Winter 1998
Exercise D
due Tuesday April 7 in class
1. Consider the following small open economy. It is a classical economy, so prices are flexible.
| C^d=350+0.8Y_d-60r | (1) Desired consumption |
| I^d=300-150r | (2) Desired investment |
| G=1220 | (3) Government expenditure |
| Y_d=Y-T | (4) Disposable income |
| T=tY, where t=0.3 | (5) Tax revenue |
| L=0.5Y-400i | (6) Real money demand |
| M=3297 | (7) Money supply (nominal) |
| pi^e=0.05 | (8) Expected inflation |
| NX=20-0.02Y+0.04Y_for-e | (9) Net exports |
| e=780-0.184Y+0.01Y_for+40(r-r_for) | (10) Real exchange rate |
| Y_bar=4500 | (11) Full employment output |
(12) Foreign Variables:
(a) Find the values of r, P and e_nom.
(b) Suppose there is a policy change in the foreign economy such that r_for=r. What would happen to M if the central bank in the domestic economy wants to maintain the value of e_nom in (a)?
(c) Suppose that the government in the domestic economy increases its spending. Describe qualitatively the effects on r, P, e_nom and NX. [Drawing pictures may help you.]
2. Suppose there are two countries in the world and NX for the domestic economy is described by NX=100-6.3e, where NX is net exports and e is the real exchange rate. Suppose domestic real interest rate is 5% and the foreign real intereat rate is 8%.
(a) Assume only two periods for this world. Using the IEB equation and the exact version of the IRP (in terms of the real rate of interest), determine the equilibrium and the future real exchange rate.
(b) Illustrate this solution using a graph.
(c) Calculate NX for both periods and for both countries.
(d) Repeat your calculations with a foreign interest rate of 6%. Explain the differences.
3. In the early 1990s Canada had loose fiscal policy and tight monetary policy, which resulted in large budget deficits and high real interest rates. Some economists have argued that the opposite combination -- looser monetary policy and tighter fiscal policy -- would have been better. This question uses simple game theory to explore this question.
Suppose that the Bank of Canada and the federal government rank the four possible outcomes this way, from best (1) to worst (4):
| Bank | government | |
| loose monetary/tight fiscal | 2 | 2 |
| loose monetary/loose fiscal | 4 | 1 |
| tight monetary/tight fiscal | 1 | 4 |
| tight monetary/loose fiscal | 3 | 3 |
(a) Draw a two-by-two game diagram to illustrate the possible outcomes.
(b) Suppose that the government moves first. What is the outcome of the game?
(c) Is there any way of improving on this outcome for either side?
4.(a) Some European countries are reluctant to agree to a regime of fixed exchange rates and free capital mobility. Why might that regime not be a good choice for macroeconomic policy?
(b) Analyze (clearly) the reasons that {\it might} have led to the withdrawal of the U.K. from the ERM in September 1992. [Please limit your answers to one page or less.]
5. Suppose that the natural rate if unemployment is 6% and that the expectations-augmented Phillips Curve is given by:
pi-pi^e = -2(u -u_bar).
(a) If expected inflation is 4%, what inflation rates would accompany 7.5% unemployment?
(b) Suppose that pi^e_{t+1}=pi_t (i.e, the forecast of next year's inflation is this year's inflation). Initially pi=pi^e=4% and u_bar=6%. Suppose that the central bank announces and then carries out a disinflation program, in which the inflation rate is 4% this year, 2% next year, and then 0 thereafter. The announcement does not affect inflation expectations. Find the unemployment rate each year.
6. Some few weeks ago, the Bank of Canada had to intervene in the foreign exchange market to prevent a fall in the Canadian dollar. Why did the Bank eventually raise interest rates? Explain how the bank
(a) intervenes in the foreign exchange market.
(b) raises (or lowers) the interest rate.
[Please limit your answers to one page or less]
Please note that the notation ^ denotes a superscript term, and _ denotes a subscript term.
A.
r=0.08,P=1.5. Since e=3.2, we get e_{nom}=2.133
b) This policy will depreciate the domestic currency. So to maintain e_{nom}, the central bank will decrease M in order to decrease P. (No need for calculations).
c) If G increases, IS cuvre shift up and r increases. Y will increase, but not much due to a fall in NX. NX fall for 2 reasons:
P will increase. e_{nom} will seem to increase due to high r, but may also fall due to fall in NX. Effect on e_{nom} ambiguous.
2. (a)e=15.655 and e^f=16.102
(students will get values close to these due to rounding of)
(b) graph.
(c) Domestic economy: NX(e)=1.374 and NX(e^f)=-1.42. Values for the foreign country is the negative of domestic values (since only two countries).
(d) If r_{for}=0.06, we get e=15.80 and e^f=15.95 (again students will get values close to these due to rounding of)
Explain the differences: a low foreign interest rate causes an increase in the demand for domestic assets which appreciates current exch. rate. NX(e) falls. But this means NX(e^f) must rise and so e^f falls.
3.(a) Normal form: payoffs 1 (best) to 4 (worst)
(b) Government moves first. Then, Nash Eqbm is LOOSE fiscal policy and TIGHT monetary policy. Payoff is (3,3).
(c) LOOSE monetary policy and TIGHT fiscal policy gives a payoff of (2,2) --- an improvement over the Nash Equilibrium. If the two authorities can co--operate or if the bank can credibly commit to a LOOSE monetary policy, then they will both be better off. Usually, if the game is played repeatedly for several periods, then a better outcome can be achieved through co--operation.
5. (a) pi=1
(b) unemployment rates: this year 6%, second year 7%, third year 7%, then it will be 6% there after.