The Inventory Theoretic Model of the Transactions Demand for Money - Case Study Example

Critically appraise the inventory theoretic model of the transactions demand for money Table of Contents Critically appraise the inventory theoretic model of the transactions demand for money 1 Table of Contents 1 Introduction 2 The Inventory Theoretic Approach 3 Transactions Demand for Money 4 Criticisms against the Baumol-Tobin Inventory Theoretic Approach for Money Demand 5 Conclusion 6 Introduction The original proponent for the determinants of the demand for money was John Maynard Keynes. He suggested that the demand for money is basically dependent on three components, namely, the speculative demand for money, the precautionary demand for money and finally the transactions demand for money. All the three types of demand for money depend upon the rationality aspect of consumer behaviour. Speculative demand for money depends upon the individual’s consideration of money as an alternative to interest-earning assets so that the rational consumer might protect himself from any potential capital losses due to fluctuations in the rate of interest. Precautionary demand for money on the other hand, implies the stocking up of liquid money for use in times of exigencies. Lastly, transactions demand for money is that which the rational individual needs as a medium of exchange, to buy goods and services. The last component is the most important of all the three, because people need money mainly for transaction purposes (Dornbusch & Fischer, 2005). The demand for money to serve the other two purposes arise only at some particular points of time, viz., at times of exigencies or situations when the economy is at the edge of some emergency; however, transactions demand for money remains vibrant almost throughout a year, whatever the economic situation might be. This is the reason why Baumol in 1952 and Tobin in 1956, separately took up the case for the transactions demand for money so as to explain its operation through a more realistic perspective, with the help of the inventory-theoretic approach (Mishkin, 2004). The present paper tries to explore the subject of transactions demand for money from an inventory-theoretic approach as was introduced by Baumol and Tobin separately. In addition, it also includes the criticisms, as raised by many eminent observers, which have followed their adaptation. The Inventory Theoretic Approach The inventory theoretic approach is closely associated with the names of Baumol and Tobin, who had explained the theory behind the transactions demand for money with the help of the same. According to the theory developed by the two observers, the transactions demand for money depends upon some factors mentioned as under – 1. The amount of money that an individual needs for making payments at a particular point of time, T, 2. The amount of money that he needs to withdraw for the same, C, 3. The number of times that he withdraws the money, 4. The opportunity cost of withdrawing or borrowing the sum for making payments – suppose the payments are made from bank deposits or borrowings made by the individual, so that the opportunity cost in this regard is, the rate of interest foregone on the amount of cash withdrawn, i and 5. The non-interest payments made for withdrawing or borrowing the required sums, for instance brokerage fees that are borne when the amount of money is withdrawn from an investment project. Suppose this sum is represented by b. In addition, there are a number of other factors, like the number of times that the sums of money are withdrawn or borrowed. This depends upon the amount of money to be paid, T and the sum of money withdrawn each time, C. This number is equal to T/ C, where T must be greater than or equal to C for the rational individual’s demand to be optimally served. The number of withdrawals made can also be determined from the intersection between the marginal cost and marginal benefits of making transactions as has been shown in the above figure. The marginal cost of making a transaction is equal to a constant, while the marginal benefit of a transaction is diminishing as the number of withdrawals rise, since that would indicate the person having to incur higher opportunity cost in the form of foregoing more and more interest payments (Dwivedi, 2005; Gowland, 1991). Again, the total amount of money that is exempted as brokerage fees also depends upon the number of times that the borrowings or withdrawals are made. Thus if the total number of withdrawals is (T/ C), then the total amount borne as brokerage fees is equal to . On the other hand, the aggregate interest payments depends upon the amount of money that the individual holds at any particular point of time to sustain his regular flow of payments. It is assumed that the individual withdraws an amount C at time period 1 and does not withdraw or borrow the next amount unless the previous amount completely wears out. Thus the total amount of interest payments made by the individual is, . Assuming that there are only two components of opportunity cost incurred in keeping a regular stock of money for transaction purposes, the total cost incurred for the same, can be expressed as, TC =  The rate of interest, i and the amount of money paid out as brokerage fees, b, are exogenous to the individual. Hence, to minimise the total opportunity cost, of making payments the consumer can only manage the amount of money that he withdraws at each point of time, i.e., C. So, deriving the total cost incurred (TC) with respect to C, and equating the derivative with 0,  =  +  = 0. Hence, the optimal amount of money withdrawn each time is, C =. Transactions Demand for Money The transactions demand for money depends upon the vigorousness of transactions. Since the amount of money withdrawn at any particular point of time depends upon the amount of transaction demand for money, so the latter can easily be derived from the expression for the former. The cost of money is borne at an average rate of C/ 2 at each point of time throughout a given span of time. It is assumed that the amount of money that the individual holds at each point of time is equal to the aggregate transaction demand for money, M. So, it can be easily concluded from this aspect that M =  =  =  Hence, from the inventory theoretic approach, it can be said that the transaction demand for money is