- Keynes’s Fundamental Equations From The Treatise on Money (by Professor of political economy at Concordia university, Montréal)
※ 발췌 / excerpts of which: Book Ⅲ, The Fundamental Equations of Money,
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Chapter 10. The Fundamental Equations for the Value of Money (p. 133)
The Fundamental Problem of Monetary Theory is not merely to establish identities or statistical equations relating (e.g.) the turnover of monetary instruments to the turnover of things traded for money. The real task of such a Theory is to treat the problem dynamically, analysing the different elements involved, in such a manner as to exhibit the causal process by which the price-level is determined, and the method of transition from one position of equilibrium to another.
The forms of the Quantity Theory, however, on which we have all been brought upㅡI shall give an account of them in detail in Chapter 14ㅡare but ill adapted for this purpose. They are particular examples of the numerous identities which can be formulated connecting different monetary factors. But they do not, any of them, have the advantages of separating out those factors through which, in a modern economic system, the causal process actually operates during a period of change.
Moreover, they have a further fault, in that the standard, to which they apply, is neither the Labour Standard nor the Purchasing Power Standard, but some other, more or less artificial, standard, namely, either the Cash-Transactions Standard or the Cash-Balances Standard, as defined in Chapter 6 above. This is a serious fault, because it must be the two former standards which are our true quaesita. For the Labour Power of Money and the Purchasing Power of Money are fundamental in a sense in which price-levels based on other types of expenditure are not. Human efforts and human consumption are the ultimate matters from which alone economic transactions are capable of deriving any significance; and all other forms of expenditure only acquire importance from their having some relationship, sooner or later, to the effort of producers or to the expenditure of consumers.
I propose, therefore, to break away from the traditional method of setting out from the total quantity of money irrespective of the purposes on which it is employed, and to start insteadㅡfor reasons which will become clear as we proceedㅡwith the flow of the community's earnings or money-income, and with its twofold division (1) into the parts which have been earned by the production of consumption-goods and of investment-goods respectively, and (2) into the parts which are expended on consumption-goods and on savings respectively.
We shall find that, if the first of these divisions of the community's income is in the same proportion as the second, i.e. if the output measured in cost of production is divided between consumption-goods and investment-goods in the same proportion as expenditure is divided between current consumption and savings, then the price-level of consumption-goods will be in equilibrium with their cost of production. But if the proportionate divisions are not the same in the two cases, then the price-level of consumption-goods will differ from their cost of production.
The price-level of investment-goods, on the other hand, depends on a different set of considerations, which we shall come to later.
(1) The Fundamental Equations for the Value of Money (p. 135)
 Let [:]
- E be the total money-income, or Earnings of the community in a unit of time,
- I' the part of it which has been earned by the production of investment-goods,
- so that I' measures the cost of production of new investment and E－I' the cost of production of the current output of consumption-goods.
- S be the amount of Savings as defined above[Chapter 9],
- so that E－S measures the current expenditure of income on consumption-goods.
- O be the total output of goods in terms of these units in a unit of time,
- R the volume of liquid Consumption-goods and Services flowing on to the market and purchased by consumers,
- and C the net increment of Investment, in the sense that O＝R＋C.
