Explain the effects of a permanent increase in the U.S. money supply in the short run and in the long run.  Assume that the U.S. real national income is constant.

A raise in the nominal money supply increases the real money supply and lowering the interest rate in the short run. The money supply enhance is considered to maintain in the future therefore, it will influence the exchange rate expectations.  This will make the predictable return on the euro more desirable and therefore the dollar depreciates.  In the case of an enduring increase in the U.S. money supply then the dollar depreciates more than under a temporary increase in the money supply.

Currently in the long run prices will increase until the real money balances are the same as prior to the permanent increase in the money supply.  Ever since the output level is given the U.S. interest rate which decreased prior to start to increase until it will move back to its original level. 

The balance interest rate should be the same as its original long -run value. This raise in the interest rate should cause the dollar to appreciate against the euro after its sharp depreciation as a result of the permanent raise in the money supply. Thus a large depreciation is followed by an appreciation of the dollar.  Ultimately the dollar depreciates in proportion to the increase in the price level which in turn enhance by the same proportion as the permanent increase in the money supply.  Therefore money is neutral in the sense that it can't affect in the long run real variables for instance investment, output, and so on.