1. For this problem assume that the economy is initially at potential. Inflation is 3% and the real interest rate is equal to the marginal product of capital, which is 4%. As well, when the economy is at potential unemployment is 5%. Finally, v=1/2 and b=2. The questions need graphs, equations and a brief written explanation.

a. What is the nominal interest rate when the economy is at potential?
b. Now suppose a sudden drop in the stock market causes a decline in the share of investment equal to 2% of potential output. What happens to the output gap?
c. What is the unemployment rate now?
d. What is the inflation rate? What is the change in inflation?
e. If the Fed does not change the nominal interest rate in response to the decline in investment what will happen to the real rate and output? What is the unemployment rate now?
f. What does the Fed have to change the nominal interest rate to in order to bring the economy back to potential?

2. For this problem assume that the economy is initially at potential. Inflation is 2% and the real interest rate is equal to the marginal product of capital, which is 3%. As well, when the economy is at potential unemployment is 6%. Finally, v=1/2 and b=1. The questions need graphs, equations and a brief written explanation.

a. Suppose fears of economic sanctions-in response to the US annexing Quebec-cause the financial system to demand a risk premium of 4% above the risk free real rate. What will this do to the economy?
b. What will this do to the unemployment rate and the inflation rate?
c. How low can the Federal Reserve lower the real rate in response? What is output now?
d. How can the government bring the economy back to potential?

3. HARD QUESTION For this problem, assume that the economy is initially at potential. Inflation is 3% and the real interest rate is equal to the marginal product of capital, which is 4%. As well, when the economy is at potential unemployment is 5%. Finally, v=1 and b=2. The questions need graphs, equations and a brief written explanation.

a. If a war suddenly breaks out, and that causes an increase in military spending of 5% of potential l GDP, what will the inflation rate be this year (one period=one year)
b. If the Fed takes no action to offset the increased military spending and the spending continues for many years what will the inflation rate be next year and for each of the following two years (i.e. time t+1, t+2, and t+3)?
c. If the war only lasts for one year and at the end of that year the increase in military spending evaporates, what will the inflation rate be next year (i.e. time t+1)