Carefully Answer Each Of The Questions Below You Need To Sho

Carefully Answer Each Of The Questions Belowyou Need To Show Your Wor

Carefully answer each of the questions below. You need to show your work, not just the final answer. You can write or type your answers for the questions. Please put your name and PSU ID number at the top of the 1st page. You may use as many sheets of paper as needed. If you did parts by hand: Scan your entire document (including the parts you typed and the parts done by hand), save the file in PDF format, and upload it to the ANGEL dropbox for this homework assignment. Merge the separate PDFs into one file using a service such as PDFMerge. Failure to submit a single file will result in points being deducted. If you typed everything: Save the file as a .doc or .docx file and upload it to the ANGEL dropbox. Ensure your assignment is all in one file. Failure to submit a single file will result in points being deducted (25 points total).

Consider the inter-temporal model with two time periods t=0 and t=1. Home is a small open economy that can borrow and lend at a fixed world real interest rate of 5%. In period 0, output is X0=200. Due to environmental decline, output in period 1 is expected to fall to X1=150. The country begins with no external assets or liabilities.

1. Optimal Consumption, Current Account, and Financial Account in Period 0

Solve for the optimal level of consumption in period 0 that achieves perfect consumption smoothing across the two periods, considering the country’s ability to borrow or lend at the given interest rate. Determine the current account balance and the financial account balance in period 0, justifying your calculations.

2. External Accounts in Period 1

Calculate the net foreign income and assets (NFIA), the trade balance, and the current account balance in period 1, considering the initial borrowing/saving decisions made in period 0 and the change in output. Explain how these accounts evolve in the second period based on the earlier choices.

3. Explanation of Differences in CA and TB in Period 1

Provide an intuitive explanation for why the current account and trade balance differ in period 1. Focus on factors such as income changes, savings behavior, and partial repayment or accumulation of net foreign assets.

4. Graphical Illustration of International Financial Markets and Consumer Utility

Create a graph with labeled indifference curves showing that the country benefits from access to international financial markets. Label the indifference curve when the country is a closed economy as IC closed, and when open as IC open. Clearly illustrate how access to international markets shifts the consumer's utility frontier and improves welfare.

5. Investment Opportunity and Borrowing Decision

A country has an investment opportunity costing 10 units of current consumption to generate an increase of 20 units of future consumption. The current and future GDP without the investment is 120 each, and the real interest rate is 10%.

1. Determine whether the country should borrow to undertake this investment by analyzing its payback and discounted future gains.
2. Assuming the country aims to smooth consumption, calculate the trade balance or current account in period 0 and period 1 based on the decision.
3. Explain the differences in the trade balance and current account between periods 0 and 1, considering the investment’s impact and interest rate.
4. Draw a labeled graph with indifference curves showing that the country is better off with international financial markets access, differentiating between policies of non-investment and investment decisions.

6. Effect of Interest Rate Exorbitant Privilege on Borrowing

Suppose the country is the US with an "exorbitant privilege," where the borrowing interest rate is only 1%, instead of 10%. Calculate the new levels of consumption in both periods under this lower rate. Compare the trade balances at interest rates of 10% versus 1%. Does the lower rate lead to more or less borrowing in period 0?

7. Diversification and Output Volatility

1. As the sovereign wealth fund director, assume 100% home bias: no foreign investment. Calculate the expected output and its volatility under this scenario.
2. Now, diversify with 50% home and 50% foreign investments. Compute the expected output if State 1 occurs and if State 2 occurs.
3. Discuss whether the expected output depends on the state that occurs and how diversification affects output variability and risk mitigation.