Problem set 6
Money, inflation and Exchange rates in the long run
6.1. (Money demand) The following figure describes possible adjustments in the money market, following a once-and-for-all contraction in the money supply, from M0 to M1. Which case corresponds to the:
V Md PQ
M
P M0
0=3
M1
1
2
a) Conventional IS-LM model?
b) IS-LM framework with liquidity trap?
c) The Classical/RBC model?
6.2. (PPP vs LOOP) Consider a world with a single homogeneous good, which can either be produced domestically or abroad under conditions of perfect competition.
Initially, the world price of this good is 100 USD and the price of the USD in terms of domestic currency (pesos) is 2.
a) Suppose the price of the good in the domestic economy was initially 190 pesos. In the absence of trade costs, what do you think it would happen?
b) In the real life, do you believe the adjustment described in a) would be instantaneous? Why?
c) Suppose now that transport and other trade costs amounted to 20% of the price of the good. In this case, how would the non-arbitrage condition hold for exports and for imports? Find out the implied band for the real exchange rate.
6.3. (PPP, Quantitative theory) Considere um mundo com duas economias, a Pesólia e a Libraria, cujas moedas são, respectivamente, o Peso e a Libra. Na Libraria, existem N*=1000 trabalhadores e o volume de produção são Y*=1000 unidades. Na Pesólia, existem N=100 trabalhadores e o volume de produção são Y=50 unidades. Sabe-se ainda que a quantidade de Libras emitida pelo Banco Central da Libraria é M*=1000. Para simplificar, assuma ao longo de todo o exercício que a velocidade de circulação da moeda é unitária.
a) Quanto deverá custar uma unidade de produto na Libraria (em libras)?
b) Qual deverá ser o salário médio de um trabalhador na Libraria (em libras)?
c) Se na Pesólia a moeda emitida for igual a 50.000 pesos, quanto deverão ser os preços e os salários (em pesos)?
d) Admitindo que ambos os países produzem exactamente o mesmo bem e que esse bem pode ser importado e exportado, qual deverá ser a cotação do peso em libras no mercado cambial (no longo prazo)?
e) Mantendo as hipóteses anteriores, onde é que o poder de compra dos salários é mais elevado, na Pesólia ou na Libraria? Porquê?
f) Admita agora que o banco central da Pesólia resolvia duplicar a quantidade de moeda na sua economia. O que aconteceria aos preços, salários e taxa de câmbio?
g) Explique o que aconteceria aos preços, salários e taxa de câmbio se na Pesólia cada trabalhador passasse a produzir metade do que produzia antes. (g2) Se o objective do Banco Central fosse inflação zero, o que deveria fazer?
6.4. (Balassa-Samuelson) Consider a small open economy producing a tradable good (T) and a non-tradable (N) good. The corresponding production functions are
T
T aL
Y and YN bLN. Assume that the foreign prices of these goods are
* 1
* N
T P
P and that the nominal exchange rate is e1. Finally, assume the weight of each good in the consumer price index is 50%. Define w as the nominal wage rate, PT as the price of T , PN as the price of N and as the real exchange rate.
1. Assume first that ab1
a) Find out the labor demand equations in the two sectors.
b) Compute the equilibrium for the wage rate, the price level and the real exchange rate.
2. Consider an increase in the productivity of the tradable good from a1 to a 2. c) Describe the implications of such a shift on PT, PN, w and the equilibrium real
exchange rate, assuming that the nominal exchange rate was fixed.
d) If instead the central bank’ goal was to keep the inflation rate equal to zero, what should happen to prices and to the nominal exchange rate?
e) What should happen to the real exchange rate if the productivity shock was instead on parameter b?
6.5. (Balassa-Samuelson) Consider a small open economy producing a tradable good (T) and a non-tradable (N) good. The corresponding production functions are
T
T aL
Y and YN LN. Assume that the foreign prices of these goods are
* 1
* N
T P
P and that the nominal exchange rate is e100. Finally, assume the weight of each good in the consumer price index is 50%. Define w as the nominal wage rate, PT as the price of T , PN as the price of N and as the real exchange rate.
