Question

Consider the basic model of interest rate determination:

MD = $Y · L(i) and MS = M

where L(i) = (0.5 − 2i), M = 60 and $Y = 200.

(a) Solve for equilibrium nominal interest rate (i).

(b) Suppose the Fed wants the equilibrium interest rate to be 5%. What value of M would achieve this goal?

Answer 1

(a) At equilibrium, MD = MS

=> $Y (0.5 - 2i) = 60

=> 200 (0.5 - 2i) = 60

=> 100 - 400i = 60

=> 100 - 60 = 400i

=> 40 = 400i

=> i = (40 /400)

=> i = 0.1

=> i = 10%

Equilibrium interest rate is 10%

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(b) Fed wants the equilibrium interest rate to be 5% (or 0.05)

Set, MD = MS

=> $Y (0.5 - 2i) = MS

=> 200 (0.5 - 2(0.05)) = MS

=> 200 (0.5 - 0.1) = MS

=> 200 (0.4) = MS

=> 80 = MS

=> MS = 80

The M should be 80 in order to keep interest rate at 5%.