshold strategies with a fixed ( 1+), how does this change your answer to part (a)? Hint: after computing () in this new setting, plot () against over the interval [0 1] to identify the condition that must characterize