A Tract on Monetary Reform: Chapter III - The Theory of Money and of the Foreign Exchangeby@jmkeynes
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A Tract on Monetary Reform: Chapter III - The Theory of Money and of the Foreign Exchange

by John Maynard KeynesJune 16th, 2022
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The evil consequences of instability in the standard of value have now been sufficiently described. In this chapter 19 we must lay the theoretical foundations for the practical suggestions of the concluding chapters. Most academic treatises on monetary theory have been based, until lately, on so firm a presumption of a gold standard régime that they need to be adapted to the existing régime of mutually inconvertible paper standards.
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A Tract on Monetary Reform, by John Maynard Keynes is part of HackerNoon’s Book Blog Post series. You can jump to any chapter in this book here. Chapter III: The Theory of Money and of the Foreign Exchange


The evil consequences of instability in the standard of value have now been sufficiently described. In this chapter19 we must lay the theoretical foundations for the practical suggestions of the concluding chapters. Most academic treatises on monetary theory have been based, until lately, on so firm a presumption of a gold standard régime that they need to be adapted to the existing régime of mutually inconvertible paper standards.

 Parts of this chapter raise, unavoidably, matters of much greater difficulty to the layman than the rest of the book. The reader whose interest in the theoretical foundations is secondary can pass on.

I. The Quantity Theory of Money

This Theory is fundamental. Its correspondence with fact is not open to question.20 Nevertheless it is often misstated and misrepresented. Goschen’s saying of sixty years ago, that “there are many persons who cannot hear the relation of the level of prices to the volume of currency affirmed without a feeling akin to irritation,” still holds good.

 “The Quantity Theory is often defended and opposed as though it were a definite set of propositions that must be either true or false. But in fact the formulæ employed in the exposition of that theory are merely devices for enabling us to bring together in an orderly way the principal causes by which the value of money is determined” (Pigou).

The Theory flows from the fact that money as such has no utility except what is derived from its exchange-value, that is to say from the utility of the things which it can buy. Valuable articles other than money have a utility in themselves. Provided that they are divisible and transferable, the total amount of this utility increases with their quantity;—it will not increase in full proportion to the quantity, but, up to the point of satiety, it does increase.

If an article is used for money, such as gold, which has a utility in itself for other purposes, aside from its use as money, the strict statement of the theory, though fundamentally unchanged, is a little complicated. In present circumstances we can excuse ourselves this complication. A Currency Note has no utility in itself and is completely worthless except for the purchasing power which it has as money.

Consequently what the public want is not so many ounces or so many square yards or even so many £ sterling of currency notes, but a quantity sufficient to cover a week’s wages, or to pay their bills, or to meet their probable outgoings on a journey or a day’s shopping. When people find themselves with more cash than they require for such purposes, they get rid of the surplus by buying goods or investments, or by leaving it for a bank to employ, or, possibly, by increasing their hoarded reserves. Thus the number of notes which the public ordinarily have on hand is determined by the amount of purchasing power which it suits them to hold or to carry about, and by nothing else. The amount of this purchasing power depends partly on their wealth, partly on their habits. The wealth of the public in the aggregate will only change gradually. Their habits in the use of money—whether their income is paid them weekly or monthly or quarterly, whether they pay cash at shops or run accounts, whether they deposit with banks, whether they cash small cheques at short intervals or larger cheques at longer intervals, whether they keep a reserve or hoard of money about the house—are more easily altered. But if their wealth and their habits in the above respects are unchanged, then the amount of purchasing power which they hold in the form of money is definitely fixed. We can measure this definite amount of purchasing power in terms of a unit made up of a collection of specified quantities of their standard articles of consumption or other objects of expenditure; for example, the kinds and quantities of articles which are combined for the purpose of a cost-of-living index number. Let us call such a unit a “consumption unit” and assume that the public require to hold an amount of money having a purchasing power over k consumption units. Let there be n currency notes or other forms of cash in circulation with the public, and let p be the price of each consumption unit (i.e. p is the index number of the cost of living), then it follows from the above that n = pk. This is the famous Quantity Theory of Money. So long as k remains unchanged, n and p rise and fall together; that is to say, the greater or the fewer the number of currency notes, the higher or the lower is the price level in the same proportion.

