Question

a. Let the demand for real balances, [M/P] d , equals kY, where k is a constant of proportionality and Y is real income. Derive an expression for the velocity of money.

b. Let the demand for real balances, [M/P] d , equals 4Y/800i, where Y is real income and i is the nominal interest rate. Derive an expression for the velocity of money.

c. Suppose the Fed announces that it is reducing the growth rate of the money supply in six months, and the public believes this will occur. Compare and contrast the impact of the Fed’s announcement on prices TODAY given your answers in part a and part b.

Answer 1

Solution:

a)

From the quantity theory of money we know that MV=PY where M is money supply, V is velocity, P is price and Y is real GDP and PY=real GDP

Thus V=(P/M)Y

Given M/P=kY and so P/M=1/kY

Thus here Velocity V=(1/kY)*Y=1/k

b)

Given M/P = 4Y/800i

Thus P/M = 800i/4Y = 200i/Y

Thus Velocity V = (P/M)*Y = (200i/Y)*Y=200iy

c)

From the quantity theory of money, we can say that other things remaining constant, growth rate of money=growth rate of price

So in part (a) when the growth rate of money falls, the prices also fall.

In part b, when money supply falls the velocity also falls becuase the interest rate also falls due to reduction in money supply. Thus growth rate of prices=Growth rate of money supply+growth rate of velocity and so as both growth rate of money supply and growth rate of velocity also falls and so growth rate of prices also fall but in case (b) growth rate of prices fall is more becuase the fall in growth rate of money also reduces growth rate of velocity.

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