- P.R represents the current expenditure on consumption-goods [※ R을 매출＝산출물 가치로 간주, P.R＝E.R/O]
- and E.C/O ( ＝I' ) is the cost of production of new investment. [※ C를 비용(＝?요소소득)으로 간주, E.C/O＝I']
since the expenditure of the community on consumption goods is equal to the difference between its income and its savings, we have
P.R ＝ E－S ＝ E/O(R＋C)－S
＝ E/O.R＋I'－S [by way of E.C/O＝I'] ; or
P ＝ E/O ＋ (I'－S)/R , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (ⅰ)
which is the first of our Fundamental Equations. Let [:]
- W be the rate of earnings per unit of human effort (so that the inverse of W measures the Labour Power of Money),
- W1 the rate of earnings per unit of output, i.e. the rate of efficiency-earnings,
- and e the coefficient of efficiency (so that W＝e.W1). [※ W1이 산출물 단위당 소득금액이므로 E＝W1.O ]
P [＝E/O＋(I'－S)/R] ＝ W1 ＋ (I'－S)/R . . . . . . . . . . . . . . . . (ⅱ)[Therefore,]
＝ 1/e.W ＋ (I'－S)/R . . . . . . . . . . . . . . (ⅲ)
The price-level of consumption-goods (i.e. the inverse of the purchasing power of money) [, P,] is made up, therefore, of two terms, (1) the first of which represents the level of efficiency-earnings, i.e. the cost of production, and (2) the second of which is positive, zero or negative, according as the cost of new investment exceeds, equals or fall short of the volume of current savings. It follows that the stability of the purchasing power of money involves the two conditionsㅡ [:]
- that efficiency-earnings should be constant
- and that the cost of new investment should be equal to the volume of current savings.
Thus the price-level, as determined by the first term[?the second term, or maybe ?the first of the FE], is upset by the fact that the division of the output between investment and goods for consumption is not necessarily the same as the division of the income between savings and expenditure on consumption. For[:]
- [1. regarding division of income: ] workers are paid just as much when they are producing for investment as when they are producing for consumption; but having earned their wages, it is they who please themselves whether they spend or refrain from spending them on consumption.
- Meanwhile,[2: regarding division of output: ] the entrepreneurs have been deciding quite independently in what proportions they shall produce the two categories of output.
The reader will observe that the price-level of consumption-goods is entirely independent of the price-level of investment-goods. Given the level of efficiency wages and the difference between the cost of new investment-goods (as distinguished from their selling price) and the volume of saving, the price-level of consumption-goods is unequivocally determined, quite irrespective of the price-level of investment goods.
This latter price-level depends, as we have stated above, on a different set of considerations, which we will examine in Section (ⅲ) of this Chapter. Meanwhile, if we may be allowed to assume the price-level of new investment-goods as given, we can obtain a formula as follows for the price-level of output as a whole.
- P' be the price-level of new investment-goods,
- Π the price-level of output as a whole, and
- I (＝P'.C) the value (as distinguished from I', the cost of production) of the increment of new investment goods.
Π ＝ (P.R＋P'.C)/O ＝ ((E－S)＋I)/O
＝ E/O ＋ (I－S)/O , . . . . . . . . . . . . . . . . . (ⅳ)
which is the second of our Fundamental Equations.As before, we can re-write Equation (ⅳ):
Π ＝ W1 ＋ (I－S)/O . . . . . . . . . . . . . . . . . . . (ⅴ)
＝ 1/e.W ＋ (I－S)/O . . . . . . . . . . . . . . . . . (ⅵ)
(2) The Characteristics of Profit (p. 137)
Next, let Q1 be the amount of the profit (defined as above) on the production and sale of consumption-goods, and Q2 the corresponding profit on investment-goods, and Q the total profit.
Q1 ＝P.R－E/O.R [※? P는 매출=산출물 가치(가격), E/O(?E)는 비용=요소가격]
＝(E－S)－(E－I') ＝ I'－S ; . . . . . . . (ⅶ)and, since Q2 ＝ I－I',
Q ＝ Q1＋Q2 ＝ I－S . . . . . . . . . . . . . . (ⅷ)
- the profits on the production and sale of consumption-goods are equal to the difference between the cost of new investment[I'] and savings[S], being negative when savings exceed the cost of new investment;
- and the total profits on output as a whole are equal to the difference between the value of new investment[I] and savings[S], being negative when savings exceed the value of new investment.