So far we have assumed that the whole of the public requirement for purchasing power is satisfied by cash, and on the other hand that this requirement is the only source of demand for cash; neglecting the fact that the public, including the business world, employ for the same purpose bank deposits and overdraft facilities, whilst the banks must for the same reason maintain a reserve of cash. The theory is easily extended, however, to cover this case. Let us assume that the public, including the business world, find it convenient to keep the equivalent of k consumption units in cash and of a further k´ available at their banks against cheques, and that the banks keep in cash a proportion r of their potential liabilities (k´) to the public. Our equation then becomes

n = p(k + rk´).

So long as k, k´, and r remain unchanged, we have the same result as before, namely, that n and p rise and fall together. The proportion between k and k´ depends on the banking arrangements of the public; the absolute value of these on their habits generally; and the value of r on the reserve practices of the banks. Thus, so long as these are unaltered, we still have a direct relation between the quantity of cash (n) and the level of prices (p).21

 My exposition follows the general lines of Prof. Pigou (Quarterly Journal of Economics, Nov. 1917) and of Dr. Marshall (Money, Credit, and Commerce, I. iv.), rather than the perhaps more familiar analysis of Prof. Irving Fisher. Instead of starting with the amount of cash held by the public, Prof. Fisher begins with the volume of business transacted by means of money and the frequency with which each unit of money changes hands. It comes to the same thing in the end and it is easy to pass from the above formula to Prof. Fisher’s; but the above method of approach seems less artificial than Prof. Fisher’s and nearer to the observed facts.

We have seen that the amount of k and k´ depends partly on the wealth of the community, partly on its habits. Its habits are fixed by its estimation of the extra convenience of having more cash in hand as compared with the advantages to be got from spending the cash or investing it. The point of equilibrium is reached where the estimated advantages of keeping more cash in hand compared with those of spending or investing it about balance. The matter cannot be summed up better than in the words of Dr. Marshall:

“In every state of society there is some fraction of their income which people find it worth while to keep in the form of currency; it may be a fifth, or a tenth, or a twentieth. A large command of resources in the form of currency renders their business easy and smooth, and puts them at an advantage in bargaining; but on the other hand it locks up in a barren form resources that might yield an income of gratification if invested, say, in extra furniture; or a money income, if invested in extra machinery or cattle.” A man fixes the appropriate fraction “after balancing one against another the advantages of a further ready command, and the disadvantages of putting more of his resources into a form in which they yield him no direct income or other benefit.” “Let us suppose that the inhabitants of a country, taken one with another (and including therefore all varieties of character and of occupation), find it just worth their while to keep by them on the average ready purchasing power to the extent of a tenth part of their annual income, together with a fiftieth part of their property; then the aggregate value of the currency of the country will tend to be equal to the sum of these amounts.”22

 Money, Credit, and Commerce, I. iv. 3. Dr. Marshall shows in a footnote as follows that the above is in fact a development of the traditional way of considering the matter: “Petty thought that the money ‘sufficient for’ the nation is ‘so much as will pay half a year’s rent for all the lands of England and a quarter’s rent of the Houseing, for a week’s expense of all the people, and about a quarter of the value of all the exported commodities.’ Locke estimated that ‘one-fiftieth of wages and one-fourth of the landowner’s income and one-twentieth part of the broker’s yearly returns in ready money will be enough to drive the trade of any country.’ Cantillon (a.d. 1755), after a long and subtle study, concludes that the value needed is a ninth of the total produce of the country; or, what he takes to be the same thing, a third of the rent of the land. Adam Smith has more of the scepticism of the modern age and says: ‘it is impossible to determine the proportion,’ though ‘it has been computed by different authors at a fifth, at a tenth, at a twentieth, and at a thirtieth part of the whole value of the annual produce.’” In modern conditions the normal proportion of the circulation to this national income seems to be somewhere between a tenth and a fifteenth.

So far there should be no room for difference of opinion. The error often made by careless adherents of the Quantity Theory, which may partly explain why it is not universally accepted, is as follows.

