Question

Suppose that an economy is characterized by M = $10 trillion, V = 2, P = base index = 1.0

Instructions: Enter your responses rounded to two decimal places (do not include a negative sign (-) with your answers).

a. What is the real value of output (Q)?

Now assume that the Fed increases the money supply by 20 percent and velocity remains unchanged.

b. If the price level remains constant, by how much will real output increase?

c. If, instead, real output is fixed at the natural level of unemployment (= Q from part a), by how much will prices increase in percentage terms?

d. By how much would V have to decrease to offset the increase in M (assuming Q and P did not change)?

Answer 1

(a) Real value of output = $20 trillion.

According to quantity theory of money, M*V = P*Q.

So, real GDP (Q) = (M*V)/P = (10*2)/1 = $20 trillion

(b) Now suppose M increases by 20% such that M = $10 + 20%*$10 = $12.

V and P remains constant.

So, Q will now become = (M*V)/P = $12*2 = $24.

So, the % by which real output increases = ($24-$20)/$20 * 100 = 20%.

(c) Now suppose Q is fixed at $20 trillion.

But when Fed increases M by 20% and V and Q remains constant.

So, P will also increase by 20% such that the quantity theory of money holds.

(d) Now let us assume Q and P does not change. Q is fixed at $20 trillion and P is fixed at 1.00.

M has increased by 20%.

So, V = (20*1)/12 = 20/12 = 1.67

Therefore, the % change in V to offset the increase in M = (1.67 – 2)/2 * 100 = 16.67%