1. Assume first that a4.
a) Find out the labor demand equations in the two sectors.
b) Compute the equilibrium wage rate, the corresponding price level and the real exchange rate.
c) Now suppose that the nominal exchange rate depreciated to e125. What would happen to the price level and to the real exchange rate? Was PPP a good theory in that case? In absolute terms or in relative terms?
2. Departing again from e 100, examine the impact of a fall in the productivity of the tradable good from a4 to a3
d) Describe the implications of such a shift on PT, PN, and the equilibrium real exchange rate, assuming that the nominal exchange rate was fixed.
e) If non-tradable good prices were sticky, how could the central bank easy the adjustment process setting the nominal exchange rate?
6.6. (Fisher effect) Consider a borrower that signed a one month 1000 pesos loan at a 55% monthly nominal interest rate during the Argentinean hyperinflation process in 1985. At that time the expected inflation was about 50% per month.
a) What was the approximate real interest rate?
f) The government surprised everyone with a disinflation programme that reduced inflation to 5%. What were the implications for the borrower and the lender?
g) Which complementary measures should be taken by the Argentinean government to solve this problem?
6.7. (Inflation surprise) Consider an economy where both prices and the exchange rate are fully flexible, and where the Fisher principle and the purchasing power parity hold instantaneously. Moreover, it is known that the domestic real interest rate is constant and equal to r 0.04 and that the demand for real money balances is given by mD Y
20i , where Y 100 refers to output (constant) and i is the nominal interest rate. The foreign price level is constant and equal to 2.a) Assume that initially the money supply is constant and equal to M 250. Describe the initial equilibrium, quantifying namely the inflation rate, nominal interest rate, the real money demand, the price level, the money velocity and the nominal exchange rate.
b) Unexpectedly, the central bank decided to expand the money supply by 16%
every year. What should happen to the inflation rate, the interest rate, real money demand and money velocity? Describe graphically the new money market equilibrium in the (M/P, i) space.
c) Explain, quantifying, what should happen to the price level at the time of the policy change.
6.8. (Stopping an hyperinflation) Arcadia is an economy where prices and exchange rates are flexible, and there is no growth. Assume that the inflation rate in the rest of the world is 2% and that the equilibrium real interest rate is 2%. Annual inflation has been constant and equal to 200%. The ACB – Arcadia Central Bank wants to reduce the inflation rate to 10%. To do so, the ACB announces a reduction in the rate of money growth to 10% per year.
a) Assuming that the commitment is credible and the policy was not anticipated, explain the temporal path (at the time of the shock and after the shock) of the:
nominal interest rate; real money demand; price level; inflation rate; nominal exchange rate.
b) In the real world, it happens that prices are pretty flexible upwards – especially during hyperinflation episodes – but sticky downwards. Given this, what could the monetary authorities in Arcadia do instead, to achieve a successful disinflation?
6.9. (Money multiplier) Consider the following initial situation in a given banking system: D=100; C=20; R=10; eBC* 30.
a) How much will be the money supply, the monetary base, and domestic credit by granted by commercial banks?
b) Find out the values of the reserves ratio, liquidity preference coefficient and the money multiplier.
c) Assuming that the ratio of desired reserves and the liquidity preference coefficient were constant, what would be the impact on money supply of an open market operation increasing the central bank liabilities by 40?
d) Returning to the initial situation, assume that, due to a bank scare, citizens in this economy wanted to hold half of its money on the form of cash. Also assume that, in face of such change, banks decided to increase the amount of reserves to 20. (d1) if the central bank did not intervene, what would happen to domestic credit? (d2) if the central bank, as a lender of last resort, decided to extend a credit line to the banking system amounting to LC 40, would this cause the money supply to expand? Compute the new parameters of the money multiplier and explain.
e) Returning again to the initial situation, suppose that non-performing loans in this economy amounted to one third of the credit granted by commercial banks. What would be the monetary implications of rescuing the banking system using central bank’ money?
