The BaumolâTobin 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 oneâs 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 oneâs 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.
Jump to Implications of the Model - The model does not represent M2 money demand, which. One of the most useful feature of the Baumol-Tobin square root. Given the money demand elasticities derived from the model (+ ½ for. The transaction motive assumed regular income and a smooth flow of expenses.
Formal exposition of the model[edit]
Suppose an individual receives her paycheck of Y{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 Y{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to money, incurs a fixed transaction cost equal to C{displaystyle C} per transfer (which is independent of the amount withdrawn). Let N{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, i{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).
As a result the total cost of money management is equal to the cost of withdrawals, NC{displaystyle NC}, plus the interest foregone due to holdings of money balances, iM{displaystyle iM}, where M{displaystyle M} 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, Y/2{displaystyle Y/2}, 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 Y/4{displaystyle Y/4}. In general, the personâs average money holdings will equal Y/2N{displaystyle Y/2N}.
This means that the total cost of money management is equal to:
NC+Yi2N{displaystyle NC+{frac {Yi}{2N}}}
The optimal number of withdrawals can be found by taking the derivative of this expression with respect to N{displaystyle 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:
CâYi2N2=0{displaystyle C-{frac {Yi}{2{N^{2}}}}=0}
Solving this for N we get the optimal number of withdrawals:
Nâ=(Yi2C)12{displaystyle N^{*}=left({frac {Yi}{2C}}right)^{frac {1}{2}}}
Using the fact that average money holdings are equal to Y/2N we obtain a demand for money function:
MP=(CY2i)12{displaystyle {frac {M}{P}}=left({frac {CY}{2i}}right)^{frac {1}{2}}}
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)=MP=(CY2i)12{displaystyle L(Y,i)={frac {M}{P}}=left({frac {CY}{2i}}right)^{frac {1}{2}}}
See also[edit]
References[edit]
- Original works
- Allais, Maurice (1947). Ãconomie et intérêt, Paris: Librairie des publications officielles.
- Baumol, William J. (1952). 'The Transactions Demand for Cash: An Inventory Theoretic Approach'. Quarterly Journal of Economics. 66 (4): 545â556. doi:10.2307/1882104. JSTOR1882104.
- Tobin, James (1956). 'The Interest Elasticity of the Transactions Demand for Cash'. Review of Economics and Statistics. 38 (3): 241â247. doi:10.2307/1925776.
- Baumol, William J.; Tobin, James (1989). 'The Optimal Cash Balance Proposition: Maurice Allais' Priority'. Journal of Economic Literature. 27 (3): 1160â1162. JSTOR2726778.
- Extensions to general equilibrium
- Jovanovic, Boyan (1982). 'Inflation and Welfare in the Steady State'. Journal of Political Economy. 90 (3): 561â577. doi:10.1086/261074.
- Romer, David (1986). 'A Simple General Equilibrium Version of the BaumolâTobin Model'. Quarterly Journal of Economics. 101 (4): 663â686. doi:10.2307/1884173. JSTOR1884173.
Further reading[edit]
- Dornbusch, Rüdiger; Fischer, Stanley (1990). Macroeconomics (Fifth ed.). New York: McGraw-Hill. pp. 354â362. ISBN0-07-017787-2.
- Fisher, Douglas (1983). Macroeconomic Theory: A Survey. London: Macmillan. pp. 159â177. ISBN0-333-30100-5.
- Glahe, Fred R. (1985). Macroeconomics: Theory and Policy (Third ed.). Orlando: Harcourt Brace Jovanovich. pp. 232â244. ISBN0-15-551268-4.
Retrieved from 'https://en.wikipedia.org/w/index.php?title=BaumolâTobin_model&oldid=861967082'
Baumol Model :The Baumol model of cash managementis extensively used and highly useful for the purpose of cashmanagement. The Baumol model enables companies to find out theirdesirable level of cash balance under certainty. There are certainassumptions or ideas that are critical with respect to the Baumolmodel of cash management: * The particular company should be ableto change the securities that they own into cash, keeping the costof transaction the same. Under normal circumstances, all such dealshave variable costs and fixed costs. * The company is capable ofpredicting its cash necessities. They should be able to do thiswith a level of certainty. The company should also get a fixedamount of money. They should be getting this money at regularintervals. * The company is aware of the opportunity cost requiredfor holding cash. It should stay the same for a considerable lengthof time. * The company should be making its cash payments at aconsistent rate over a certain period of time. In other words, therate of cash outflow should be regular. EquationalRepresentations in Baumol Model : * Holding Cost = k(C/2) *Total Cost = k(C/2) + c(T/C) * Transaction Cost = c(T/C)
When was William Baumol born?
What is BAT in financial modelling?
Baumol-Allais-Tobin (BAT) Model - classic means of analysing the cash management problem Read More
How do you pronounce baumol?
you pronounce it like it is written as 'ba-maal' Read More
What is a pattern plan representation or description designed to show the structure or workings of an object system or concept?
