Assume that absolute purchasing power parity holds in the long-run, that the money market clears in each country, and that in both countries the demand for real balances or "liquidity preference" takes the form

L=aY-bi

where Y is the log of real income, and i is the nominal interest rate. Derive an expression for the log price level, in the home (US) and foreign country, and for the nominal exchange rate in terms of money supplies, outputs, and interest differentials. Analyze and describe in words the impact for the exchange rate in the long-run of each of the following:

a) A tightening of US monetary policy

b) A decline in the foreign country's natural output level

c) An increase in the domestic natural output level and explain your answers carefully.