Question

Let's assume that your baumol-tobin model is $ 54,000 a year. The annual interest rate of the savings deposit account is 2.5% and we assume that you keep your income in your account.

1- Assume you go to the bank 4 times a month, how many times do you go to the bank in total?

2- How much money do you keep on average for a year?

3- Now, every time you go to the bank, let F cost $ 0.42. how much is the total cost of keeping your income?

4- Optimal number of trips to the bank for one year based on your income, considering savings deposits, interest rates and the cost of each trip to the bank. What is N * (ie the number of visits to the bank that will minimize the cost of wanting to keep cash in your hand)?

5-according to N* that you calculated it in (4) Calculate the amount of money you will keep on average.

Answer 1

1. The number of trips in an year are

12*4=48.

2. The average amount of money is

54000/2*48=562.5

3. We know that total cost is given by

Cost from foregone interest + cost of trips to the bank

=i(Y/2N)+F*N

=.025*(54000/2*48)+.42*48

=$34.2225

4. optimal number of trips in Baumol tobin model is given by

N*=(iY/2F)^.5

N*=(.025*54000/2*.42)^.5

N*=40.089=~40

5. The average amount of money would be

54000/2*40=675