3. When the real interest rate increases, banks have an incentive to lend a greater portion of their deposits, which reduces the reserve–deposit ratio. In particular, suppose that res = 0.4 - 2r, where res is the reserve–deposit ratio and r is the real interest rate. The currency–deposit ratio is 0.4, the price level is fixed at 1.0, and the monetary base is 60. The real quantity of money demanded is L(Y, i) = 0.5Y - 10i, where Y is real output and i is the nominal interest rate. Assume that expected inflation is zero so that the nominal interest rate and the real interest rate are equal.

a. If r = i = 0.10, what are the reserve–deposit ratio, the money multiplier, and the money supply? For what real output, Y, does a real interest rate of 0.10 clear the asset market?

b. Repeat Part

(a) for r = i = 0.05.

c. Suppose that the reserve–deposit ratio is fixed at the value you found in Part

(a) and isn’t affected by interest rates. If r = i = 0.05, for what output, Y, does the asset market clear in this case?

d. Is the LM curve flatter or steeper when the reserve–deposit ratio depends on the real interest rate than when the reserve–deposit ratio is fixed? Explain your answer in economic terms.