The Baumol-Tobin Model

The Baumol- Tobin model is based on a formula called the square- root rule. 
The square root rule states that stores should hold inventories proportional to the square-root of sales.  The same rule applies to the demand for money also.  

•  The square-root rule provides a household’s transactions demand for cash. 
• The household holds less money if the opportunity cost of holding money or the rate of interest increases. 
• The model  examines the costs and benefits of holding money. 
• The cost of holding money is the loss of interest that would have accrued if the money had been deposited in an interest bearing saving account. 
• The benefit of holding money is the convenience that accrues in that people do not have to go to the bank every time they desire to make a transaction. 
• The model assumes that the price level is constant.  The level of real spending  also remains constant over the year. 

Consider a person who has plans to spend Rs.Y gradually during the period of a year. In the process of spending this amount he holds an optimal size of an average cash balance. This depends on the number of trips the person makes to the bank over the year. 1. Suppose, he makes one trip to the bank each year. He could withdraw the entire Rs.Y at the start of the year and then spend the money gradually. His money holdings at the beginning of the year are Y and at the end of the year is zero. The average money holdings over the year are Y/2.   2. He makes two trips to the bank during the year. At the beginning of the year are Y/2 since he withdraws this amount right in the beginning and then spends it gradually during the first half of the year. At the end of the year are zero since he makes another trip in between to withdraw Y/2 for spending during the second half of the year. The average money holdings over the year are Y/4. The advantage of this plan is that the individual has to forgo less interest because he holds less money on an average. The disadvantage is that he has to make 2 trips to the bank while in the first case he had to make only one trip. Similarly, he can make N trips to the bank during the year. To determine the optimal choice of N and hence the demand for money we assume. The cost of going to the bank will be higher when the number of trips are more and smaller will, therefore, be the interest loss. Thus, an individual would prefer to hold more money if the fixed cost of going to the bank is higher, the amount of expenditure Y is higher, and the interest rate i is lower.  Thus, an individual would prefer to hold more money if the fixed cost of going to the bank is higher, the amount of expenditure, Y is higher and the rate of interest, i is lower. So far this model has been utilized to explain the amount of money holdings outside of banks. However, this model can be used in a broader sense to describe a person’s demand for monetary assets.

The Baumol- Tobin model has been criticized for not being stable over time. There may be changes in the demand for money function if there is a change in the fixed cost of going to the bank.