Suppose That Bank Reserves (Res)are a Function of the Nominal

Essay

Suppose that bank reserves (res)are a function of the nominal interest rate (i):
res = 0.3 - 3i.
The money multiplier is (cu + 1)/(cu + res),where cu is the currency-deposit ratio.Initially,suppose the real interest rate (r)equals 0.03,the expected inflation rate (p^e)equals 0.03,and the currency-deposit ratio equals:
cu = 0.4 - (10 × p^e).
The real money demand function is L(Y,i)= 0.8Y - 1500i,where Y is the level of output.The monetary base equals 100.The price level equals 1.0 initially and will not change in the short run,but will adjust in the long run.
(a)Calculate the currency-deposit ratio,the reserve-deposit ratio,the money multiplier,the money supply,and the equilibrium level of output.Assume that this level of output equals full-employment output,so you are assuming that the economy is in general equilibrium with the price level equal to 1.0.Show your work.
(b)Suppose financial innovation causes the reserve-deposit ratio to decline to res = 0.2 - 3i.Calculate the new currency-deposit ratio,the reserve-deposit ratio,the money multiplier,the money supply,and the equilibrium level of output in the short run,assuming a Keynesian model with the price level fixed in the short run.Show your work.
(c)Calculate the equilibrium price level in the long run.Show your work.