Question

Suppose the Baumol-tobin model of money demand is correct. The typical person has annual money income of $80,000, the product of 40,000 real income and a price level of 2. The brokerage fee is $1. The money supply per person is $1000. What is the value of the nominal interest rate? why? Now suppose the fed wants to reduce nominal interest rate to 2% (.02). What will they need to do to the money supply - by how much and in what direction must it be changed? The fed wants to maintain the interest rate at 2% despite what they expect will be a 10% increase in real income. By how much, in what direction, and by what percent should the money supply be changed? (Before the change the money supply is at the level you found above). Instead of real income, suppose the Fed expects the price level to increase by 10%. To maintain its .02 target for the interest rate, by how much and in what percent should they increase the money supply?

Answer 1

Calculation of equilibrium rate of interest:-

Now the formula is :-

TC = I*Y /2N + F*N

Where Total Cost is F*i

Where F is the brokerage cost =$1

​N = Number of trips to the bank

ps to the bank (LET us assume it as 1 that is the whole money is withdrawn at once )

Amount of money held Y/2N

I*80000/2N = i *80000/2N +1*N

Thus I =1%

Change in supply to maintain interest rate at 2%:-

There is a positive relationship between money supply and interest rate thus if at a money supply of $1000 the rate of interest is 1% ,to increase the rate rate at two percent :-

a) We will increase the Supply to $2000

b) There will be an upward movement in supply curve

Increase in the real income by 10 %:-

Price level =2

Y0 = 40000

Y1 = 44000

If equilibrium supply at Y0 was 2000

Therefore new equilibrium supply will be

S1=Y1*S0/Y0=2200$

Thus

a) The supply will be increased by $200

b) The supply curve will move upwards

c) %change in money supply = (2200-2000)/2000*100=10%

Increase in price level by 10% :-

P0=2

P1=2.2

S0=2000

Thus new supply will be S1 =P1*S0/P0=(2.2*2000)/2*=2200

Thus

a) The supply will increase by $200

b) The supply curve will move upwards

c) % change in supply = (2200-2000)/2000*100=10%