6.10. (Money supply under fixed exchange rates) (Feenstra and Taylor, Ch.9) Consider the central bank balance sheet for the country of Patria. Patria currently
has 2,500 million lira in its money supply, 1,800 million of which is backed by domestic government bonds. Assume that Patria maintains a fixed exchange rate and the foreign interest rate remains unchanged.
a) Show Patria’s central bank balance sheet, assuming there are no private banks.
Calculate the backing ratio.
b) Suppose that Patria’s central bank buys 300 million lira in government bonds.
Show how this affects the central bank balance sheet.
c) Calculate the new backing ratio. Does this change affect Patria’s money supply? Explain why or why not.
d) Now suppose that there is an economic recession in Patria, so that output falls by 5%. How will this affect money demand in Patria? How will forex traders respond to this change? Explain
e) Using a new balance sheet, show how the change described in (d) affects Patria’s central bank (starting from the new balance sheet in [b]), assuming that real money balances change by 200 million lira. What happens to domestic credit? What happens to Patria’s foreign exchange reserves?
Calculate the new backing ratio.
6.11. (Money supply under fixed exchange rates) (Feenstra and Taylor, Ch.9) Using the central bank balance sheet diagrams, evaluate how each of the following shocks affects the country’s ability to defend a fixed exchange rate.
a) The foreign interest rate decreases.
b) An economic recession leads to a reduction in money demand.
c) The central bank sells government bonds.
d) Currency traders expect a depreciation in the currency in the future.
6.12. (Money and Prices in the long run) Consider the following initial balance sheet of given central bank: eBC* 20 and BC 80 pesos. Further assume that the money multiplier is equal to one and that the real money demand is given by
i Y
mD 10 , where Y is output (assumed 50) and i is the nominal interest rate. The real interest rate is 5%. In this economy, PPP holds and the foreign price level is
* 1 P .
a) Describe in a graph the money market equilibrium. Find out the equilibrium levels of prices and of the exchange rare.
b) Suppose that the central bank decided to expand the domestic credit by 20 pesos. What would be the implications for the price level and the nominal exchange rate? Could the central bank keep prices and the exchange rate constant despite the expansion of domestic credit? How?
c) Suppose that there was a fall in output to Y=80. What would be the implications for prices and the exchange rate? Could the central bank keep prices and the exchange rate constant and at the same time avoid the contraction of domestic credit? What if output fell to Y=70?
d) On the basis of your results, explain why is a good idea for central banks to have a stock of foreign reserves.
6.13. [1st Generation Crisis model] Consider an economy where the currency (peso) is initially pegged to the dollar at e=1. Assume that the foreign price level is constant (P* 1), PPP holds, prices are fully flexible and full employment is always met (Yf 432). The real interest rate is the same at home and abroad and equals 5%. In this economy the money demand is given by mD Y 20i.
a) Assume first that agents expect the money supply to remain constant at M=432. Describe the money market equilibrium, assuming that the peg is credible. How does the interest parity condition look like in that case?
b) Consider now the case where, unexpectedly, the central bank abandons the fixed exchange rate regime and the nominal money supply starts increasing at 20% per year. What would happen to the interest rate, real money demand and the price level at the time of the surprise?
c) Instead of assuming that agents are taken by surprise, consider a case where agents have rational expectations and perfect foresight. At moment zero, the central bank balance sheet is as follows: M eBC* BC 38250. In the years that follow, the domestic credit component expands 20% each year.
Assuming that the domestic credit expansion is fully sterilized by a foreign market intervention:
c1) Describe the central bank balance sheet at t=2, and compute the backing ratio. Would it make sense for economic agents to launch a speculative attack at that date? Explain.
c2) Assuming that there was no attack at t=2, describe the central bank balance sheet at t=3, and compute the backing ratio. Would it make sense for economic agents to launch a speculative attack at that date? Explain.
c3) Assuming that there was no attack at t=3, describe the central bank balance sheet at t=4. Would it make sense for economic agents to launch a speculative attack at that date? Explain.
