Question

2. An individual receives a total of ¢19,200 as annual income. The transaction cost of going to the bank each time to withdraw money is fixcd at ¢10 in addition to an interest rate of 16% on financial assets. Using Baumol's inventory-theoretic approach to the demand for money:

a. Find the amount of money this individual would have to withdraw in order to minimize cost. (3 marks)

b. How many trips should this individual make to the bank in a year? (2marks)

c. On average, how many trips should this individual make to the bank every month ? (2 marks)

d. What is the implication of an increase in interest rate on this iindividual's average cash holding?

Answer 1

Solution:

a.). The Baumol formula: W = $\sqrt{\frac{2bY}{r} }$

Where: W = amount to withdraw

            b = cost of trip = 10

           Y = Income = 19,200

           r = Interest rate = 16$\%$ or 0.16

W = $\sqrt{\frac{2\times 10\times 19,200}{0.16} } = \sqrt{\frac{384,000}{0.16} } = \sqrt{2,400,000 } = 1,549.19$

The individual will have to withdraw 1,549.19 in order to minimize cost.

 

b.). Number of trips (N^*) = $\sqrt{\frac{Yr}{2F} }$

N^* = $\sqrt{\frac{0.16\times 19,200}{2\times10} } = \sqrt{\frac{3,072}{20} } = \sqrt{153.6 } = 12.39$

The number of trips in a year = 12 trips

 

c.). Year = 12 months

No. of trips per month = $\frac{12}{12} = 1$ trip

The individual should make an average of 1 trip per month.

 

d.). When interest rates increase relative to the rates that can be earned on money deposits, the individual will tend to hold less money.