Question 1
Consider the following small open economies. They are classical so prices are flexible. Economy #1 is such that real interest rates are equalized across countries and purchasing power parity holds. For Economy #2 purchasing power parity holds and real interest rates are allowed to differ. For Economy #3 real interest rates are allowed to differ and purchasing power parity does not necessarily hold. Each Economy is described by the following equations:
ECONOMY #1
r=r*=.05 (1) Equality of Real Interest Rates E=(Enom x P)/P* = 1 (2) Purchasing Power Parity Condition P* = 1 (3) Foreign Price Level Y* = 5000 (4) Foreign Income
E is the real exchange rate, Enom is the nominal exchange rate and P is the Domestic Price Level.
Cd = 300 + .8(Y-T) -100r (5) Desired Consumption
Id = 200 - 300r (6) Desired Investment
G=T=500 (7) Government Expenditures(G) and Net
Taxes(T).
Yf= 3500 (8) Full Employment Output
Md/P = .5Y -200i (9) Money demand equation
M= 1730 (10) Supply of Money
Expected Inflation = .05 (11) Expected Inflation
ECONOMY #2
Equations (2),(3),(4),(5),(6),(7),(8),(9),(10),(11) and an equation for net exports:
NX = 10 -.02Y + .038Y* -10E (12) Net Exports
ECONOMY #3
Equations (3),(4),(5),(6),(7),(8),(9),(10),(11),(12) and an equation for the real exchange rate:
E = 1 - .0015Y + .00105Y* + 4(r-r*) (13) Real exchange rate
A) For Economy #1 find the values of net exports, the Domestic Price level and the nominal exchange rate.
B) For Economy #2 find the values of the domestic real interest rate, the Domestic price level and the nominal exchange rate.
C) For Economy #3 find the values of the domestic real interest rate , the domestic price level and the nominal exchange rate.
D) Suppose that a payroll tax is introduced in Economy #2. Describe qualitatively the effects on the domestic real interest rate, the domestic price level and the nominal exchange rate in that economy.
Question 2 Exchange Rates
A) Suppose that the current value of the Canadian dollar in terms of the American dollarin is .75. Lucien Bouchard announces another referendum. This increases political uncertainty. What effect will this have on the exchange rate? What should the bank of Canada do if it wants the exchange rate to go back to its original value (.75)?
B) What happens to the fundamental value of a country's exchange rate when it raises its money supply in a fixed exchange rate system?
C) Explain why a currency can't be overvalued forever.
Question 3 Phillips Curve
The Relationship between inflation and unemployment is given by:
p = pe -3(u - .08), p is inflation, pe is expected inflation and u is the unemployment rate.
A) What is the natural rate of unemployment?
B) If expected inflation is 5% and the unemployment rate is .08 what is the inflation rate? Is there a unique inflation rate in the long run?
C) Suppose that the government makes unemployment insurance more generous. Following that change draw the new short run Phillips curve and the new long run Phillips curve. Assume that expected inflation is 5%.
D) Explain Lucas' critique of historical relationships between macroeconomic variables. Is it consistent with a long run tradeoff between unemployment and inflation?
Question 4 Money Supply
Suppose that the currency-deposit ratio is .2 and the reserve-deposit ratio is res = .4 -2i, i is the nominal interest rate. Assume that the monetary base is 200.
A) Find money supply when the real interest rate is .05 and expected inflation is.05.
B) If the real interest rate goes up from .05 to .10 what will happen to money supply? Find its new value.
C) Consider a closed economy with price flexibility (classical case). Describe what will happen to the price level if government expenditures increase in that economy.
Question 5 Monetary Policy
A Central Bank knows that it can reduce inflation if Unions accept lower wage increases. If wages go up labour is more costly and firms start increasing their prices. Assume that when Unions raise wages, businesses do not fully adjust their prices ( Example: If wages go up by 5% , prices go up by 3%). We are looking at Short Run Monetary Policy.
The following normal form is representative of the game being played between the Central Bank and Unions.
UNIONS
INCREASE DON'T INCREASE
WAGES WAGES
INCREASE Payoff Union: 2 Payoff Union: 2
MONEY Payoff Bank: 0 Payoff Bank: 2
Inflation: 6% Inflation: 0%
Unemployment: 8% Unemployment: 6%
CENTRAL Outcome A Outcome B
BANK
DON'T Payoff Union: 0 Payoff Union: 1
INCREASE Payoff Bank: -1 Payoff Bank: 1
MONEY Inflation: 6% Inflation: 0%
Unemployment: 10% Unemployment: 6%
Outcome C Outcome D
CENTRAL BANKS LIKE LOW INFLATION AND LOW UNEMPLOYMENT.
UNIONS LIKE HIGH REAL WAGES AND LOW UNEMPLOYMENT. WE ASSUME THAT WHEN UNIONS RAISE WAGES THEY ALSO RAISE REAL WAGES.
A) What is the bank's optimal strategy?
B) What will be the outcome(s) of this game?
C) Suppose that the Unions are biased toward wage increases.The payoff from outcome A for unions rises form 2 to 3. Will the central bank be able to keep inflation at a low level?
