At the time of writing Keynes’ approach to the demand for money was radical. However, The General Theory received much criticism and lead other economists to try and justify Keynes’ findings, particularly in respect to the inverse relationship between the interest rate and the demand for money. Of these, the most widely quoted model is the Baumol/Tobin inventory-theoretic-model developed separately by William Baumol (1952) and James Tobin (1956) resulting in similar conclusions. They are often referred to as Neo-Keynesian models as they agree with a central argument in Keynes’ general theory that the monetary and real sectors of the economy are related through interest rates. (Howells & Bain, 2009, p433) To be able to draw precise conclusions about the variables that determine this segment of the demand for money a number of assumptions are made. A) The model assumes that an individual agent, be it a firm or household, receives a known lump-sum payment of T once at the start of each period, say one year. All income received is spent at a constant rate over the period. B) The individual can invest the payment in interest yielding financial asset such as bonds that pay a known interest rate r if held for a full month or proportionately less than this if held for a shorter amount of time, or they can hold money in cash form paying no interest. C) In order to obtain cash in equal amounts of K, the individual must sell bonds. Therefore, at the start of the period, the individual will exchange most of T for bonds and then periodically exchange bonds for cash as purchases are made. The more transactions from bonds to cash increases the average bond holding and consequently the interest earned increases. However these exchanges are subject to a brokerage fee of b per transaction, this is assumed to be fixed. Therefore, the number of transactions are determined by a trade off between the costs of transactions and the earning on bonds in term of interest rates. The number of transactions in each period determines demand for real balances. An important factor in the inventory model is “All relevant information is known with certainty” (Cuthbertson, 1985). The formula below is taken from (Cuthbertson, 1985). T/K is the number of times bonds are sold to finance expenditure where T=the real income and total value of transactions and K=the real value of assets turned in to cash every time a transfer takes place. This incurs a total brokerage fee of b(T/K) as all income is spent, where b is the real cost of turning assets into cash. Conversely, if money is held instead of bonds no interest rate is paid and this is also treated as a cost. Since expenditure is assumed to be smoothed over the period, average money holding for the period is K/2, half the receipts for the sale of bonds. When this is multiplied by r it gives the amount of interest lost known as the opportunity cost of money. The total cost (TC) of making transactions can be written as:

TC=bTK+rK2

(1.1)

An assumption in the model is that economic agents will minimise the total cost for turning bonds in to cash. To find the value of K that minimises cost we differentiate (1.1) and take the resulting derivative with respect to K, set it equal to zero, and solve for K.

∂TC∂K= -bTK2 +r2= 0

(1.2)

So that

K= 2bTr

(1.3)

This provides us with the ‘square root rule’ and since money holding over the period holds an average value of K/2, the demand for money equation is as follows (Laidler, 1985) Md=K2=12 2bTr

(1.4)

Thus, the transactions demand for money is inversely related to the interest rate supporting Keynes’ general theory. Nominal value of transactions and brokerage fees vary in proportion to the price level. (Laidler, 1985) This results in a 1:1 ratio between an increase in the price level and an increase in the demand for money. Md=12 2bTr P=Ab0.5T0.5r-0.5P

(1.5)

Where

A=12 2

(1.6)

An important variable to consider is the...