Problem Set 6. November 8, 2007

Transcription

1 Problem Set 6 Macroeconomics II Ana Fernandes November 8, Suppose that, in the beginning of period t 1, two economic agents Paul and Ringo, agree upon a debt contract. Paul will lend Ringo $100 in return for $120 in the beginning of period t. 1. What is the nominal interest rate that Paul and Ringo agreed upon? The nominal interest rate equals 20%. Debt contracts normally specify a nominal amount for repayment. This amount is $120 in this exercise. R = =20%. 2. Suppose Paul expects inflation to be π e P =0.1, whereas Ringo thinks it will be π e R =.08. What is Paul s expected real interest rate, rp e associated with this loan? What about Ringo s real expected return, rr? e Paul s expected real rate of return is approximately r e P = =10% whereas Ringo s is r 3 R = = 12%. 3. In the beginning of period t, the economic agents become aware that the actual value of π was 0.1. What was Paul s inflation forecasting error? How about Ringo s? Pauls expectation s error: π π e P = =0.

2 Paulgotitexactlyright. Ringo s expectation s error was π π e R = = 2%. Inflation turned out to be higher than Ringo s expectations. He underpredicted inflation. 4. What was the actual real interest rate, r, in this economy? Actual interest rate: r = R π = =10%. 5. Consider Paul s inflation forecast. Provide an expression which relates the real interest rate r to Paul s forecast error. The difference between the actual and expected real interest rates is: r r e P =(R π) (R π e P )= (π π e P ). Consequently, r = rp e (π π e P ). {z } forecast error The real interest rate equals the expected real interest rate minus the forecast error. 6. Compared to his initial expectation, does Paul feel he did better or worse? Explain. Paul s forecast error was exactly 0. So, the actual and expected real interest rates coincided and he did exactly as he expected, neither better nor worse. 7. Compared to his initial expectation, does Ringo feel he did better or worse? Explain. For Ringo: r = r e R (π π e R)=r e R ( ) = r e R The actual real interest rate was lower than Ringo had expected by 2%. Since Ringo has to pay back the loan to Paul, he is better off whenever inflation turns out to be higher than he expected. Although he has to pay back the same $120 in interest, in real terms they are worth less than he expected. 2

3 8. Suppose now that Paul and Ringo had the same inflation forecast: π e P = πe R = πe. For which values of π wouldpaulfeelthathewas better off than initially expected? Explain. Since Paul collects the $120, for him to be better off it must be the case that the realized real interest rate exceeds his expectations. Forthistobethecase: r rp e 0 (π π e ) 0 π e π. Therefore, for Paul to feel lucky with the outcome of inflation it would have to be the case that actual inflation, π, turned out to be below his expected value, π e. 9. For which values of π would Ringo find himself better than expected at the time the contract was agreed upon? Explain. Ringo will feel better off whenever the real value of his loan repayment isbelowwhatheexpected. Putdifferently, he is better off whenever the realized real interest rate is lower than he expected: r rr e 0 (π π e ) 0 π π e R. 10. In view of your answers, what can you say about the redistributive effects of unexpected inflation? As we saw in class, (positive) unexpected inflation has redistributive effects that favor borrowers at the expense of lenders. A value of π above expectation hurts lenders as it decreases the real value of the repayment; for a symmetric reason, it benefits borrowers. 2. In prisoner camps during World War II, detained soldiers would sometimes use cigarettes as their currency. Suppose that a camp has just been set up and cigarettes have been distributed to prisoners. Each soldier gets the same amount of cigarettes, m. Adding up over soldiers, the total stock of cigarettes is M. 1. Suppose that the daily desired volume of transactions remains constant at the quantity Y. Also, assume for now that the nominal interest rate on intertemporal trades also remains constant at R. What is the price level P 1,inday1 of this prisoner camp? Thepricelevelissuchthat M P 1 = Φ (Y,R,...) P 1 = 3 M Φ (Y,R,...).

4 2. Suppose that all soldiers are equally addicted to cigarettes. They all smoke at a constant daily rate of µ. How does the stock of cigarettes evolve through time? (That is, relate M t to M t 1.) Soldiers destroy currency at the rate µ by smoking. Therefore: M t =(1 µ) M t What happens to the price level in this camp? For a given real interest rate r, what is the nominal interest rate in this economy? Does the nominal interest rate stay constant through time? The money stock is decreasing over time but the real volume of transactions remains constant at Y. We guess that the price level is decreasing at the rate µ and proceed to verify the guess. If the price level is decreasing at the same rate as the money stock, real balances stay constant. Output is constant at Y. The nominal interest rate will be, approximately, R = r + π = r µ. This rate will stay constant over time. This ensures that the real demand for money is constant and so that the equilibrium condition in the money market will be satisfied for all periods. 4. In day t, a new shipment of cigarettes unexpectedly arrives. Each soldier again receives m additional cigarettes, and the aggregate amount of cigarettes distributed to the camp equals M. Fromthisdayon,sol- diers continue to smoke at the rate µ. They do not expect any new shipments of cigarettes. What happens to the price level at date t? At t, the price level jumps up in order to restore equilibrium in the money market. Higher prices deflate thevalueoftheoutstanding money stock which, as we are told, increased unexpectedly. After this jump, it resumes its decreasing trajectory at the rate µ. 5. What is the nominal interest from date t onwards? The nominal interest rate remains at its previous value, r µ, since the rate of monetary destruction has not changed. 6. Define neutrality. Is money neutral in this model? We say money is neutral if a one time change in the stock of money does not affect real variables in the economy. 4

5 Money is indeed neutral in the camps as all real variables, including the real demand for money, stay at the values they had previous to the unexpected increase in M. 7. Finally, disregard for now the unexpected shipment of cigarettes. Suppose that, in day t, soldiers increase their smoking rate from µ to µ 0. What are the consequences of this change for the nominal interest rate and real money holdings? Following our previous guess, a higher rate of monetary destruction reduces the nominal interest rate to r µ 0. Since the volume of transactions stays constant, at a lower nominal interest rate people want to hold more real balances. Therefore, real balances will go up under the higher rate of monetary destruction. 8. What happens to the price level at t? The price level jumps down so as to raise the value of real balances and restore equilibrium in the money market. After the initial jump, prices will decrease at rate µ Define superneutrality. Is money superneutral? Money is superneutral if arbitrary changes in the path of the money supply do not affect real variables. As we saw, real balances increase after the reduction in the nominal interest rate, the increase itself caused by the decline in the rate of monetary destruction. Therefore, money is not superneutral in our model. 5