Is There an Optimal Money Supply?*
The title question of this chapter is provocative and interesting, inasmuch as it encapsulates a whole area of rapid recent development in monetary theory in an apparently simple question. Yet it is really a trick question, the answer to which must be ‘yes’ if the terms are properly defined, and the difficulty of which inheres in such proper definition of the terms. Since the question has confused some theorists, I make no apology for spending much of this chapter on clarification of the issues, even though this requires restatement of some elementary theoretical points.
To begin with – in case anyone is under any illusions on this point – the question has nothing to do with the optimal conduct of short-run stabilization policy. Instead it belongs to the pure theorists’ world of continuous full employment of resources; as such, its policy relevance is to the framework of monetary organization and the long-run environmental objectives of monetary policy.
Within this frame of reference, the first point to be noticed is the elementary one that while the monetary authority fixes the nominal quantity of money, the public determines the quantity of real balances by driving the price level up or down until the real value of the given nominal money stock is what the public is content to hold. Since any nominal stock can provide any desired real stock through appropriate price-level adjustment, it obviously makes no sense to ask whether there is an optimal money supply, if ‘money supply’ is interpreted as it should be in terms of the nominal money supply that the authorities in fact control. The question has to be posed in terms of the real money supply. In fact there are two questions. First, is there an optimal real quantity of money generally different from what will be established by the actions of the public? Second, given that the monetary authorities cannot alter the real quantity of money directly by altering the nominal quantity of it, how can they alter it indirectly and what policy should they follow to establish the optimum quantity of real balances? To comprehend these two issues, the title question would better have been phrased ‘Is there an optimal money supply policy?’
This compound question can be approached from two different angles: by the construction and exploration of a model of a monetary economy, and by a welfare analysis of the existing monetary arrangements of actual economies. I begin with the former.
The simplest type of monetary model to construct is one that employs a non-interest-bearing fiat money – assumed costless to create – as a medium of exchange and store of value. The use of money, as contrasted with barter, must be motivated somehow – a point on which Tobin’s important writings in this area can be faulted. Writers in the Chicago tradition of monetary theory – Friedman, Levhari–Patinkin and myself, among others – have recognized but bypassed this issue (the transition from a barter to a monetary economy) by treating money as both a consumer’s good yielding a flow of services contributing to utility and a producers’ good (an inventory) contributing to output.
Any problem of sub-optimality in the working of a competitive system can be put in terms of a divergence of private from social cost, or of the presence of externalities. In the fiat money model, sub-optimality of the stock of real balances arises from the fact that while by assumption money can be created at zero social cost, to the holder it has an alternative opportunity cost given by the yield on capital; hence less of it will be held than the socially optimal quantity, which would equate the marginal utility yield of money to consumers and the marginal productivity yield to producers to zero. Friedman has recently produced a suggestive supplementary explanation in terms of externalities: in order to accumulate extra cash balances the individual must forgo real resources; but these resources accrue to his fellow citizens through a (negligible) temporary fall in the price level, and do not constitute a social cost.
To attain optimality, it is necessary to provide a yield on real balances equal to the yield on real capital, in order to equate the marginal utility and productivity yields of money to zero and thus ‘satiate the demand for real balances’. One way of doing this would be to pay interest on money equal to the real rate of return on real capital, financed by the usual hypothetical non-distorting lump-sum taxes. (As will be apparent immediately, this policy would have to be accompanied by a policy of monetary growth ensuring stability of prices over time.) An alternative possibility arises from the fact that, apart from their explicit zero nominal yield, in an economy in which inflation or deflation is going on and is fully anticipated, holders of cash balances knowingly bear a cost or enjoy a return from holding them equal to the expected (and actual) rate of inflation or deflation respectively. Hence, by providing a rate of monetary growth (or contraction) that will produce a rate of price deflation equal to the rate of return on real assets, the monetary authority can achieve the optimum stock of real balances. An alternative way of putting this point, for an economy containing bonds bearing a monetary rate of interest, is that formulated by Friedman, that monetary policy should aim at making the monetary rate of interest zero. In a growth model in which government simultaneously establishes a savings ratio consistent with the golden rule, as Patinkin and Levhari have shown, the appropriate monetary policy simplifies to keeping the money supply constant (since the rate of interest is equal to the rate of growth of output in golden-rule conditions).