It follows from the above that we can we-write Equations (ⅱ) and (ⅴ):
P [＝W1＋(I'－S)/R] ＝ W1＋Q1/R , . . . . . . . . . . (ⅸ)
Π [＝W1 ＋ (I－S)/O] ＝ W1＋Q/O . . . . . . . . . . (ⅹ)
These equations tells us that the price of consumption-goods is equal to the rate of earnings of the factors of production plus the rate of profits per unit of output of consumption-goods ; and correspondingly with output as a whole.
These conclusions are, of course, obvious and may serve to remind us that all these equations are purely formal; they are mere identities; truisms which tell us nothing in themselves. In this respect, they resemble all other versions of the Quantity Theory of Money. Their only point is to analyse and arrange our material in what will turn out to be a useful way for tracing cause and effect, when we have vitalised them by the introduction of extraneous facts from the actual world.
There is one peculiarity of profits (or losses) which we may note in passing, because it is one of the reasons why it is necessary to segregate them from income proper, as a category apart.
- If entrepreneurs choose to spend a portion of their profits on consumption (and there is, of course, nothing to prevent them from doing this), the effect is to increase the profit on the sale of liquid consumption-goods by an amount exactly equal to the amount of profits which have been thus expended. This follows from our definitions, because such expenditure constitutes a diminution of saving, and therefore an increase in the difference between I' and S. Thus, however much of their profits entrepreneurs spend on consumption, the increment of wealth belonging to entrepreneurs remains the same as before. Thus profits, as a source of capital increment for entrepreneurs, are a widow's cruise which remains undepleted however much of them may be devoted to riotous living.
- When, on the other hand, entrepreneurs are making losses, and seek to recoup these losses by curtailing their normal expenditure on consumption, i.e. by saving more, the cruise becomes a Danaid jar which can never be filled up; for the effect of this reduced expenditure is to inflict on the producers of consumption-goods a loss of an equal amount. Thus the diminution of their wealth, as a class, is as great, in spite of their savings, as it was before.
Since the volume of the public's savings, plus the profits (or minus the losses) of entrepreneurs turning out liquid consumption-goods, is always exactly equal to the cost of production of investment-goods[S＋Q1＝I'], does it follow that investment-goods must always sell at a price equal to their cost of production?
Noㅡfor the reason that if investment-goods sell at a price above (or below) their cost of production, the resulting profit (or loss) to entrepreneurs producing investment-goods necessarily provides the difference between the selling price of the investment-goods, whatever this may be, and their actual cost of production. Thus whatever the price-level of investment-goods, the amount forthcoming for their purchase, out of current savings augmented by the profits or diminished by the losses on current production, will be exactly equal to their value.
 If entrepreneurs producing investment-goods are spending part of their profits on consumption, this must necessarily mean that entrepreneurs producing liquid consumption-goods will have an extra profit accruing to them available for the purchase of investment-goods; so that the net result is the same as if the entrepreneurs producing investment-goods were spending these profits on the purchase of investment-goods.
The question, what does determine the price of new investment-goods, we shall consider in a moment. Our present conclusion is, [:]
- in the first place, that profits (or losses) are an effect of the rest of the situation rather than a cause of it. For this reason it would be anomalous to add profits to (or subtract losses from) income; for, in that case, savings could never fall off, however great the expenditure of the public on current consumption, and equally savings could never be increased by a reduced expenditure on consumption; provided merely that entrepreneurs were continuing to produce the same output of investment-goods as before.
- But, in the second place, profits (or losses) having once come into existence become, as we shall see (for this will be the main topic of several succeeding chapters), a cause of what subsequently ensues; indeed, the mainspring of change in the existing economic system. This is the essential reason why it is useful to segregate them in our Fundamental Equation.
When a man is deciding what proportion of his money-income to save, he is choosing between present consumption and the ownership of wealth. In so far as he decides in favour of consumption, he must necessarily purchase goodsㅡfor he cannot consume money. But in so far as he decides in favour of saving, there still remains a further decision for him to make. For he can own wealth by holding it either in the form of money (or the liquid equivalent of money) or in other forms of loan or real capital. This second decision might be conveniently described as the choice between "hoarding" and "investing", or, alternatively, as the choice between "bank-deposits" and "securities".
