Question

1. Use the quantity theory of money to answer the following questions.
   1. Find the number of times a year on average each dollar is spent when the price level is 20, the money supply is 55,000 and real gdp is 70,000.
   2. Calculate the money supply when nominal GDP is $1,254,987 and the velocity of money is 18 and the price level is 7.
   3. The growth rate of real GDP is 7%. Assume the growth rate of velocity is constant at a rate of 3%. If wish to set a target rate for inflation of 3% and maintain its current growth rate of real GDP, according to the quantity theory of money, what will the growth rate of the money supply need to be?

Answer 1

Quantity theory - MV = PY; M-money supply, V-velocity, Y-price level, Y-real GDP, PY-nominal GDP

a. P=20; M=55000; Y=70000

V = PY/M = 20*70000/55000 = 25.45

b. PY = 1254987; V=18; P=7

M = PY/V = 1254987/18 = 69721.5

c. From quantity theory of money,

percentage change in M * percentage change in V = percentage change in P * percentage change in Y

percetage change in M = percentage change in P*percentage change in Y/ percentage change in V

= 3*7/3 = 7

So the percentage change in money supply will have to be 7%

note that percentage changes refer to the growth rate. Growth rates are calculated as percentage change.