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Econ 318S: Open Economy Macroeconomics (Spring Term 2020)
PROBLEM SET #2.
Please answer at least one of following two questions. The submission deadline for this problem set is Wednesday 25th March 2020. Please submit your answers on Canvas no later than noon on that date. If you attempt two questions, your mark for the assignment will be the higher mark you receive for either of your answers.
1.Dornbusch Model with Demand Determined Output.
Consider the following version of the Dornbusch model:
dp/dt = π(y – yn), (1)
y = δ(e – p) + g, (2)
m = p + y – λi, (3)
i = i* + de/dt. (4)
Notation is as in the lectures, except for yn, which can be interpreted as the ‘natural rate of output’ and should be assumed constant. The endogenous variables are hence e, p, y and i. Equation (1) is a Phillips curve, stating that inflation is proportional to the difference between actual output (which is now endogenous) and its natural rate. Equation (2) states that output (which is demand determined) depends positively on the real exchange rate and on government spending. Equation (3) is a standard money market equilibrium condition and equation (4) is uncovered interest parity with rational expectations. You may assume that and are all positive (and, in particular, can be greater than 1).
(a) By appropriate substitution, derive expressions for the dp/dt = 0 and de/dt = 0 loci which do not contain either y or i. (20 marks)
(b) Derive expressions for the slopes of the loci derived in your answer to (a). What can be said about the slopes of the loci? (20 marks)
(c) Depict the dynamic system characterised by the equations derived above in a diagram with e on the horizontal axis and p on the vertical axis. Include the saddlepath in the diagram. What can be said about the slope of the saddlepath? (20 marks)
(d) Consider the effects of a permanent, unexpected decrease in the money supply. Assume that e is a ‘jump’ variable, whereas p is a state variable and cannot jump (i.e. it is instantaneously sticky). What happens to the interest rate, exchange rate and output, instantaneously, on the transition to the new steady state, and in the new steady state? Depict what happens diagrammatically. (30 marks)
(e) What conclusions do you draw from the above analysis as to whether exchange rate overshooting occurs in response to monetary shocks? (10 marks)
2.Two-Country Mundell-Fleming.
Consider the following model:
y = ae + g, (5)
y* = -ae + g, (6) m = -br + gy, (7) m = -br* + gy, (8) r = r, (9)
where y (y) is domestic (foreign) income, m (m) is the domestic (foreign) money supply,
e is the domestic exchange rate (domestic currency price of foreign exchange),
r (r) is the domestic (foreign) interest rate, g (g) is domestic (foreign) government spending,
abandg are positive constants.
Equations (5) and (6) are goods market equilibrium conditions for each country, respectively and equations (7) and (8) are the money market equilibrium conditions. Equation (9) is the uncovered interest parity condition with zero expectations of exchange rate change. Each country’s price level is constant and normalised to unity. With a flexible exchange rate, money supply equals money demand for each country separately, and each country’s money supply is exogenous. So y, y, r, r and e are the endogenous variables, whereas m, m, g and g are policy instruments.
(a) Derive expressions for domestic income and for foreign income in terms of the policy variables and parameters of the model. (20 marks)
(b) Derive expressions for the exchange rate and for interest rates in terms of the policy variables and parameters of the model. (20 marks)
(c) Discuss the effect on domestic income of a rise in the foreign money supply. Explain the role of interest rate and exchange rate changes in generating the result. (20 marks)
(d) Discuss the effects on domestic income of a rise in foreign government spending. Explain the role of interest rate and exchange rate changes in generating the result. (20 marks)
(e) What are the implications of your results for the international transmission of policy changes? Would you expect the results derived in this model to survive in more realistic models? Discuss. (20 marks)
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