 It is difficult to decide what is the most convenient exploitation of existing non-technical language for exact technical meaning. Unfortunately I have already had to use the terms "hoarding" and "investing" with meanings different from the above; for I have defined "hoards" (pp. 128-9) to mean stocks of liquid consumption-goods, and "investing" (p. 126) to mean, not the purchase of securities by members of the public, but the act of the entrepreneur when he makes an addition to the capital of the community. I shall, therefore, use the second set of terms in what follows.There is also a further significant difference between the two types of decision. The decision as to the volume of saving, and also the decision relating to the volume of new investment, relate wholly to current activities. But the decision as to holding bank-deposits or securities relates, not only to the current increment to the wealth of individuals, but also to the whole block of their existing capital. Indeed, since the current increment is but a trifling proportion of the block of existing wealth, it is but a minor element in the matter.
Now when an individual is more disposed than before to hold his wealth in the form of savings-deposits and less disposed to hold it in other forms, this does not mean that he is determined to hold it in the form of savings-deposits ^at all costs^. It means that he favours savings-deposits (for whatever reason) more than before at the existing price-level of other securities. But his distaste for other securities is not absolute and depends on his expectations of the future return to be obtained from savings-deposits and from other securities respectively, which is obviously affected by the price of the latterㅡand also by the rate of interest allowed on the former. If, therefore, the price-level of other securities falls sufficiently, he can be tempted back into them. If, however, the banking system operates in the opposite direction to that of the public and meets the preference of the latter for savings-deposits by buying the securities which the public is ^less^ anxious to hold and creating against them the additional savings-deposits which the public is ^more^ anxious to hold, then there is no need for the price-level of investments to fall at all. Thus the change in the relative attractions of savings-deposits and securities respectively has to be met either by a fall in the price of securities or by an increase in the supply of savings-deposits, or partly by the one and partly by the other. A fall in the price-level of securities is therefore an indication that the "bearishness" of the publicㅡas we may conveniently designate, in anticipation of later chapter, an increased preference for savings-deposits as against other forms of wealth and a decreased preference for carrying securities with money borrowed from the banksㅡhas been insufficiently offset by the creation of savings-deposits by the banking systemㅡor that the "bullishness" of the public has been more than offset by the contraction of savings-deposits by the banking system.
It follows that the actual price-level of investments is the resultant of the sentiment of the public and the behaviour of the banking system. This does not mean that there is any definite numerical relationship between the price-level of investments and the additional quantity of savings-deposits created. The amount by which the creation of a given quantity of deposits will raise the price of other securities above what their price would otherwise have been depends on the shape of the public's demand curve for savings-deposits at different price-levels of other securities.[1 (p. 143)]
There may be also the case, as we shall see in Chapter 14, where "two opinions" develop between different schools of the public, the one favouring bank-deposits more than before and the other favouring securities. In this case the result depends on the willingness of the banking system to act as an intermediary between the two by creating bank-deposits, not against securities, but against liquid short-term advances.
Without forgetting that we are dealing with a case of multiple equilibrium in which each element affects every other element more or less, and without anticipating unduly the subject-matter of Chapter 15, we may sum up the matter thus.
The price-level of investments as a whole, and hence of new investments, is that price-level at which the desire of the public to hold savings-deposits is equal to the amount of savings-deposits which the banking system is willing and able to create. [2 (p. 143)].
On the other handㅡas we have already seenㅡthe price-level of consumption-goods, relatively to the cost of production, depends ^solely^ on the resultant of the decisions of the public as to the proportion of their incomes which they save and the decisions of the entrepreneurs as to the proportion of their production which they devote to the output of investment-goodsㅡthough both of these decisions, and particularly the latter, may be partly influenced by the price-level of investment-goods.
