Consider an economy characterized by the following: . the debt-to-GDP ratio is 40% . the primary deficit is 4% . the output growth rate is 3% . the nominal interest rate is 6% . inflation rate is 1% (i) (2 points) Compute the debt-to-GDP ratio for the next year. (ii) (3 points) Suppose that nominal interest rate falls to 4%. Compute the debt-to-GDP ratio again for the same year. Compare your answer to part (i). (iii) (3 points) Suppose that the output growth increases to 4%. Using the original set-up, compute the debt-to-GDP ratio again for the same year. Compare your answer to part (i). (iv) (2 points) How do changes in r and g affect the evolution of debt-to-GDP? Why is it useful to analyze debt-to-GDP rather than primary deficit or debt? Discuss