What is a pattern plan representation or description designed to show the structure or workings of an objects system or concept?
What is a pattern plan representation or description designed to show the structure or workings of an object sustem or concept?
What can economic theory contribute to managerial economicswilliam j baumol?
what does economic theory contribute to managerial economics Read More
![Deriving Baumol-tobin Model Of Cash Management Deriving Baumol-tobin Model Of Cash Management](http://cdn.economicsdiscussion.net/wp-content/uploads/2015/08/clip_image004_thumb28.jpg)
Who can tell you what is the difference between a Baumol Static Revenue-Maximization Model with a Dynamic one?
The main difference is that in the dynamic model the profit is reinvented allowing for more growth in the future, so it is a trade off between profit now or higher profits later, the management will need to get the shareholder to agree on that, a trust must be established between the shareholders and management. Hence, int he dynamic model, the minimum profit is not actually a constraint as it is in the static model. Read More
What has the author Derek R Atkins written?
Derek R. Atkins has written: 'A re-examination of the Baumol and Quandt paradox' Read More
What is a surface model?
It's an object that's displayed at any angle with a solid surface or with the surface transparent, enabling the user to see the inner workings of the object. Read More
Need to assemble in workings?
Need to assemble inner workings of clock# 610-134 with the picture Read More
What is the LCM of 5 and 20 with workings?
Since 20 is a multiple of 5, it is automatically the LCM. No workings necessary. Read More
Is a model of a solar system a physics model?
Yes. . Physics is the science of modeling the universe around us, and then examining that model to better understand the characteristics and workings of our universe. Our current heliocentric model of the solar system lets us understand the orbital parameters of the planets, as well as the characteristics of the planets, such as their mass, size, density, expected temperature, and so on. Read More
What is economic fluctuation?
Cycling periods of good and bad times. Source: 'Economics, Principles and Policy' William J Baumol and Alan S Blinder. Page 24. Read More
What are computer principles?
How can you get points on extramarks?
How did newton try to explain the workings of the universe?
Newton let mathematical results explain the workings of the Universe. Mathematics is a more rational explanation. Read More
Workings of 37611 divided by 5970?
Workings or the federal system are called?
What is a physilogical adaptation?
What is the inside of a gun known as?
Workings of the federal system are called?
What is an anolog clock?
A clock with hands, and mechanical workings. Read More
Is thermodynamics is a branch of physics?
What is the book yi jing?
Interpreting the workings of the universe Read More
What actors and actresses appeared in The Inner Workings of Outer Space - 2009?
The cast of The Inner Workings of Outer Space - 2009 includes: David Ethier as Baxon Ketorah Williams as Zora Read More
When the internal workings of a circuit network are unknown to the user it is commonly called?
A black box. It would be called a white box if the internal workings were exposed/known to the user. Read More
What kind of things happened at Auschwitz?
What is cardiac physiology?
Cardiac Physiology is the inner workings of the heart Read More
Macroeconomics focuses on?
The workings of the whole economy or large sectors of it. Read More
How is inscrutable used in a sentence?
The workings of this author were all inscrutable. Read More
What was Edgar Degas's area of study?
Does a fly have a bone?
No, they have exoskeletons that protect the internal workings of the fly. Read More
What has the author William J Baumol written?
William J. Baumol has written: 'Instructor's manual to accompany ' 'Health care as a handicraft industry' 'Perfect markets and easy virtue' 'Economics' -- subject(s): Economics 'Business behavior, value and growth' 'Welfare economics and the theory of the state' 'International trade and scale economies' 'Performing arts - the economic dilemma' 'Economics' -- subject(s): Economics 'On the social rate of discount' 'Business behaviour, value and growth' Read More
What English physician explained the workings of the human heart?
What is the excitment of physics?
Unlocking the secrets of the universe's workings would be my response Read More
Discuss briefly about email inner working?
What is the smallest multiple of 19 which is greater than 500 workings?
Anything about the J Stevens AT Co Model 225 Double barrel shotgun All it said on the side is pats applied for?
The J. Stevens A & T Company Model 225 was made between 1906 and 1909 or possibly 1910. The guns value in good or better condition would be $100 to $225 depending on overall condition of the mechanical workings, original wood, etc. Read More
How were the problems of the Articles of Confederation solved?
The workings of the Constitutional Convention, which included the Virginia Plan, New Jersey Plan, and the Connetticut Comprimise. The workings of the Constitutional Convention, which included the Virginia Plan, New Jersey Plan, and the Conneticut Comprimise. Read More
What is a good topic that has to do with technology?
A very good topic to write a report about would be the inner workings of the internet, the evolution of technology from the 80 to present, or the inner workings of a computer with its operating system. There is a ton of information online about all of these topics. Read More
Lessee books short workings recoverable in future years?
What was the concentration camp Auschwitz known for?
For it mass killings and its profittable labour workings Read More