directly related to 1. Amount of payment to be made after each interval, T and 2. The amount of expenses incurred as brokerage fees, b. Similarly, it depends inversely on the amount of money paid out as interest expenses, i. This is a very realistic conclusion given that higher the rate of interest is, lower will the individual want to withdraw money from his bank deposits, and thus lower will his demand be for liquid money (Bryant, 1967). The adjoining diagram explains the concept about the transactions demand for money, as introduced by Baumol and Tobin through an inventory theoretic approach. It is assumed in the diagram that the amount of transaction payments made by the individual is equal to her income, T. So, when at time period, t0, the rational individual receives an income equal to T, she already has the knowledge that at the end of some more consecutive periods, all her income will be drained out as transaction payments. After the individual receives her income of T at the beginning of t0, she invests an amount B1 out of it in bonds and the remaining amount, Z is spent out for transactional purposes. However, when this amount wears out completely, the individual withdraws liquid money from the money that he had previously invested in bonds. Suppose that he withdraws the same amount Z, so that now the amount of money that he has left as investment in bonds is equal to B2, where, B2 = B1 – Z. The point to be noted here is that the financial wealth with the individual diminishes over time until at time period t4, it is equalled to 0. This decreasing wealth is represented by the downward sloping line Tt4 in the diagram. The gradual fall in the amount of bond-holdings of the individual is shown by the dashed steps and the amount of money held at each point of time is represented by the lines at the bottom of the figure drawn in the form of saw-tooth. It must be noted that since the individual is expected to behave rationally, he will withdraw exactly the amount that he will need for transaction purposes, so that the average amount of money demand by the individual is equal to Z/ 2 (Baumol, 1952; Laidler, 1969). Criticisms against the Baumol-Tobin Inventory Theoretic Approach for Money Demand The Baumol-Tobin model of money demand is considered to be one of the most realistic approaches for determining transactions demand for money, M. However, certain criticisms have been raised forward by some observers in this regard. The grounds of criticism are the unrealistic and often too simplified assumptions made in order to conclude about the model. Assumptions that have helped in establishing the Inventory Theoretic Model for transactions demand for money are – 1. The amount of transaction payments made at the end of each period of time, is assumed to be fixed at T. However, this is completely unrealistic given that there can be some exogenous changes in the demand for money in a particular period, which can make it different from that in the previous period. Clearly, the model does not make provisions for any external changes in transactions demand. 2. Secondly, it is also assumed that the amounts of withdrawals are made from the savings account until the cash balance in the account is exactly nullified. However, this too is rather an unrealistic approach, since the banks generally have some regulations regarding the minimum amounts of cash balances that could be kept with them as account deposits. Moreover, it is also assumed that the firms keep on withdrawing the same amount, which again is quite small in quantity, to keep a constant flow of cash balances, which is quite unlikely, given that the firms have to bear a wide variety of institutional expenses as well (Frazer, 1967). Conclusion The Baumol-Tobin model of inventory theoretic approach of transaction demand for money is one of the most widely accepted theories determining the demand for money. It draws an important conclusion regarding the determinants of the transactions demand for money. The approach finds that the average demand for money at any point of time is equal to half of the amount of cash withdrawn at the beginning of that period and is directly related to the amount of non-interest opportunity costs being incurred for the same as well as the amount of money being drawn after each interval, while being inversely related to the amount of money paid as interest expenses. The conclusions from the model might be a very truthful one, with implications for real-life situations, but the problem is that the assumptions being made in this regard are oversimplified in nature. The worst problem with the model is that there is no room for any uncertainties in the approach, which is the most unrealistic of its kind. Though economists like Miller and Orr have tried to introduce uncertainties in the model, but as Sprenkle had pointed out, this provision does not correct the assumption about the absence of institutional factors in the gross expenses or transaction demand for money. However, despite all the drawbacks and bottlenecks in the approach, the Baumol-Tobin model continues to be one of the most popular of all models explaining the demand for money for its simple description of the same. References Baumol, W. J. (1952). ‘The transactiuons demand for cash: An inventory theoretic approach’, The Quarterly Journal of Economics, Vol. 66, No. 4. Bryant, J. (1978). Transactions Demand for Money. Research Dept., Federal Reserve Bank of Minneapolis Dornbusch, R. & Fischer, S. (2005). Macroeconomics (6th Edition). New York: McGraw-Hill. Dwivedi, D. N. (2005). Macroeconomics Theory and Policy (2nd Edition). New York: McGraw-Hill. Frazer, W. J. (1967) The Demand for Money. USA: The University of Michigan. Gowland, D. (1991) Money, Inflation and Unemployment: The role of money in the economy (2nd Edition). USA: Palgrave Macmillan. Laidler, D. E. W. (1969). The demand for money: Theories and evidence. USA: International Textbook Co. Mishkin, F. (2004) The economics of money, banking and financial markets. USA: Pearson. Bibliography Baro, R. J. (1997) Macroeconomics.USA: MIT Press. Bryant, R. C. (1980) Money and monetary policy in interdependent nations. California: Brookings Institution. Friedman, M. (1959) The demand for money: Some theoretical and empirical results. USA: National Bureau of Economic Research. Gale, G. (1982). Money: In equilibrium. London: Nisbet. Read More