Baumol-Tobin model

The Baumol–Tobin model is an economic model of the transactions demand for money as developed independently by William Baumol (1952) and James Tobin (1956). The theory relies on the tradeoff between the liquidity provided by holding money (the ability to carry out transactions) and the interest forgone by holding one’s assets in the form of non-interest bearing money. The key variables of the demand for money are then the nominal interest rate, the level of real income that corresponds to the amount of desired transactions, and the fixed transaction costs of transferring one’s wealth between liquid money and interest-bearing assets. The model was originally developed to provide microfoundations for aggregate money demand functions commonly used in Keynesian and monetarist macroeconomic models of the time. Later, the model was extended to a general equilibrium setting by Boyan Jovanovic (1982) and David Romer (1986).

For decades, debate raged between the students of Baumol and Tobin as to which deserved primary credit. Baumol had published first, but Tobin had been teaching the model well before 1952. In 1989, the two set the matter to rest in a joint article, conceding that Maurice Allais had developed the same model in 1947.

Suppose an individual receives her paycheck of ${\displaystyle Y}$ dollars at the beginning of each period and subsequently spends it at an even rate over the whole period. In order to spend the income she needs to hold some portion of ${\displaystyle Y}$ in the form of money balances which can be used to carry out the transactions. Alternatively, she can deposit some portion of her income in an interest bearing bank account or in short term bonds. Withdrawing money from the bank, or converting from bonds to money, incurs a fixed transaction cost equal to ${\displaystyle C}$ per transfer (which is independent of the amount withdrawn). Let ${\displaystyle N}$ denote the number of withdrawals made during the period and assume merely for the sake of convenience that the initial withdrawal of money also incurs this cost. Money held at the bank pays a nominal interest rate, ${\displaystyle i}$, which is received at the end of the period. For simplicity, it is also assumed that the individual spends her entire paycheck over the course of the period (there is no saving from period to period).

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