Consider the inter-temporal model with two time periods t=0 and 1. Home is a small open economy that can borrow and lend in the first period at a fixed world real interest rate of 5%. In the first period output is X0=200. Because of a deteriorating environment, output in the second period is expected to fall to X1=150. The country wants to smooth consumption as much as possible. The country begins with no external assets or liabilities.

Solve for the optimal level of consumption consistent with perfect consumption smoothing, the current account, and financial account in the first period (t=0).

Solve for NFIA, the trade balance, and the current account in the second period (period 1).

Explain the intuition as to why the CA and TB is different in period 1.

Draw a graph, completely labeled with indifference curves depicting clearly that Home is better off when they have access to international financial markets as compared to being a closed economy. In particular, label the indifference curve under a closed economy assumption as ICclosed and the indifference curve under an open economy assumption as ICopen.

Suppose a country has an investment opportunity that costs them 10 units of current consumption for an increase in 20 units of future consumption. The current and given real rate of interest is 10% (0.10). GDP, without the investment, in period 0 and period 1 is equal 120. The country has access to international capital markets.

Do the math and determine whether or not this country should borrow to take advantage of this investment opportunity. Explain. As is normally the case, the country prefers to completely smooth consumption.

Solve for the trade balance = current account in period 0 and the trade balance, NFIA, and the current account in period 1.

Explain the intuition as to why the CA and TB is different in period 1.

Draw a graph, completely labeled with indifference curves depicting clearly that Home is better off when they have access to international financial markets as compared to being a closed economy. In particular, label the indifference curve under a closed economy assumption assuming the country elected not to make the investment as ICclosed and the indifference curve under an open economy assumption (where the country did make the investment) as ICopen.

Suppose instead that this country was the US and had exorbitant privilege so that the (borrowing) interest rate was only 1% (.01) rather than 10% (.10) as above. Solve for the new level of consumption in both periods and compare the trade balance in period 0 when interest rates are 10% vs. the trade balance in period 0 with interest rates at 1%. Does the existence of exorbitant privilege result in this country borrowing more less in period 0?

This problem entails the benefits of diversification - suppose we have the following conditions - assume you are the director of a sovereign wealth fund for Home.

Suppose you decide to have 100% home bias in that you do not invest in Foreign at all. What is your expected output = consumption and what is the volatility of your output = consumption?

Suppose instead that you diversify so that your share of Home is 50% and your share of Foreign is 50%.

What is your expected output if State 1 occurs?

What is your expected output if State 2 occurs? Does your output depend on which State occurs?