It follows that the price-level of output as a whole and the amount of total profit depend on all four factorsㅡ(1) the rate of saving, (2) the cost of new investment, (3) the "bearishness" of the public, (4) the volume of savings-deposits; or, if you like, on the two factorsㅡ(1) the excess of saving over cost of investment, and (2) such excess of bearishness on the part of the public as is unsatisfied by the creation of deposits by the banking system.
Thus given the rate of new investment and the cost of production, the price-level of consumption-goods is solely determined by the disposition of the public towards "saving". And given the volume of savings-deposits created by the banking system, the price-level of investment-goods (whether new or old) is solely determined by the disposition of the public towards "hoarding"  money.
 Using this term, for once, to mean their scale of preference for savings-deposits and other securities at different price-levels of the latter.I hope I have made clear the distinction between the two types of decision which the earning and wealth-owning public is being constantly called on to make. But however clear we may be about the distinction, it is nevertheless difficult to keep the causes and the results of the two types of decision disentangled, since they act and react on one another in a most perplexing way. For the amount of saving and the amount of investment, and consequently the difference between them, partly depend on the price-level of investment-goods relatively to their cost of production; and at the same time the attitude of the public towards savings-deposits and other securities respectively may be partly influenced by expectations as to the price-level of consumption-goods relatively to their cost of production. In particular, a change in the disposition of the public towards securities other than savings-deposits, uncompensated by action on the part of the banking system, will be a most potent factor affecting the rate of investment relatively to saving and a cause of disturbance, therefore, to the purchasing power of money.
Nevertheless, although these factors react on one another, the excess-saving factor and the excess-bearish factor[1 (p. 145)] (as perhaps we may call them) are independent in the sense that any degree, positive or negative, of the one is compatible in appropriate attendant circumstances with any degree, positive or negative, of the other.
 i.e. bearishness on the part of members of the public which is not balanced by increased credit creation by the banking system.Before leaving this section it may be well to illustrate further the conclusion stated above, that a fall in the price of consumption-goods due to an excess of saving over investment does not in itselfㅡif it is unaccompanied by any change in the bearishness or bullishness of the public or in the volume of savings-deposits, or if there are compensating changes in these two factorsㅡrequire any opposite change in the price of new investment-goods. For I believe that this conclusion may be accepted by some readers with difficulty.
It follows from the fact that, on the above assumptions, the total value of the investment-goods (new and old) coming on to the market for purchase out of current savings is ^always^ exactly equal to the amount of such savings and is irrespective of the current output of ^new^ investment-goods. For if the value of the new investment-goods is less than the volume of current savings, entrepreneurs as a whole must be making losses exactly equal to the difference. These losses, which represent a failure to receive cash up to expectations from sales of current output, must be financed, and the non-receipt of the expected cash receipts must be somehow made good. The entrepreneurs can only make them good either by reducing their own bank-deposits or by selling some of their other capital assets. The bank-deposits thus released and the securities thus sold are available for, and are exactly equal to, the excess of current savings over the value of new investment.
In the more general case where the public sentiment towards securities or the volume of savings-deposits is changing, then if the extent to which the entrepreneurs have recourse to the expedient of releasing bank-deposits ^plus^ the increase in savings-deposits allowed by the banking system just balances the increase in the desire of the public to employ their resources in bank-deposits, there is no reason for any change in the price of securities. If the former is in excess of the latter, the price of securities will tend to rise; and if the latter is in excess of the former, the price of securities will tend to fall.
(4) The Relation of the Price-Level to the Quantity of Money (p. 146)
The reader will have perceived by now that the relationship of the purchasing power of money (or price-level of the consumption-goods) and of the price-level of output as a whole to the quantity of money and the velocity of circulation is not of that direct character which the old-fashioned quantity equations, however carefully guarded, might lead one to suppose.
( ... p. 146 )