Consider a two-period economy characterized by the following decision problem: max log + log subject to budget constraints: Cl+k4-bSY1, 02 -l- (1 + r)b, where is an exogenous endowment. Furthermore, assume that Y2 = Aka* with O < < 1 and productivity A. We assume that capital fully depreciates after use (6 1), and therefore k is both the first period investment and the second period capital stock. Also note that we assume bo = O, and hence b is both first period current account and second period net foreign assets. 1. Explain how this special environment maps into the general framework of National Income Accounts, and in particular why: Cal = Yl k = b and Ca2 = rb + c2 = b. 2. Explain how you derive thc intertemporal budget constraint: Given this budget constraint, characterize the optimal capital investment k Of the country. Explain why it is possible to determine optimal investment without characteriz- ing the optimal consumption-savings decision (in other words, why investment and savings decisions separate). Why do we expect a country with a very high A to run a current account deficit? What may be real-world examples of such countries? 3. Characterize the optimal consumption choice for a given interest rate r. How does a reduction in r affect thc optimal consumption and investment decisions and why? What are the implications for the current account? 4. Without doing algebra, explain the notion of the autarky interest rate rA in this economy? What happens to consumption, investment and current account if the world interest rate r > 7A?