Both the payment of explicit interest on money, and the control of the behaviour of the nominal money stock over time, can and should be regarded as monetary policies. Hence there are two alternative policies available for achieving the optimum stock of real balances at every point in time – and of course these can be mixed in any desired proportion. In fact they are the extremes of the menu of possible mixtures: no deflation and an explicit rate of interest on money equal to the return on real capital, and no interest on money and deflation at a rate equal to the return on real capital. The possibility of achieving optimality of the money stock through interest payments as well as through deflation has generally been recognized as an afterthought in the literature, but put in the context of the difference between a competitive inside-money system and an outside-money system. As Pesek and Saving and I have shown, however, the difference essential for monetary theory is not between inside and outside money, but between non-interest-bearing and competitive interest-bearing money. There is, though, a serious practical problem about how to arrange interest payments on currency, a problem to which I shall return.
The alternative approach to the question of optimal money supply is through the welfare analysis of existing national monetary arrangements. These can be thought of, if we set aside the conventional conception of the government as something apart from its electorate that has been developed to justify the treatment of government liabilities to the public as ‘outside money’ and hence to give empirical relevance to the Pigou effect, as an inside-money system with certain distortions from the conditions of competitive optimality. Specifically, through its monopoly of legal tender, the government is able to force holders of currency to make it interest-free loans; similarly, through its monopoly of central banking, the government is able to force commercial bank holders of central bank deposits to make an interest-free loan directly to the central bank and indirectly to itself. Alternatively, the government is able through monopoly to impose a tax on the holding of these assets. To the extent that the prohibition of explicit interest on demand deposits is effective (which is doubtful), the government also levies a tax on deposit-holders for the benefit of the banks. It also taxes deposit-holders indirectly through other regulations and restrictions falling on banks and on bank entry. All these taxes imply sub-optimization of the stock of real balances held, by comparison with a situation in which commercial banks were free to compete for deposits (and obliged to do so by freedom of entry) and in which government paid commercial rates of interest on currency and on commercial bank deposits at the Federal Reserve. (The Federal Reserve could still control the nominal money supply in these circumstances.)
Elimination of restrictions and regulations and the payment of competitive interest rates on government and central bank obligations would achieve optimality of the real-money stock, as in the fiat-money model. The practical difficulty, which in this context is obviously practical and not introduced by extraneous assumption, is how to arrange payment of interest on government-issued currency. Presumably interest could be paid on the banks’ vault cash, on the basis of average or daily figures; the problem is to devise a method of paying interest on the public’s holdings of currency. Friedman has suggested giving the banks permission to compete in the issuance of notes – as they used to do before the Bank Charter Act of 1844 in the United Kingdom and the National Banking Act of 1863 in the United States – and leaving them to figure out the technicalities of how to pay interest on such notes.
The alternative, as in the theoretical model, would be to manage the money supply so as to deflate prices at the rate required to make the money rate of interest zero, thus eliminating the monopoly profits now accruing to government, the central bank and (possibly) the commercial banks. This is the policy recently recommended by Friedman, even though he has both to recognize the political and economic difficulties entailed in such a potentially major change from the present situation of price inflation (‘potentially major’ because he presents alternative calculations involving quite different rates of price deflation) and to admit to some embarrassment in reconciling this recommendation with his long-standing record of recommending pursuit of a monetary policy (adoption of a monetary rule) that would guarantee price stability. I would agree with Friedman that the step from monetary policy as presently conducted to a policy ensuring price stability is more potentially beneficial than the further step to a policy of price deflation at the appropriate rate; but I would argue further, against his general thesis, that if the steps that could feasibly be taken towards the establishment of competitive interest payments on money were in fact taken, there would probably be little further gain to be had from instituting the appropriate rate of price deflation.
It seems to me irrational to accept institutional arrangements that lead to economic inefficiency on the one hand, and on the other hand to try to persuade government to manipulate the growth of the money supply so as to offset the inefficiencies that result. Either government is unaware of the inefficiencies its practices cause, in which case it should be possible to persuade it to change those practices, specifically to terminate the prohibition of interest payments on demand deposits, to pay interest on reserve deposits of commercial banks at the Federal Reserve and on vault cash, and possibly to seek means of paying interest on the public’s currency holdings. Or government is quite aware that it makes a profit out of these practices, and is determined to hold onto it, in which case, as controller of the behaviour of the money supply, it will certainly not act so as to deprive itself of those profits.
Assuming that government could be persuaded to eliminate the obviously and easily remediable institutional sources of inefficiency in the money supply – prohibition of interest on commercial bank demand deposits, non-payment of interest on commercial bank deposits at the Federal Reserve and on commercial bank cash – the remaining source of inefficiency in the provision of money (assuming for the moment the maintenance of price stability) would be the non-payment of interest on currency. Here there would be a double source of inefficiency: under present arrangements the holder of currency receives no interest but bears none of the costs of printing and minting required to create and to maintain the currency stock, whereas under efficient arrangements he would receive competitive interest on his bank deposit but pay charges for using bank money for payments. There would thus be incentives to economize on currency holding but to use currency rather than cheques for making payments.
