In class, we derived the Baumol-Tobin money demand function under the assumption that at the beginning o each period, the individual receives his income in the form of an interest-bearing deposit. Suppose instead that the individual receives his income in his hand. The individual can still make trips to the bank and deposit money in an interest-bearing account. The only difference with the setting we discussed in class is that at the beginning of each period he receives his income in his hand rather than into the bank. The individual spends all of his income by the end of the period. Suppose that Y =500,i=0.02,andψ=0.1 where Y, i and ψ denote, respectively, income, the interest rate, and the cost of each trip to the bank.

1. Explain why it would not be optimal for the the individual to make only one trip to the bank.

2. Write the formulas for the total cost of going to the bank 0 times and n times, where n is any integer other than one.

3. Using a spreadsheet, calculate the total cost when n takes the values 0, 2, 3, 4, 5, 6, 7, 8, 9, 10. What is the number of trips that minimizes the cost?

4. Write the formula for the average money holdings for 0 trips and for n trips.

5. What are the average money holdings when the individual makes the optimal number of trips to the bank?