Suppose Melania borrows $100 from Jill for one year. They agree that the ex-ante real interest rate should be 1 percent and they agree to set a fixed nominal interest rate.
(a) According to the Fisher Equation, what nominal interest rate should Jill charge on the loan to ensure an ex-ante real interest rate of 1 percent, assuming the expected inflation rate is 4 percent? What if the expected inflation rate is 2 percent? 8 percent?
(b) Suppose the expected inflation rate is 4 percent and the nominal interest rate is set according to the Fisher equation, as in part (a). Now suppose the actual inflation rate turns out to be 3 percent. What is the ex-post real interest rate? Who wins and who loses as a result of this actual inflation rate?
(c) Re-do part (b), assuming that the actual inflation rate turns out to be 7 percent.
(d) Return to the scenario of part (a), and assume that there is no zero lower bound on the nominal interest rate. According to the Fisher Equation, what nominal interest rate should Jill charge on the loan to ensure an ex-ante real interest rate of 1 percent, assuming that the expected inflation rate is zero? What if the expected inflation rate is -3 percent (in other words, what if they expect a 3 percent deflation)? What if the expected inflation rate is -6 percent?
(e) Now suppose there is a zero lower bound on the nominal interest rate. How will this change your previous answers from part (d)? In other words, what will be the nominal interest rate in each of the scenarios outlined in part (dy?
(f) What is the ex-ante real interest rate implied by the nominal Interest rates you solved for in part (e)? Explain why the ex ante real interest rate can be higher than one percent in some of these cases (g) Now suppose that Melania and Jill agree to use a variable interest rate loan, instead of a fixed interest rate loan. They agree that the ex-post interest rate should be 1 percent. How much in dollar terms should Melania repay Jill after one year if the inflation rate turns out to be 4 percent? 2 percent? 3 percent? 6 percent? (Assume there is no zero lower bound on ex-post nominal nterest rates in a variable interest rate loan)
(h) What is the ex-post real-interest rate that Melania pays Jill in each of the scenarios from part (g)?
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Suppose Melania borrows $100 from Jill for one year. They agree that the ex-ante real interest rate...
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