Question 1: Money demand, purchasing power parity and interest rate parity

a) Money demand and purchasing power parity

Consider the following demand for money (M) functions for two countries A and B. The coefficient, q, is the elasticity of money demand with respect to real GDP (Y) and is the same for each country. For this question, you can think of Y as potential output in each country.

M_A^D - M_A = P_AY_A

M_B^D - M_B = P_BY_B

1) Based on the definition of purchasing power parity in the text (where a rise in the nominal exchange rate (enom) is an appreciation), write out an expression for the exchange rate of country A, using the two money demand equations.

2) If the money supply in country A rose by 5%, by how much would the exchange rate change in the long run and in which direction? Briefly explain what is driving your result. [Hint: it will be easier to use natural logarithms to find percentages changes.

3) Suppose instead that real potential output in country B rose by 5% due to an improvement in productivity, but the money supply in that country remained unchanged. In this case, what would be the effect of the productivity shock in country B on country A's exchange rate? What is the process at work?

b) Interest rate parity (IRP)

1) Suppose that the one-year interest rate on bonds in the euro area was 4%, while those in Canada were paying 31/2%. The Canadian dollar-euro exchange is 0.7 (E per C$) and it is expected to appreciate to 0.701 by the end of the year. Use the interest parity condition to determine to which economy funds would flow.

2) Assume that the interest rates in each economy are fixed. Under what conditions would there be no movement in funds in either direction?

3) Suppose now, because of weakness in oil prices, the C$ depreciates to 0.65 E/C$.

How would that affect your answer in part 2)?

4) Assume that the future value of the Canadian dollar is fixed at the level you found in part 2). Calculate the effect on the Canadian dollar of a decline in Canadian interest rates to 3% assuming that interest parity holds.

Question 2: The closed economy IS-LM-AD model in the short and tong run

The key macroeconomic relationships in this economy are:

(1) M^d/P = 4 + 0.5Y -200(r + Π)

(2) C^d = 12 +0.6(Y - T) - 300r

(3) I^{d =} - 35 - 500r Money demand

Desired consumption Desired investment

Y = real output r = the real rate of interest P = the price level and it = expected future inflation.

a) Based on the above information, derive the IS and LM curves for this economy with r on the left hand side in each case. As well, derive the AD curve with Y on the left hand side.

b) Total taxes (7) are 10 and the government is running a deficit of 5. As well, the money supply is 60, P = 1.2 and Π = 0. Use this information to find the levels of Y and r. Verify that your results are consistent with the national accounts identity; that is, C + I + G add up to Y. Keep the variable it in your equations, as you will be asked to change it later.

You may assume that the level of Y you found is the long-run equilibrium value of output.

c) The government has made reducing the deficit a key policy priority. Use the model to find separately the short-run effects on output (Y) and the real interest rate (r) of (I) an increase in taxes (7) or (2) a reduction in spending (G) sufficient to balance the budget. Based on your analysis, which policy has the least negative short-run effect on I'? Explain briefly why each policy action is different.

d) Suppose that the central bank can credibly commit to increasing inflation in the future and that this has the effect of increasing expected inflation (n). Use the model to determine by how much it would have to rise to offset the effects of first the reduction in G and then separately the increase in T that you calculated in part c). In each case, calculate the effect on the real rate of interest as well as the nominal interest rate (1).

e) Assume again that it = 0 and now calculate separately the long-rim effect on the price level and the real rate of interest in the case of each fiscal measure. Describe briefly the forces driving the economy from its short- to its long-run equilibrium position.

Question 3: The small open economy IS-LM model in short and long run under flexible and fixed exchange rates

The key macroeconomic relationships in this economy are:

(1) M^d = P (13+ 0.6Y -500r^w) Money demand

(2) C^d = 12 + 0.8(Y -T)-400r^w) Desired consumption

(3) I^d = 50 - 600r^w Desired investment

(4) NX^d = 37 -0.2Y - 2e Desired net exports

Y = real output, r^w = the world real rate of interest, P= the domestic price level and e= the real effective exchange rate.

Assume initially that the nominal exchange rate is flexible

a) Derive expressions for the IS and LM curves in this economy, in each case with the world real interest (rw) on the left-hand side.

b) Government revenues (7) are 10 and the budget is balanced. The world real interest rate (r') is 5% and the nominal domestic money supply is 75. Find Y and e. If the domestic price level is 1.25 and the foreign price level (Por) is 1, what would be the level of the nominal exchange rate (exam)? For future reference, use your results to calculate C and NX. As well, you can assume that the value of Y that you found is the economy's long-run potential output.

c) The government is worried about future pension liabilities as the population ages. It decides to increase its saving to 1 by cutting spending (C). Will the resulting restrictive fiscal policy cause a recession in the short run? Support your analysis by using the model to estimate the effects of this policy; in particular, what would happen to net exports (NX) as well as the real and nominal exchange rates (e and enam)?

Suppose now that the nominal exchange rate was fixed at the value you found in part b).

d) Given this new information, use the model to estimate the short-run effects on Y of the fiscal initiatives described in part c). Would the economy avoid a recession in the short run? How would the monetary authorities respond?

e) Assume again that the exchange rate is flexible and the budget is balanced. Suppose that agents in the economy economise on their holdings of money balances and that this is represented by a fall in the W constant term from 13 to 10. At the same time the supply of money remains unchanged. Use the model to find the short-run effects on Y as well as C and NX. Explain briefly the forces driving these developments.

0 Use the model to determine what happens in the long run in the wake of the change to the money demand function. In particular, calculate the effect of the change in M^d on Y, NX, P, e and e_nom.