Would the resulting welfare losses be sufficient to justify the adoption of a policy of deflating prices at the current rate of return on capital in order to avoid them? It seems very doubtful, though it may be worth someone’s while to quantify. (With currency in circulation among the public running at about 5 per cent of GNP, and the elasticity of substitution between currency and interest-bearing bank deposits probably rather low, the welfare loss calculated on Friedman’s lines would probably be a negligible fraction of national income.) The answer would be even more doubtful if, following Friedman’s suggestion, commercial banks were allowed to experiment with the issue of interest-bearing notes.
As a digression on the question of interest-bearing currency, it should not be too difficult to devise it – any more than it has been difficult for the banks to develop new instruments such as certificates of deposit permitting them to pay higher interest on large savings deposits than on the ordinary savings deposits. In the early nineteenth century, after all, bills of exchange used to circulate in the north of England in place of money. Presumably banks would offer interest only on the higher denominations of notes, choose face values so that interest could be expressed as a gain in value of so many cents per week, and affix a maturity date so that if they overestimated the interest rate they could pay the holder could not extract indefinite ransom. (Actually, a return of so many cents per week would be a declining rate of weekly interest, so that this problem would take care of itself if the cents offered per week were constant.)
The payment of competitive interest on money, then, is one way of achieving the optimal money supply. Yet this proposition has recently encountered considerable opposition from monetary theorists. This opposition I believe to be mistaken.
One source of criticism is to be found in Pesek and Saving’s book on Money, Wealth, and Economic Theory, wherein it is argued that the essential characteristic of money is its non-interest-bearingness, and that if money were to bear interest it would cease to be used as money. One basis of this argument is a confusion between the two notions (i) that if banks were permitted to compete with each other in supplying socially costless money, they would expand the nominal money supply until its purchasing power fell to zero, and (ii) that if they were allowed to compete with each other in supplying money within some overall constraint on the total quantity supplied, they would drive the rate of interest paid on deposits up to a level competitive with other yields, thereby reducing the value of the marginal liquidity services of money to zero. Another is the idea that if money had a yield people would not forgo that yield for the sake of purchasing goods and services – an obvious fallacy since the function of all asset-holding is to carry purchasing power forwards through time, and this implies no desire to hold forever an asset once acquired.
Another line of criticism focuses on the vagueness of the explanation of the function of money in a monetary economy, already mentioned in connection with writers in the Chicago tradition and perhaps even more characteristic of writers in the Keynesian tradition, and specifically on the possibility that the holding of a larger (optimum) quantity of real balances induced by the payment of interest on money may introduce an offsetting waste of resources through efforts to economize on the use of money in effecting transactions. This criticism was raised vehemently by Robert Clower, in connection with an effort by Paul Samuelson to state ‘What Classical and Neoclassical Monetary Theory Really Was’. Samuelson’s restatement was admittedly faulty; but Clower has apparently recanted on his belief that there is something seriously wrong with the argument outlined above.
The issue can be put most clearly in terms of the Baumol–Tobin model of transactions demand for cash. That model assumes that transactions from money into goods occur in an even flow over time, and are costless. Holding all one’s income in the form of money for the purposes of effecting this flow of transactions, however, means losing interest; money can be converted into interest-bearing assets and back again, but there is both a fixed and a proportional cost per such transaction; because of the fixed cost, there will be an optimum frequency of conversions of assets into cash and an optimum proportional cash balance holding varying inversely with income and the rate of interest on earning assets. Optimality would be achieved by paying interest on cash balances and so eliminating the real costs of conversions between cash and securities.
Now assume instead that there is no interest on cash, and that conversion of money into goods has both a fixed and a proportional cost. That is, there is an overhead time and real resource cost of going to the supermarket, and a time cost per item of shopping. These would indicate one trip per pay period; but there is also a storage cost proportional to their value on the holding of stocks of goods, which can be reduced by making more trips to market and holding a lower average stock of goods. Hence there is a total-cost-minimizing stock of goods in storage and of cash in hand.
It would appear that the payment of interest on money, by raising the alternative opportunity cost of holding stocks of goods, would reduce average stocks and so increase the real resources used in making trips to the supermarket, thereby wasting resources by comparison with the zero-interest-money situation. Hence the ‘optimum quantity of money’ achieved by paying interest on money would appear to be socially sub-optimal when the transactions costs of extra marketing induced by the payment of interest on money are taken into account.
