Question

MS = 1/rrm(TR) MD = 75 –220(i) + 3.0(Y) where i represents the rate of interest, Y represents national income, rrm represents the fractional reserve requirment ratio, and TR represents total reserves. Assume national income in 2019 was $1,000 and is projected to be 10 percent higher in 2020. Also assume the reserve requirement ratio is 0.25 and total reserves at depository institutions is 120.

a. What market clearing interest rate would you project for 2020?

b. How much must the money supply change to achieve an interest rate in 2020 of 9 percent? (Hint: using whole percent rather than decimal equivalent; e.g., using 9 rather than .09).

c. If the fractional reserve requirment ratio remains unchanged, what level of total reserves must the central bank achieve to lower the interest rate to its target of 9 percent?

Answer 1

Given information is as follows:-

Y = $1100 , In 2019 it was $1000 and in 2020 it is 10% higher, therefore

rrm = 0.25

TR = 120

(a) Market clear interest rate is a rate when demand and supply are in equilibrium. That means MS=MD. Therefore the interest rate is computed as follows:

MS= 1/rrm(TR) , where rrm= 0.25 and TR= 120

MD= 75-220(i) + 3.0 (Y) ,where Y= $1100 when money demand and money supply are equal, then we take both the equations to find i

MS=MD

i = 13.15 %

(b) Here to find the money supply lets assume that demand reamins unchanged. When the rate decreases to 9% the money supply will increase therefore the compuation will be as follows:

therefore money supply at 9% interest rate is 1875

(c) Here rrm remains unchaged that is 0.25 and money supply is 1875 at the 9% interest rate

so TR would be as follows:-

MS = 1/rrm (TR)