Question 1
A) For that economy we have purchasing power parity and equality of interest rates.
We know that Y=Cd + Id + G + NX. Full employment output is 3500.
So: 3500= 300 + .8(3500-500) -100r +200 -300r +500 + NX.
3500= 1000 +2400 -400(.05) + NX
NX = 120
In Equilibrium Md/P = M/P. 1730/P = .5(3500) - 200(.05+.05).
Thus P =1. Since E=P=P*=1 it must be the case that Enom=1.
B) This time E=1 but real interest rates can be different. We need the equation for net exports.
Substitute the equatiom for net exports in our equilibrium condition for the goods market.
Y = Cd + Id + G + NX 3500= 300 + .5(3500-500) -100r + 200 - 300r + 500 + 10 -.02(3500) -.038(5000) -10(1). 3500 = 1000 + 2400 -70 +190 -400r r= .05 so i= .10
Thus we will have the same price level and with E=1, the same nominal exchange rate value: Enom=1.
C) No purchasing power parity and no equality of real interest rates. It will only be a coincidence if E=1 and r=r*.
The first step is to substitute E in NX. The second step is to repeat what we have done in A) and B).
NX = 10 -.02Y + .038Y* -10(1- .0015Y +.00105Y* +4(r-r*)).
NX = 120 + 40r* -40r.
Repeat: Y = Cd + Id + G + NX
3500= 1000 + 2400 -400r + 120 +40(.05) -40r
3500= 3522 -440r
r= .05 so i= .10
With the same nominal interest rate, the price level will not change. What about Enom? First we must use our real exchange rate equation:
E= 1 -.00150(3500) + .00105(5000) + 4(.05-.05)
E= 1 so with E=P=P*=1 we know that Enom=1
D) In Economy #2 , E=1. The payroll tax will reduce employment. This will reduce output. This will cause an increase of the real interest rate. With lower output and a higher real interest rate the demand for real balances will go down. Thus the price level must rise to reastablish the equilibrium in the asset market. With a higher price level and E=1 the nominal exchange rate has to go down.
Question 2
A) One has to look at the reaction of Canadian Investors and Foreign Investors. Both will want to reconsider their portfolio allocations. Canadian investments will not be as attractive due to the uncertainty. This means that Canadians will try to convert some canadian funds to buy foreign assets. It also means that foreigners will demand less Canadian dollars then they were demanding before the announcement. The supply of Canadian dollars will shift to the right. The demand for Canadian dollars will shift to th left. Hence we will see a depreciation. The Bank of Canada will intervene by using its reserves to boost the demand for the Canadian dollar so that the exchange rate can go back to its original level.
B) Under a fixed exchange rate regime monetary policy serves one purpose: fixing the exchange rate. If a country raises its money supply there will be downward pressure on the exchange rate. The supply of money would have to go back to its original level. Otherwise the fundamental value of the exchange rate would be lower.
C) Simple. A Central Bank does not have unlimited reserves. Sooner or later it won't be able to increase the demand for its own currency to keep the exchange rate at that high value.
Question 3
A) The natural rate of unemployment is .08 (8%).
B) Since the natural rate is equal to the unemployment rate for this case, it means that inflation will be equal to expected inflation. Thus in the long run inflation will be 5% For given expectations the rate is unique.
C) The long run Phillips curve shifts to the right and the short run Phillips curve shifts upward. In the long run unemployment will increase. It will increase because people will turn down more offers since unemployment insurance is more generous. Each unemployment spell will be longer.
D) Agents aren't stupid they adapt themselves to their environment. If policies are changed they will take that into account when they are making decisions. Lucas' critique is not consistent with any long term tradeoff because in the long run you will not be able to fool people. They will have extra information and will incorporate it in their decisions.
Question 4
A) The reserve ratio will be res=0.4 -2(.05 +.05) = 0.2. The money supply is given by the expression: M=Bxmm where M=Money Supply, B=Monetary Base and mm=Money Multiplier. Hence M=200xmm , mm=(1 + cu)/(cu + res), res= .2 and cu = .2.
M=200x(1+.2)/(.2+.2) = 200x3 = 600
B) The money multiplier will increase because the reserve-deposit ratio will go down. res= .4 - .2(.05+ .10) = .1.
M= 200x(1 +.2)/(.2 + .1) = 200x4 =800
C) If G increases the IS curve shifts to the right. Th real interest rate will increase. Hence the nominal interest will also go up.
So: Md/P goes down and M goes up because res will go down. To reastablish the equilibrium in the money market the price level must go up and it will go up (% wise) more than money supply.
Question 5
A) The dominant strategy for the Central Bank is to increase money. One can see that by looking at the structure of the payoffs. No matter what the union does it is always optimal to increase money.
B) Given the fact that the Central Bank has a dominant strategy we are left with two possible outcomes: Outcome A and/or Outcome B. The union gets the same payoff if it increases wages or if does not increase wages. Hence A and B are possible. Just flip a coin.
C) This time the union does better by increasing wages so we get outcome A. Inflation will be high at 6%. The bank can't reduce inflation.