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THE THEORY OF THE DEMAND FOR MONEY 117<br />

Miller <strong>and</strong> Orr’s version (1966, 1968), contains thresholds, with people only<br />

changing from money to bonds or vice versa at upper or lower thresholds of<br />

money balances. Milbourne (1986) took the Miller-Orr framework <strong>and</strong><br />

considered within it the impact of financial innovation on <strong>monetary</strong> aggregates.<br />

Box 5.3; The principal variations on the inventory-theoretic model of<br />

the transactions dem<strong>and</strong> for money<br />

(i) With fixed or partly fixed transactions costs, a person does not hold securities at all<br />

unless the interest income is greater than the transactions costs of converting money<br />

into <strong>and</strong> out of bonds. Then, a change in interest rate may not cause any change in<br />

the dem<strong>and</strong> for money. The inverse relationship between interest rate <strong>and</strong> the dem<strong>and</strong><br />

for money that the model seeks to demonstrate disappears at low rates of interest.<br />

(ii) The frequency of pay periods <strong>and</strong> the timing of payments may be influenced<br />

by institutional <strong>and</strong> technical changes (for example, the use of credit cards) <strong>and</strong><br />

by economic factors such as high <strong>and</strong> variable interest rates.<br />

(iii) Only the interest rate on bonds is included in the model; but if a firm can use<br />

an overdraft facility to obtain money, the relevant rate is the difference between<br />

the rate charged on borrowings on overdraft <strong>and</strong> the rate paid on bonds. Again,<br />

the dem<strong>and</strong> for money depends on the relative interest rate if the model is extended<br />

to include an interest rate or an implicit interest rate (in the form of bank services<br />

provided below cost) on holdings of money.<br />

(iv) The transactions dem<strong>and</strong> for money may be modelled such that money holdings<br />

are only deliberately adjusted when they reach upper or lower thresholds.<br />

(v) Individuals can be allowed to save part of their income, acquiring interest-bearing<br />

assets for holding long-term as well as for short-term reasons.<br />

(vi) Once it is accepted that some people but not others make<br />

money/bonds/money conversions with transactions balances, aggregation problems<br />

arise. It can then be shown that almost any elasticity is possible depending<br />

on the propensity to save <strong>and</strong> the proportion of income earned by those who do<br />

not make any conversions.<br />

The formal inclusion of interest rates into the precautionary dem<strong>and</strong> for<br />

money adds further to the case for an inverse relationship between interest<br />

rate <strong>and</strong> the dem<strong>and</strong> for money, without suggesting that the dem<strong>and</strong> for<br />

money function might be unstable.<br />

5.7 Tobin's portfolio model of the dem<strong>and</strong> for money<br />

Tobin’s model (1958, 1969) can be seen as a response to the common criticisms<br />

of the speculative dem<strong>and</strong> model. It introduces a wider range of<br />

assets including equities <strong>and</strong> real assets. Where, in his 1958 article, Tobin

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