The Quantity Theory of Money: Practice Problems and Solutions

Problem 11. Given that M = money supply, V = velocity of circulation, P = price level,

Y = output level, which of these is the equation describing the Quantity Theory of Money?

(a) M/V = P/Y
(b) V/M = PV
(c) MP = VY
(d) MPY = V
(e) MV = PY

(f) PV = 1/MY

Solution 11. The correct answer is (e): MV = PY

Problem 12. In Assumptionland, the Quantity Theory of Money holds perfectly. The GDP of Assumptionland is 20000, and the price level is 30. The money supply is currently at 440000. What is the velocity of circulation of money in Assumptionland?

Solution 12. We use the equation MV = PY, rearranging it to V = PY/M, where P = 30, M = 440000, and Y = 20000. Thus, V = 30*20000/440000 = V = 1.363636363636

Problem 13. The government of Assumptionland (with economic conditions as described in Problem 12) decides to increase the money supply by a factor of 1.43. Yas is a Classical economist and believes that the models of Classical economics are perfectly reflected in the real world. Which economic variable does Yas think will be affected, and what will the new value of that variable be?

Solution 13. Classical economics holds that an increase in the money supply results in a proportional increase in the price level, leaving velocity of circulation and output unchanged. So, according to Yas, the price level P will rise to 1.43*30 = P = 42.9

Problem 14. The government of Assumptionland (with economic conditions as described in Problem 12) decides to increase the money supply by a factor of 3.11. Senyek is a Keynesian economist and believes that the models of Keynesian economics are perfectly reflected in the real world. Which economic variable does Senyek think will be affected, and what will the new value of that variable be?

Solution 14. Keynesian economics holds that prices and wages are sticky, so, at least in the short run, an increase in the money supply will result in a proportional increase in output. Thus, according to Senyek, P and V will remain constant and Y will increase by a factor of 3.11 to 20000*3.11 = Y = 62200

Problem 15. Suppose that the Quantity Theory of Money holds perfectly in Equationville. Over the past year, money supply in Equationville changed by a factor of 1.22, velocity of circulation was halved, and output increased by a factor of 4. By what factor did the price level change?

Solution 15. MV = PY implies that P = MV/Y. So P will increase proportionally to M and V and in inverse proportion to Y. Thus, P will change by a factor of 1.22*0.5/4 = 0.1525

See Mr. Stolyarov's complete index of Intermediate Macroeconomics Problems and Solutions here.