Baumol–Tobin Model
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The Baumol–Tobin model is an economic model of the transactions demand for money as developed independently by
William Baumol William Jack Baumol (February 26, 1922 – May 4, 2017) was an American economist. He was a professor of economics at New York University, Academic Director of the Berkley Center for Entrepreneurship and Innovation, and Professor Emeritus at Prin ...
(1952) and
James Tobin James Tobin (March 5, 1918 – March 11, 2002) was an American economist who served on the Council of Economic Advisers and consulted with the Board of Governors of the Federal Reserve System, and taught at Harvard and Yale Universities. He devel ...
(1956). The theory relies on the tradeoff between the liquidity provided by holding money (the ability to carry out transactions) and the
interest In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct ...
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 In finance and economics, the nominal interest rate or nominal rate of interest is the rate of interest stated on a loan or investment, without any adjustments or fees. Examples of adjustments or fees # An adjustment for inflation(in contrast with ...
, the level of
real income Real income is the income of individuals or nations after adjusting for inflation. It is calculated by dividing nominal income by the price level. Real variables such as real income and real GDP are variables that are measured in physical units, ...
that corresponds to the number of desired transactions, and the fixed
transaction costs In economics and related disciplines, a transaction cost is a cost in making any economic trade when participating in a market. Oliver E. Williamson defines transaction costs as the costs of running an economic system of companies, and unlike produ ...
of transferring one’s wealth between liquid money and interest-bearing assets. The model was originally developed to provide
microfoundations Microfoundations are an effort to understand macroeconomic phenomena in terms of economic agents' behaviors and their interactions.Maarten Janssen (2008),Microfoundations, in ''The New Palgrave Dictionary of Economics'', 2nd ed. Research in microf ...
for aggregate money demand functions commonly used in Keynesian and
monetarist Monetarism is a school of thought in monetary economics that emphasizes the role of governments in controlling the amount of money in circulation. Monetarist theory asserts that variations in the money supply have major influences on national ...
macroeconomic Macroeconomics (from the Greek prefix ''makro-'' meaning "large" + ''economics'') is a branch of economics dealing with performance, structure, behavior, and decision-making of an economy as a whole. For example, using interest rates, taxes, and ...
models of the time. Later, the model was extended to a
general equilibrium In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an ov ...
setting by
Boyan Jovanovic Boyan Jovanovic is a professor of economics at New York University and a long-term consultant at the Federal Reserve Bank of Richmond. Jovanovic, of Serbian descent, received his Bachelor's and master's degrees from the London School of Economi ...
(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 his paycheck of 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 he needs to hold some portion of Y in the form of money balances which can be used to carry out the transactions. Alternatively, he can deposit some portion of his 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 C per transfer (which is independent of the amount withdrawn). Let 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, i, which is received at the end of the period. For simplicity, it is also assumed that the individual spends his 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, NC, plus the interest foregone due to holdings of money balances, iM, where M is the average amount held as money during the period. 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. 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 his income, Y/2, spends it, then in the middle of the period goes back to the bank and withdraws the rest he has made two withdrawals (N=2) and his average money holdings are equal to Y/4. In general, the person’s average money holdings will equal Y/2N. This means that the total cost of money management is equal to: NC+\frac The optimal number of withdrawals can be found by taking the derivative of this expression with respect to N 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: C-\frac =0 Solving this for N we get the optimal number of withdrawals: N^= \left ( \frac \right ) ^ Using the fact that average money holdings are equal to Y/2N we obtain a demand for money function: M= \left ( \frac \right )^ The model can be easily modified to incorporate an average price level which turns the money demand function into a demand for liquidity function: L(Y,i)=\frac = \left (\frac \right )^ where Q is the volume of goods sold at an average price P, so that Y = P*Q.


See also

*
Money demand In monetary economics, the demand for money is the desired holding of financial assets in the form of money: that is, cash or bank deposits rather than investments. It can refer to the demand for money narrowly defined as M1 (directly spendable ...
* Transactions demand * Speculative demand *
Money supply In macroeconomics, the money supply (or money stock) refers to the total volume of currency held by the public at a particular point in time. There are several ways to define "money", but standard measures usually include Circulation (curren ...


References

;Original works * Allais, Maurice (1947). ''Économie et intérêt'', Paris: Librairie des publications officielles. * * * ;Extensions to general equilibrium * *


Further reading

* * * {{DEFAULTSORT:Baumol-Tobin model Keynesian economics Demand Demand for money