Question 4 (20 marks): The velocity of money. The quantity theory of money asser

Question

Question 4 (20 marks): The velocity of money. The quantity theory of money asserts that real money demand is proportional to real income: where V denotes real money demand, Y real income, and k a constant. (a) Verify that velocity, V, is constant in this case and is equal to 1/k under the assumption that nominal money demand Md equals the actual money stock M. (b) In reality, velocity has varied over time in Canada and has been shown to depend on income and interest rates. Suppose now that real money demand is given by: = 950 + 0.5Y + 500i. Find the values of real money demand, nominal money demand and velocity assuming that P = 50, Y = 1000, and i = 0.1 (c) Now suppose the price level doubles from 50 to 100 but Y and i remain the same as in part (b). What happens to the real money demand, nominal money demand and velocity? (d) Explain why in economic terms the real money demand, the nominal money demand and velocity are affected the way they are by an increase in the price level

Explanation / Answer

a) Rearrange the equation and see that Md x 1/k = P x Y. since M = Md we have M x 1/k = P x Y.

Equation of exchange has M x v = P x Y. This comparison reveals that v = 1/k. Now v is constant because 1/k is constant (cambridge constant)

b) We have Md/P = 950 + 0.5Y + 500i

Substitutes the values and note that Md/50 = 950 + 0.5*1000 + 500*0.1 or 1500*50 = 75000. Since Md = M, money supply is 75000

c) When P = 100, we must have same Y and same i so we have unchanged Md/P at 1500. Due to this we have Md/P = 1500

Md/100 = 1500 and so Md = 15000 and so money supply will be = 15000. Money supply is also doubled.

d) Increase in price level can increase nominal money demand Md but not the real money demand due to long run neutrality of money. Hence higher price level is translated proportionately from higher money supply, leaving real money demand and output unchanged.

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