Every one admits that the habits of the public in the use of money and of banking facilities and the practices of the banks in respect of their reserves change from time to time as the result of obvious developments. These habits and practices are a reflection of changes in economic and social organisation. But the Theory has often been expounded on the further assumption that a mere change in the quantity of the currency cannot affect k, r, and k´,—that is to say, in mathematical parlance, that n is an independent variable in relation to these quantities. It would follow from this that an arbitrary doubling of n, since this in itself is assumed not to affect k, r, and k´, must have the effect of raising p to double what it would have been otherwise. The Quantity Theory is often stated in this, or a similar, form.

Now “in the long run” this is probably true. If, after the American Civil War, the American dollar had been stabilised and defined by law at 10 per cent below its present value, it would be safe to assume that n and p would now be just 10 per cent greater than they actually are and that the present values of k, r, and k´ would be entirely unaffected. But this long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is long past the ocean is flat again.

In actual experience, a change of n is liable to have a reaction both on k and k´ and on r. It will be enough to give a few typical instances. Before the war (and indeed since) there was a considerable element of what was conventional and arbitrary in the reserve policy of the banks, but especially in the policy of the State Banks towards their gold reserves. These reserves were kept for show rather than for use, and their amount was not the result of close reasoning. There was a decided tendency on the part of these banks between 1900 and 1914 to bottle up gold when it flowed towards them and to part with it reluctantly when the tide was flowing the other way. Consequently, when gold became relatively abundant they tended to hoard what came their way and to raise the proportion of the reserves, with the result that the increased output of South African gold was absorbed with less effect on the price level than would have been the case if an increase of n had been totally without reaction on the value of r.

In agricultural countries where peasants readily hoard money, an inflation, especially in its early stages, does not raise prices proportionately, because when, as a result of a certain rise in the price of agricultural products, more money flows into the pockets of the peasants, it tends to stick there;—deeming themselves that much richer, the peasants increase the proportion of their receipts that they hoard.

Thus in these and in other ways the terms of our equation tend in their movements to favour the stability of p, and there is a certain friction which prevents a moderate change in n from exercising its full proportionate effect on p.

On the other hand a large change in n, which rubs away the initial friction, and especially a change in n due to causes which set up a general expectation of a further change in the same direction, may produce a more than proportionate effect on p. After the general analysis of Chapter I. and the narratives of catastrophic inflations given in Chapter II., it is scarcely necessary to illustrate this further,—it is a matter more readily understood than it was ten years ago. A large change in p greatly affects individual fortunes. Hence a change after it has occurred, or sooner in so far as it is anticipated, may greatly affect the monetary habits of the public in their attempt to protect themselves from a similar loss in future, or to make gains and avoid loss during the passage from the equilibrium corresponding to the old value of n to the equilibrium corresponding to its new value. Thus after, during, and (so far as the change is anticipated) before a change in the value of n, there will be some reaction on the values of k, k´, and r, with the result that the change in the value of p, at least temporarily and perhaps permanently (since habits and practices, once changed, will not revert to exactly their old shape), will not be precisely in proportion to the change in n.

The terms inflation and deflation are used by different writers in varying senses. It would be convenient to speak of an increase or decrease in n as an inflation or deflation of cash; and of a decrease or increase in r as an inflation or deflation of credit. The characteristic of the “credit-cycle” (as the alternation of boom and depression is now described) consists in a tendency of k and k´ to diminish during the boom and increase during the depression, irrespective of changes in n and r, these movements representing respectively a diminution and an increase of “real” balances (i.e. balances, in hand or at the bank, measured in terms of purchasing power); so that we might call this phenomenon deflation and inflation of real balances.

It will illustrate the “Quantity Theory” equation in general and the phenomena of deflation and inflation of real balances in particular, if we endeavour to fill in actual values for our symbolic quantities. The following example does not claim to be exact and its object is to illustrate the idea rather than to convey statistically precise facts. October 1920 was about the end of the recent boom, and October 1922 was near the bottom of the depression. At these two dates the figures of price level (taking October 1922 as 100), cash circulation (note circulation plus private deposits at the Bank of England23), and bank deposits in Great Britain were roughly as follows:

 It would take me too far from the immediate matter in hand to discuss why I take this definition of “cash” in the case of Great Britain. It is discussed further in Chapter V. below.

