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 number 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.
In 1989, the two set the matter to rest in a joint article, conceding that Maurice Allais had developed the same model in 1947.
Alternatively, he can deposit some portion of his income in an interest bearing bank account or in short term bonds.
Money held at the bank pays a nominal interest rate,
, plus the interest foregone due to holdings of money balances,
Efficient money management requires that the individual minimizes this cost, given his level of desired transactions, the nominal interest rate and the cost of transferring from interest accounts back to money.
The average holdings of money during the period depend on the number of withdrawals made.
Suppose that all income is withdrawn at the beginning (N=1) and spent over the entire period.
Normalizing the length of the period to 1, average money holdings are equal to Y/2.
This means that the total cost of money management is equal to:
The optimal number of withdrawals can be found by taking the derivative of this expression with respect to
and setting it equal to zero (note that the second derivative is positive, which ensures that this is a minimum, not a maximum).
The model can be easily modified to incorporate an average price level which turns the money demand function into a micro-founded demand for liquidity function: