During any period of time an entrepreneur will have sold finished output to consumers or to other entrepreneurs for a certain sum which we will designate as A. He will also have spent a certain sum, designated by A1, on purchasing finished output from other entrepreneurs. And he will end up with a capital equipment, which term includes both his stocks of unfinished goods or working capital and his stocks of finished goods, having a value G.
Some part, however, of A + G − A1 will be attributable, not to the activities of the period in question, but to the capital equipment which he had at the beginning of the period. We must, therefore, in order to arrive at what we mean by the income of the current period, deduct from A + G − A1 a certain sum, to represent that part of its value which has been (in some sense) contributed by the equipment inherited from the previous period. The problem of defining income is solved as soon as we have found a satisfactory method for calculating this deduction.
There are two possible principles for calculating it, each of which has a certain significance; — one of them in connection with production, and the other in connection with consumption. Let us consider them in turn.
(i) The actual value G of the capital equipment at the end of the period is the net result of the entrepreneur, on the one hand, having maintained and improved it during the period, both by purchases from other entrepreneurs and by work done upon it by himself, and, on the other hand, having exhausted or depreciated it through using it to produce output. If he had decided not to use it to produce output, there is, nevertheless, a certain optimum sum which it would have paid him to spend on maintaining and improving it. Let us suppose that, in this event, he would have spent B’ on its maintenance and improvement, and that, having had this spent on it, it would have been worth G’ at the end of the period. That is to say, G’ − B’ is the maximum net value which might have been conserved from the previous period, if it had not been used to produce A. The excess of this potential value of the equipment over G − A1 is the measure of what has been sacrificed (one way or another) to produce A. Let us call this quantity, namely
(G’ − B’) − (G − A1),
which measures the sacrifice of value involved in the production of A, the user cost of A. User cost will be written U. The amount paid out by the entrepreneur to the other factors of production in return for their services, which from their point of view is their income, we will call the factor cost of A. The sum of the factor cost F and the user cost U we shall call the prime cost of the output A.
We can then define the income of the entrepreneur as being the excess of the value of his finished output sold during the period over his prime cost. The entrepreneur’s income, that is to say, is taken as being equal to the quantity, depending on his scale of production, which he endeavours to maximise, i.e. to his gross profit in the ordinary sense of this term; — which agrees with common sense. Hence, since the income of the rest of the community is equal to the entrepreneur’s factor cost, aggregate income is equal to A − U.
Income, thus defined, is a completely unambiguous quantity. Moreover, since it is the entrepreneur’s expectation of the excess of this quantity over his outgoings to the other factors of production which he endeavours to maximise when he decides how much employment to give to the other factors of production, it is the quantity which is causally significant for employment.
It is conceivable, of course, that G − A1 may exceed G’ − B’, so that user cost will be negative. For example, this may well be the case if we happen to choose our period in such a way that input has been increasing during the period but without there having been time for the increased output to reach the stage of being finished and sold. It will also be the case, whenever there is positive investment, if we imagine industry to be so much integrated that entrepreneurs make most of their equipment for themselves. Since, however, user cost is only negative when the entrepreneur has been increasing his capital equipment by his own labour, we can, in an economy where capital equipment is largely manufactured by different firms from those which use it, normally think of user cost as being positive. Moreover, it is difficult to conceive of a case where marginal user cost associated with an increase in A, i.e. dU/dA, will be other than positive.
It may be convenient to mention here, in anticipation of the latter part of this chapter, that, for the community as a whole, the aggregate consumption (C) of the period is equal to Σ(A − A1), and the aggregate investment (I) is equal to Σ(A1 − U). Moreover, U is the individual entrepreneur’s disinvestment (and − U his investment) in respect of his own equipment exclusive of what he buys from other entrepreneurs. Thus in a completely integrated system (where A1 = 0) consumption is equal to A and investment to − U, i.e. to G − (G’ − B’). The slight complication of the above, through the introduction of A1, is simply due to the desirability of providing in a generalised way for the case of a non-integrated system of production.
Furthermore, the effective demand is simply the aggregate income (or proceeds) which the entrepreneurs expect to receive, inclusive of the incomes which they will hand on to the other factors of production, from the amount of current employment which they decide to give. The aggregate demand function relates various hypothetical quantities of employment to the proceeds which their outputs are expected to yield; and the effective demand is the point on the aggregate demand function which becomes effective because, taken in conjunction with the conditions of supply, it corresponds to the level of employment which maximises the entrepreneur’s expectation of profit.
This set of definitions also has the advantage that we can equate the marginal proceeds (or income) to the marginal factor cost; and thus arrive at the same sort of propositions relating marginal proceeds thus defined to marginal factor costs as have been stated by those economists who, by ignoring user cost or assuming it to be zero, have equated supply price to marginal factor cost.
(ii) We turn, next, to the second of the principles referred to above. We have dealt so far with that part of the change in the value of the capital equipment at the end of the period as compared with its value at the beginning which is due to the voluntary decisions of the entrepreneur in seeking to maximise his profit. But there may, in addition, be an involuntary loss (or gain) in the value of his capital equipment, occurring for reasons beyond his control and irrespective of his current decisions, on account of (e.g.) a change in market values, wastage by obsolescence or the mere passage of time, or destruction by catastrophe such as war or earthquake. Now some part of these involuntary losses, whilst they are unavoidable, are — broadly speaking — not unexpected; such as losses through the lapse of time irrespective of use, and also ‘normal’ obsolescence which, as Professor Pigou expresses it, ‘is sufficiently regular to be foreseen, if not in detail, at least in the large’, including, we may add, those losses to the community as a whole which are sufficiently regular to be commonly regarded as ‘insurable risks’. Let us ignore for the moment the fact that the amount of the expected loss depends on when the expectation is assumed to be framed, and let us call the depreciation of the equipment, which is involuntary but not unexpected, i.e. the excess of the expected depreciation over the user cost, the supplementary cost, which will be written V. It is, perhaps, hardly necessary to point out that this definition is not the same as Marshall’s definition of supplementary cost, though the underlying idea, namely, of dealing with that part of the expected depreciation which does not enter into prime cost, is similar.
In reckoning, therefore, the net income and the net profit of the entrepreneur it is usual to deduct the estimated amount of the supplementary cost from his income and gross profit as defined above. For the psychological effect on the entrepreneur, when he is considering what he is free to spend and to save, of the supplementary cost is virtually the same as though it came off his gross profit. In his capacity as a producer deciding whether or not to use the equipment, prime cost and gross profit, as defined above, are the significant concepts. But in his capacity as a consumer the amount of the supplementary cost works on his mind in the same way as if it were a part of the prime cost. Hence we shall not only come nearest to common usage but will also arrive at a concept which is relevant to the amount of consumption, if, in defining aggregate net income, we deduct the supplementary cost as well as the user cost, so that aggregate net income is equal to A − U − V.
There remains the change in the value of the equipment, due to unforeseen changes in market values, exceptional obsolescence or destruction by catastrophe, which is both involuntary and — in a broad sense — unforeseen. The actual loss under this head, which we disregard even in reckoning net income and charge to capital account, may be called the windfall loss.
The causal significance of net income lies in the psychological influence of the magnitude of V on the amount of current consumption, since net income is what we suppose the ordinary man to reckon his available income to be when he is deciding how much to spend on current consumption. This is not, of course, the only factor of which he takes account when he is deciding how much to spend. It makes a considerable difference, for example, how much windfall gain or loss he is making on capital account. But there is a difference between the supplementary cost and a windfall loss in that changes in the former are apt to affect him in just the same way as changes in his gross profit. It is the excess of the proceeds of the current output over the sum of the prime cost and the supplementary cost which is relevant to the entrepreneur’s consumption; whereas, although the windfall loss (or gain) enters into his decisions, it does not enter into them on the same scale — a given windfall loss does not have the same effect as an equal supplementary cost.
We must now recur, however, to the point that the line between supplementary costs and windfall losses, i.e. between those unavoidable losses which we think it proper to debit to income account and those which it is reasonable to reckon as a windfall loss (or gain) on capital account, is partly a conventional or psychological one, depending on what are the commonly accepted criteria for estimating the former. For no unique principle can be established for the estimation of supplementary cost, and its amount will depend on our choice of an accounting method. The expected value of the supplementary cost, when the equipment was originally produced, is a definite quantity. But if it is re-estimated subsequently, its amount over the remainder of the life of the equipment may have changed as a result of a change in the meantime in our expectations; the windfall capital loss being the discounted value of the difference between the former and the revised expectation of the prospective series of U + V. It is a widely approved principle of business accounting, endorsed by the Inland Revenue authorities, to establish a figure for the sum of the supplementary cost and the user cost when the equipment is acquired and to maintain this unaltered during the life of the equipment, irrespective of subsequent changes in expectation. In this case the supplementary cost over any period must be taken as the excess of this predetermined figure over the actual user cost. This has the advantage of ensuring that the windfall gain or loss shall be zero over the life of the equipment taken as a whole. But it is also reasonable in certain circumstances to recalculate the allowance for supplementary cost on the basis of current values and expectations at an arbitrary accounting interval, e.g. annually. Business men in fact differ as to which course they adopt. It may be convenient to call the initial expectation of supplementary cost when the equipment is first acquired the basic supplementary cost, and the same quantity recalculated up to date on the basis of current values and expectations the current supplementary cost.
Thus we cannot get closer to a quantitative definition of supplementary cost than that it comprises those deductions from his income which a typical entrepreneur makes before reckoning what he considers his net income for the purpose of declaring a dividend (in the case of a corporation) or of deciding the scale of his current consumption (in the case of an individual). Since windfall charges on capital account are not going to be ruled out of the picture, it is clearly better, in case of doubt, to assign an item to capital account, and to include in supplementary cost only what rather obviously belongs there. For any overloading of the former can be corrected by allowing it more influence on the rate of current consumption than it would otherwise have had.
It will be seen that our definition of net income comes very close to Marshall’s definition of income, when he decided to take refuge in the practices of the Income Tax Commissioners and — broadly speaking to regard as income whatever they, with their experience, choose to treat as such. For the fabric of their decisions can be regarded as the result of the most careful and extensive investigation which is available, to interpret what, in practice, it is usual to treat as net income. It also corresponds to the money value of Professor Pigou’s most recent definition of the national dividend.
It remains true, however, that net income, being based on an equivocal criterion which different authorities might interpret differently, is not perfectly clear-cut. Professor Hayek, for example, has suggested that an individual owner of capital goods might aim at keeping the income he derives from his possessions constant, so that he would not feel himself free to spend his income on consumption until he had set aside sufficient to offset any tendency of his investment-income to decline for whatever reason. I doubt if such an individual exists; but, obviously, no theoretical objection can be raised against this deduction as providing a possible psychological criterion of net income. But when Professor Hayek infers that the concepts of saving and investment suffer from a corresponding vagueness, he is only right if he means net saving and net investment. The saving and the investment, which are relevant to the theory of employment, are clear of this defect, and are capable of objective definition, as we have shown above.
Thus it is a mistake to put all the emphasis on net income, which is only relevant to decisions concerning consumption, and is, moreover, only separated from various other factors affecting consumption by a narrow line; and to overlook (as has been usual) the concept of income proper, which is the concept relevant to decisions concerning current production and is quite unambiguous.
The above definitions of income and of net income are intended to conform as closely as possible to common usage. It is necessary, therefore, that I should at once remind the reader that in my Treatise on Money I defined income in a special sense. The peculiarity in my former definition related to that part of aggregate income which accrues to the entrepreneurs, since I took neither the profit (whether gross or net) actually realised from their current operations nor the profit which they expected when they decided to undertake their current operations, but in some sense (not, as I now think, sufficiently defined if we allow for the possibility of changes in the scale of output) a normal or equilibrium profit; with the result that on this definition saving exceeded investment by the amount of the excess of normal profit over the actual profit. I am afraid that this use of terms has caused considerable confusion, especially in the case of the correlative use of saving; since conclusions (relating, in particular, to the excess of saving over investment), which were only valid if the terms employed were interpreted in my special sense, have been frequently adopted in popular discussion as though the terms were being employed in their more familiar sense. For this reason, and also because I no longer require my former terms to express my ideas accurately, I have decided to discard them — with much regret for the confusion which they have caused.