 Price Level.Cash Circulation.Bank Deposits.

October 1920150£585,000,000£2,000,000,000

October 1922100£504,000,000£1,700,000,000

The value of r was not very different at the two dates—say about 12 per cent. Consequently our equation for the two dates works out as follows24:

October 1920n = 585p = 1·5k = 230k´ = 1333

October 1922n = 504p = 1   k = 300k´ = 1700

 For 585 = 1·5(230 + 1333 × ·12), and 504 = 1(300 + 1700 × ·12).

Thus during the depression k rose from 230 to 300 and k´ from 1333 to 1700, which means that the cash holdings of the public at the former date were worth 23/30, and their bank balances 1333/1700, what they were worth at the latter date. It thus appears that the tendency of k and k´ to increase had more to do, than the deflation of “cash” had, with the fall of prices between the two periods. If k and k´ were to fall back to their 1920 values, prices would rise 30 per cent without any change whatever in the volume of cash or the reserve policy of the banks. Thus even in Great Britain the fluctuations of k and k´ can have a decisive influence on the price level; whilst we have already seen (pp. 51, 52) how enormously they can change in the recent conditions of Russia and Central Europe.

The moral of this discussion, to be carried forward in the reader’s mind until we reach Chapters IV. and V., is that the price level is not mysterious, but is governed by a few, definite, analysable influences. Two of these, n and r, are under the direct control (or ought to be) of the central banking authorities. The third, namely k and k´, is not directly controllable, and depends on the mood of the public and the business world. The business of stabilising the price level, not merely over long periods but so as also to avoid cyclical fluctuations, consists partly in exercising a stabilising influence over k and k´, in so far as this fails or is impracticable, in deliberately varying n and r so as to counterbalance the movement of k and k´.

The usual method of exercising a stabilising influence over k and k´ especially over k´, is that of bank-rate. A tendency of k´ to increase may be somewhat counteracted by lowering the bank-rate, because easy lending diminishes the advantage of keeping a margin for contingencies in cash. Cheap money also operates to counterbalance an increase of k´, because, by encouraging borrowing from the banks, it prevents r from increasing or causes r to diminish. But it is doubtful whether bank-rate by itself is always a powerful enough instrument, and, if we are to achieve stability, we must be prepared to vary n and r on occasion.

Our analysis suggests that the first duty of the central banking and currency authorities is to make sure that they have n and r thoroughly under control. For example, so long as inflationary taxation is in question n will be influenced by other than currency objects and cannot, therefore, be fully under control; moreover, at the other extreme, under a gold standard n is not always under control, because it depends on the unregulated forces which determine the demand and supply of gold throughout the world. Again, without a central banking system r will not be under proper control because it will be determined by the unco-ordinated decisions of numerous different banks.

At the present time in Great Britain r is very completely controlled, and n also, so long as we refrain from inflationary finance on the one hand and from a return to an unregulated gold standard on the other. The second duty of the authorities is therefore worth discussing, namely, the use of their control over n and r to counterbalance changes in k and k´. Even if k and k´ were entirely outside the influence of deliberate policy, which is not in fact the case, nevertheless p could be kept reasonably steady by suitable modifications of the values of n and r.

 In the case of the United States the same thing is more or less true, so long as the Federal Reserve Board is prepared to incur the expense of bottling up redundant gold.

Old-fashioned advocates of sound money have laid too much emphasis on the need of keeping n and r steady, and have argued as if this policy by itself would produce the right results. So far from this being so, steadiness of n and r, when k and k´ are not steady, is bound to lead to unsteadiness of the price level. Cyclical fluctuations are characterised, not primarily by changes in n or r, but by changes in k and k´. It follows that they can only be cured if we are ready deliberately to increase and decrease n and r, when symptoms of movement are showing in the values of k and k´. I am being led, however, into a large subject beyond my immediate purpose, and am anticipating also the topic of Chapter V.87 These hints will serve, nevertheless, to indicate to the reader what a long way we may be led by an understanding of the implications of the simple Quantity equation with which we started.

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Keynes, John Maynard. 2021. A Tract on Monetary Reform. Urbana, Illinois: Project Gutenberg. Retrieved May 2022 from

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