Consider two economies, Home and Foreign. The DC/FC exchange rate (EDC/FC) is determined by the asset approach to the exchange rate.
Home: Real money demand: L(R, Y) = 0.4Y – 2500R
Money supply: MS = 15000
Foreign: Real money demand: L*(R*, Y*) = 0.25Y* – 2000R*
Money supply: MS* = 13500
Initially, both Home and Foreign are in their respective long-run equilibrium. The full-employment level of output in Home is 10000, which is 3000 units less than that of Foreign. The long-run (nominal) interest rate in Home and Foreign are 10% and 12.5% respectively.
Note: Interest rates are expressed in decimal points (i.e., if R = 0.1, then R = 10%). Keep your answer in 4 decimal points if needed. Be sure to show your work.
a) What are the initial long-run equilibrium domestic and foreign price levels if the market expects 1.5 DC will exchange 1 FC? Find the long-run exchange rate. (4 points)
Now, suppose there is a breakthrough in the payment technology in Foreign such that the foreign money demand changes permanently to
L*(R*, Y*) = 0.24Y* – 2000R*
Also, any permanent change will cause the expected DC/FC exchange rate to change by 0.225 DC per FC.
b) Find the short-run equilibrium foreign interest rate and the DC/FC exchange rate in the short run. (4 points)
c) Find the new long-run equilibrium DC/FC exchange rate and foreign real money balance. (4 points)
d) If the central bank of Home finds the change in the short-run exchange rate in part (b) undesirable and wants to keep it at the initial long-run level, can they to achieve this goal? Yes/No, explain. (8 points)
• If yes, find the level of domestic MS that will achieve this goal.
• If the answer is no and the central bank of Home wants to bring the exchange rate as close to the initial long-run level as possible, find the level of money supply that they should set. What will be the DC/FC exchange rate that is consistent with that level of money supply?
Note: You can assume the change in domestic money supply as a temporary one.
