$1.$

a$.$ Does a permanent monetary policy expansion lead to monetary neutrality? Making use of the equations and diagrams from the simple exchange rate and interest rate parity relationship, explain and demonstrate your answer. In your answer, make sure you discuss the role of expectations and that you explain both the short run and the long run responses of the economy to a monetary expansion. $($Assume the country has a floating exchange rate regime and that the real income is constant.$)$

b$.$ Will the long run exchange rate response to a monetary expansion be different than the short run one? Why or why not?

c$.$ Will the real exchange rate response be different than the nominal exchange rate? Why or why not?