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 monetaristmacroeconomic 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.
Formal exposition of the model
Suppose an individual receives her paycheck of 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 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from bonds to money, incurs a fixed transaction cost equal to per transfer (which is independent of the amount withdrawn). Let 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, , 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).
As a result the total cost of money management is equal to the cost of withdrawals, , plus the interest foregone due to holdings of money balances, , where is the average amount held as money during the period. Efficient money management requires that the individual minimizes this cost, given her 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. In that case the individual starts with money holdings equal to Y and ends the period with money holdings of zero. Normalizing the length of the period to 1, average money holdings are equal to Y/2. If an individual initially withdraws half her income, , spends it, then in the middle of the period goes back to the bank and withdraws the rest she has made two withdrawals (N=2) and her average money holdings are equal to . In general, the person’s average money holdings will equal .
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 condition for the optimum is then given by:
Solving this for N we get the optimal number of withdrawals:
Using the fact that average money holdings are equal to Y/2N we obtain a demand for money function:
The model can be easily modified to incorporate an average price level which turns the money demand function into a demand for liquidity function:
- Original works
- Extensions to general equilibrium
Pearson's RED Critical Thinking Model
The RED model lays out a path for understanding how critical thinking works and for developing each of the essential skills. Let's take a look at each critical thinking skill.
Pearson’s RED Model of Critical Thinking
This is the ability to separate fact from opinion. It is deceptively easy to listen to a comment or presentation and assume the information presented is true even though no evidence was given to back it up. Noticing and questioning assumptions helps to reveal information gaps or unfounded logic. Taking it a step further, when we examine assumptions through the eyes of different people (e.g., the viewpoint of different stakeholders), the end result is a richer perspective on a topic.
How to use it: When you’re gathering information, listening to what people say, or assessing a situation, think about what assumptions you have going in. Perhaps you assume that a trusted co-worker is providing reliable information – but is there really evidence to back that up? Learn to see gaps in logic, and opinion disguised as fact.
The art of evaluating arguments entails analyzing information objectively and accurately, questioning the quality of supporting evidence, and understanding how emotion influences the situation. Common barriers include confirmation bias, or allowing emotions-yours or others-to get in the way of objective evaluation. People may quickly come to a conclusion simply to avoid conflict. Being able to remain objective and sort through the validity of different positions helps people draw more accurate conclusions.
How to use it: We often have problems sorting through conflicting information because unknowingly let our emotions get in the way, or because – like just about everyone – we sometimes only hear what we want to hear. Learn how to push all that aside, and analyze information accurately and objectively.
People who possess this skill are able to bring diverse information together to arrive at conclusions that logically follow from the available evidence, and they do not inappropriately generalize beyond the evidence. Furthermore, they will change their position when the evidence warrants doing so. They are often characterized as having "good judgment" because they typically arrive at a quality decision.
How to use it: This is the payoff. When you think critically, the true picture become clear, and you can make the tough decision, or solve a difficult problem.