Use the Baumol-Tobin model to find money demand under the following assumptions.

Question

Use the Baumol-Tobin model to find money demand under the following assumptions. Income is $5000 per month (which can be broken down into 2500 in real income and a price level of 2) paid at the beginning of each month in the form of interest-earning bonds. Bonds earn an interest rate of 3.2% Each time you sell bonds a brokerage cost of $5.00 is incurred.

a .Find optimal money demand

b .How often are bonds sold and how much are sold each time?

c. Assume that all have the same money demand, as above. Suppose the Fed reduces the money supply to $500 per person. Find the new equilibrium interest rate.

Explanation / Answer

At the beginning of each month, the income is deposited into an interest-bearing bonds.

Let PY be the nominal income, i be the nominal interest rate

P be the transaction costs or brokerage fees.

Z be the amount of withdrawal each time.

According to Baumol-Tobin model, the optimal number of times the bonds are sold is given by:

n = (iY/2)1/2

and the transaction demand for money is

Md = P(Y/2i)1/2

For the question given, P = 2, Y = 2500, = 2.5 and i = 3.2

a)

Hence, the demand for real money is given as:

Md = 2(2.5*2500/2*0.032)1/2

= $312.50

This also implies that the demand for cash balance is $625.

b)

The number of times the bonds are sold is n = (0.032*2500/2*2.5)1/2 = 4 times.

The size of the bonds sold is Z and is computed as 2*Md. Thus around $625 worth of bonds are sold each month.

c)

When money supply is reduced to $500, this implies real money supply is now only $250 while the demand for real balance is $312.5. Interest rate will rise.

At equilibrium, Md = Ms

(Y/2i)1/2 = Ms/P

(2.5*2500/2*i) = 2502

3125/i = 625000

i = 5%

Hence the interest rate increases to 5%.

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