The Baumol-Tobin model is an economic theory showing how individuals and firms manage cash holdings to minimize the total costs associated with cash transactions and holding cash.
It thus explores the trade-off between liquidity provided by holding cash that doesn’t earn any interest, and the correlated opportunity cost of not investing that cash in interest-bearing assets.
According to the Baumol-Tobin model, individuals withdraw cash in fixed amounts at regular intervals to minimize these two summed costs:
- Transaction Costs: costs which are incurred as cash is converted from interest-bearing assets (think bonds or CDs) to cash. These costs may be bank fees, the time spend in making withdrawals and processing funds, and so on.
- Holding Costs: this is the opportunity cost of holding cash (without earning interest on it) as opposed to investing it. Holding costs are proportional to the interest rate of the best alternative investment.
So, the optimal cash withdrawal amount minimizing these total costs (TC) is given by this Baumol-Tobin formula:
C* = sqrt(2TF/i)
Let’s break that down:
- C* is the optimal cash withdrawal volume.
- T is the total cash needed for transactions over a specific period.
- F is the fixed cost per withdrawal transaction.
- i is the interest rate on the best alternative asset (opportunity cost).
- So, costs equal the square root of 2 multiplied by the fixed costs of transacting by the total cash need for transactions divided by the opportuinty cost.
Thus, by applying this formula, we can determine how much cash to withdraw to minimize total costs. If transactions costs or total cash needs increase, then the optimal withdrawal amount increases, and vice versa. Rising interest rates means that holding cash becomes more expensive, so individuals and firms will withdraw smaller amounts more frequently.
Hope that answered your question about the Bahim-Tobin model! Check out my other articles on economics here.