But this conclusion would be correct only if the true social and private alternative opportunity cost of storing goods included only the real resources employed in storage, and not the interest on the resources invested in the stock itself. This is clearly not the case. Both society and the stockholding individual could convert the stocks into explicitly productive capital goods. Hence the storage cost of consumers’ inventories already includes the interest rate, and is not increased by the payment of interest on money; and the payment of interest on money serves as before to eliminate the costs of converting cash into earning assets and vice versa (these costs may be thought of, following Samuelson, as the cost of shoe leather wasted on trips to the bank).
Figure 5.1
This point is illustrated by Figure 5.1, based on the Baumol–Tobin analysis of transactions demand for money. For the purposes of the diagram it is assumed that the individual receives an income per period of 2t, which he receives either in interest-bearing assets or in money; that if he receives assets he earns an interest rate i per period on his average asset holding but he has an overhead charge per withdrawal of B and a proportional charge of 
K per unit of money withdrawn; that shopping involves an overhead cost b per shopping trip and a proportional cost of k per unit monetary value purchased; and that storage of goods (in amount g on the average) involves a proportional real cost of s per period and the interest charge i. If he receives no interest on money, it is assumed that he will choose to be paid in assets; it is also assumed for simplicity, at the cost of full generality, that he will combine trips to convert assets into money with trips to the market to convert money into goods, to avoid interest loss on idle money. His cost curve as a function of his average stock of goods will be C1 and his cost-minimizing average goods stock g1. If, on the other hand, he received interest on money at the same rate as on earning assets, so that he could avoid conversions, his cost-minimizing stock of goods would be g2, smaller than g1. If, incorrectly, the rate of interest were not regarded as a proper social cost of stockholding, and comparison were made between interest-paying and non-interest-paying money, there would be a third curve C3 representing costs of holding stocks of goods excluding any interest-rate cost of stockholding, with a minimum point below and to the right of C2, incorrectly suggesting a social waste from the payment of interest on money.
A final line of criticism contends that payment of competitive interest on money would lead to money’s replacing all other financial assets, and banks replacing all other financial intermediaries. This criticism seems to me quite unconvincing, unless the proposal is misinterpreted to mean that not only is interest to be paid on money, but that the rate is to be uncompetitively high and that no charges are to be made for the use of money in making payments. The recommendation to pay interest on money equal to the rate of return on real capital is to be understood as a shorthand phrase that abstracts from various kinds of transactions and intermediation costs that would be taken account of in a fully competitive banking system.
REFERENCES
R. W. Clower, ‘What Traditional Monetary Theory really Wasn’t’, Canadian Journal of Economics, Vol. 2, No. 2 (May, 1969), pp. 299–302.
‘On the Technology of Monetary Exchange’ (Mimeograph for the Southern Economic Association, 1969).
M. Friedman, ‘The Optimum Quantity of Money’, in his The Optimum Quantity of Money and Other Essays (Chicago: Aldine Publishing Co., 1969), Ch. 1, pp. 1–50.
H. G. Johnson, ‘Money in a Neo-classical One-sector Growth Model’, in his Essays in Monetary Economics (London: Allen & Unwin, Ch. IV, above, pp. 143–78.
‘Problems of Efficiency in Monetary Management’, Journal of Political Economy Vol. 76, No. 5 (September/October 1968), pp. 971–90.
‘Inside Money, Outside Money, Income, Wealth and Welfare in Contemporary Monetary Theory’, Journal of Money, Credit, and Banking, Vol. 1. No. 1 (February, 1969), pp. 30–45; Ch. VII above.
‘Pesek and Saving’s Theory of Money and Wealth: a comment’, op. cit. Vol. 1, No. 3 (August, 1969), pp. 535–7: Appendix to Ch. VII above.
D. Levhari and D. Patinkin, ‘The Role of Money in a Simple Growth Model’, American Economic Review, Vol. 58, No. 4 (September, 1968), pp. 713–53.
M. Perlman, ‘The Roles of Money in an Economy and the Optimum Quantity of Money’ (Mimeograph, 1969), subsequently published in Economics.
B. P. Pesek and T. R. Saving, Money, Wealth, and Economic Theory (New York: Macmillan, 1967).
P. A. Samuelson, ‘What Classical and Neoclassical Monetary Theory really Was’, Canadian Journal of Economics, Vol. 1, No. 1 (February, 1968), pp. 1–15.
‘Nonoptimality of Money Holdings under Laissez faire’, op. cit., Vol. 2, No. 2 (May, 1969). pp. 303–8.
J. Tobin, ‘Money and Economic Growth’, Econometrica, Vol. 33, No. 4 (October, 1965), pp. 671–84.
‘Notes on Optimal Monetary Growth’, Journal of Political Economy, Vol. 76, No. 4, Pt III (July/August, 1968), 833–59.
* Reprinted from Journal of Finance, Vol. XXV, No. 2 (May 1970), pp. 435–42.