Question

5. Suppose that this year’s money supply is $500 billion, nominal GDP is $10 trillion, and real GDP is $8 trillion.

a. What is the price level? What is the velocity of money?

b. Suppose that velocity is constant and the economy’s output of goods and services rises by 10 percent each year. What will happen to nominal GDP and the price level next year if the Fed keeps the money supply constant?

c. What money supply should the Fed set next year if it wants to keep the price level stable?

d. What money supply should the Fed set next year if it wants inflation of 5 percent?

Answer 1

5. Ms = $500 billion

PY = $10 trillion

Y = $8 trillion.

a. P = PY/Y = 10/8 = 1.2

Velocity V = PY/Ms = 10000/500 = 20.

b. Now velocity is constant at 20 and the economy’s output of goods and services rises by 10 percent each year. Also, Fed keeps the money supply constant. Hence % change in Ms = % change in V = 0

We know that PY = VMs according to equation of exchange and

% change in Ms + % change in V = % change in P + % change in Y

The left side is 0 so the right side must be 0

% change in P + % change in Y = 0

% change in P = - % change in Y = -10%

Hence, price level declines by 10% next year and nominal GDP remains unchanged.

c. Now % change in P is 0. Also, % change in Y is 10% and % change in V is 0. This implies that

% change in M = 0% + 10% - 0% = 10%.

Hence money supply is increased by 10%. New money supply is 500*1.1 = $550 billion

d. Now % change in P is 5. Also, % change in Y is 10% and % change in V is 0. This implies that

% change in M = 5% + 10% - 0% = 15%.

Hence money supply is increased by 15%. New money supply is 500*1.15 = $575 billion