Question: The government of the Republic of Andea is currently pegging the Andean peso to the dollar at E = 1 peso per dollar. Assume the following:
In year 1 the money supply M is 2,250 pesos, reserves R are 1,250 pesos, and domestic credit B is 1,000 pesos. To finance spending, B is growing at 50% per year. Inflation is currently zero, prices are flexible, PPP holds at all times, and initially, P = 1. Assume also that the foreign price level is P* = 1, so PPP holds. The government will float the peso if and only if it runs out of reserves. The U.S. nominal interest rate is 5%. Real output is fixed at Y = 2,250 at all times. Real money balances are M/P = 2,250 = L(i) Y, and L is initially equal to 1.
a. Assume that Andean investors are myopic and do not foresee the reserves running out. Compute domestic credit in years 1, 2, 3, 4, and 5. At each date, also compute reserves, money supply, and the growth rate of money supply since the previous period (in percent).
b. Continue to assume myopia. When do reserves run out? Call this time T. Assume inflation is constant after time T. What will that new inflation rate be? What will the rate of depreciation be? What will the new domestic interest rate be? (Hint: Use PPP and the Fisher effect.)
c. Continue to assume myopia. Suppose that at time T, when the home interest rate i increases, then L(i) drops from 1 to 2/3. Recall that Y remains fixed. What is M/P before time T? What will be the new level of M/P after time T, once reserves have run out and inflation has started?
d. Continue to assume myopia. At time T, what is the price level going to be right before reserves run out? Right after? What is the percentage increase in the price level? In the exchange rate? [Hint: Use the answer to part (c) and PPP.]
e. Suppose investors know the rate at which domestic credit is growing. Is the path described above consistent with rational behavior? What would rational investors want to do instead?
f. Given the data presented in the question so far, when do you think a speculative attack would occur? At what level of reserves will such an attack occur? Explain your answer.