Our short-run model is described by the following system of 2 equations = ^f + [(^' )/E] and M/P = (,)

where the first equation refers to the interest rate parity condition and the second equation gives real money demand in money market equilibrium. Here 1 + is the dollar rate of return on a one-year US government bond, and 1 + ^f is the rate of return on a foreign- currency denominated one-year government bond. The exchange rate is defined, as usual, to be the number of dollars per foreign currency. E is the current equilibrium value of the exchange rate and is the expected value of next year's (future) exchange rate. M, P, Y are the US money supply, aggregate price level and output respectively. We assume that the money market is in equilibrium so that ^d = ^s = .

We assume that P is fixed in the short-run and flexible in the long-run. You can also assume that Y and ^f are fixed too.

a) (6pts) Explain the rationale for the interest parity relation. That is, state the assumptions behind it and how one can go from those to the interest parity relation.

b) (6pts) In real life, the carry trade, the trading strategy of borrowing in low interest rate currencies and investing in high interest rate currencies is profitable, suggesting that the interest rate parity condition does not hold. How might you explain this, given the answer to a)?

c) (6pts) Explain how real money demand, (, ), depends on the interest rate R and output Y. What is the rationale for postulating such relations?

d) (6pts) What kind of a relationship between inflation (changes in prices) and money growth does this money demand structure imply?

e) (10pts) Holding the expected exchange rate ! fixed, what is the effect, on today's exchange rate, , of an increase in the US interest rate R? Show the effect graphically and explain the forces at play.

f) (10pts) Now assume that concurrent with the interest rate drop, the foreign Central Bank makes a surprise announcement that, starting next year, they will keep the exchange rate fixed at a level ₁ > (greater than the current expectations). How does that affect the exchange rate market today? Draw a new graph that incorporates both this effect and the interest rate increase. What is different?

g) (15pts) Go back to the original equilibrium, e.g. assume the events in c) and d) do not happen and the equilibrium exchange rate is E, the interest rate is R, and etc. Using figures for both the short and the long-run, show the effects of a permanent decrease in the US money supply. Explain what happens.

h) (5pts) Display in a set of graphs how R, P, and E would evolve over time.

i) (3pts) According to those dynamics, does the exchange rate display "overshooting'' or "undershooting"? Explain why.

j) (15pts) Go back to the original equilibrium, e.g. assume that none of the previous events happen and the equilibrium exchange rate is E, the interest rate is R, and etc. Using figures for both the short and the long-run, show the effects of a permanent increase in the foreign money supply.