Suppose that a government has an initial debt of $5 trillion and that the nominal interest rate is 5%.
a. If the government keeps its primary budget in balance, what is the growth rate of its debt? Why?
b. If the government keeps its total budget in balance, what is the growth rate of its debt? Why?
c. Suppose the country's GDP grows at 4% per year. What happens to the debt to GDP ratio over time in the two cases above? Are either of these cases sustainable? Why or why not?