Consider an economy characterized by the following facts:

i. The debt-to-GDP ratio is 40%.

ii. The primary deficit is 4% of GDP.

iii. The normal growth rate is 3%.

iv. The real interest rate is 3%.

a. Using your favorite spreadsheet software, compute the debt-to-GDP ratio in 10 years, assuming that the primary deficit stays at 4% of GDP each year; the economy grows at the normal growth rate in each year; and the real interest rate is constant, at 3%.

b. Suppose the real interest rate increases to 5%, but everything else remains as in part (a). Compute the debt-to GDP ratio in 10 years.

c. Suppose the normal growth rate falls to 1%, and the economy grows at the normal growth rate each year. Everything else remains as in part (a). Calculate the debt-to-GDP ratio in 10 years. Compare your answer to part (b).

d. Return to the assumptions of part (a). Suppose policymakers decide that a debt-to-GDP ratio of more than 50% is dangerous. Verify that reducing the primary deficit to 1% immediately, and that maintaining this deficit for 10 years, will produce a debt-to-GDP ratio of 50% in 10 years. Thereafter, what value of the primary deficit will be required to maintain the debt-to-GDP ratio of 50%?

e. Continuing with part (d), suppose policy makers wait five years before changing fiscal policy. For five years, the primary deficit remains at 4% of GDP. What is the debt to-GDP ratio in five years? Suppose that after five years, policy makers decide to reduce the debt-to-GDP ratio to 50%. In years 6 through 10, what constant value of the primary deficit will produce a debt-to-GDP ratio of 50% at the end of year 10?

f. Suppose that policy makers carry out the policy in either parts (d) or (e). If these policies reduce the growth rate of output for a while, how will this affect the size of the reduction in the primary deficit required to achieve a debt to-GDP ratio of 50% in 10 years?

g. Which policy-the one in part (d) or the one in part (e)-do you think is more dangerous to the stability of the economy?