II. Saving and Investment
Amidst the welter of divergent usages of terms, it is agreeable to discover one fixed point. So far as I know, everyone is agreed that saving means the excess of income over expenditure on consumption. Thus any doubts about the meaning of saving must arise from doubts about the meaning either of income or of consumption. Income we have defined above. Expenditure on consumption during any period must mean the value of goods sold to consumers during that period, which throws us back to the question of what is meant by a consumer-purchaser. Any reasonable definition of the line between consumer-purchasers and investor-purchasers will serve us equally well, provided that it is consistently applied. Such problem as there is, e.g. whether it is right to regard the purchase of a motor-car as a consumer-purchase and the purchase of a house as an investor-purchase, has been frequently discussed and I have nothing material to add to the discussion.
The criterion must obviously correspond to where we draw the line between the consumer and the entrepreneur. Thus when we have defined A1 as the value of what one entrepreneur has purchased from another, we have implicitly settled the question. It follows that expenditure on consumption can be unambiguously defined as Σ(A − A1), where A is the total sales made during the period and A1 is the total sales made by one entrepreneur to another. In what follows it will be convenient, as a rule, to omit and write A for the aggregate sales of all kinds, A1 for the aggregate sales from one entrepreneur to another and U for the aggregate user costs of the entrepreneurs.
Having now defined both income and consumption, the definition of saving, which is the excess of income over consumption, naturally follows. Since income is equal to A − U and consumption is equal to A − A1, it follows that saving is equal to A1 − U. Similarly, we have net saving for the excess of net income over consumption, equal to A1 − U − V.
Our definition of income also leads at once to the definition of current investment. For we must mean by this the current addition to the value of the capital equipment which has resulted from the productive activity of the period. This is, clearly, equal to what we have just defined as saving. For it is that part of the income of the period which has not passed into consumption. We have seen above that as the result of the production of any period entrepreneurs end up with having sold finished output having a value A and with a capital equipment which has suffered a deterioration measured by U (or an improvement measured by − U where U is negative) as a result of having produced and parted with A, after allowing for purchases A1 from other entrepreneurs. During the same period finished output having a value A − A1 will have passed into consumption. The excess of A − U over A − A1, namely A1 − U, is the addition to capital equipment as a result of the productive activities of the period and is, therefore, the investment of the period. Similarly A1 − U − V; which is the net addition to capital equipment, after allowing for normal impairment in the value of capital apart from its being used and apart from windfall changes in the value of the equipment chargeable to capital account, is the net investment of the period.
Whilst, therefore, the amount of saving is an outcome of the collective behaviour of individual consumers and the amount of investment of the collective behaviour of individual entrepreneurs, these two amounts are necessarily equal, since each of them is equal to the excess of income over consumption. Moreover, this conclusion in no way depends on any subtleties or peculiarities in the definition of income given above. Provided it is agreed that income is equal to the value of current output, that current investment is equal to the value of that part of current output which is not consumed, and that saving is equal to the excess of income over consumption — all of which is conformable both to common sense and to the traditional usage of the great majority of economists — the equality of saving and investment necessarily follows. In short-
Income = value of output = consumption + investment.
Saving = income − consumption.
Therefore saving = investment.
Thus any set of definitions which satisfy the above conditions leads to the same conclusion. It is only by denying the validity of one or other of them that the conclusion can be avoided.
The equivalence between the quantity of saving and the quantity of investment emerges from the bilateral character of the transactions between the producer on the one hand and, on the other hand, the consumer or the purchaser of capital equipment.
Income is created by the value in excess of user cost which the producer obtains for the output he has sold; but the whole of this output must obviously have been sold either to a consumer or to another entrepreneur; and each entrepreneur’s current investment is equal to the excess of the equipment which he has purchased from other entrepreneurs over his own user cost. Hence, in the aggregate the excess of income over consumption, which we call saving, cannot differ from the addition to capital equipment which we call investment. And similarly with net saving and net investment. Saving, in fact, is a mere residual. The decisions to consume and the decisions to invest between them determine incomes. Assuming that the decisions to invest become effective, they must in doing so either curtail consumption or expand income. Thus the act of investment in itself cannot help causing the residual or margin, which we call saving, to increase by a corresponding amount.
It might be, of course, that individuals were so tête montée in their decisions as to how much they themselves would save and invest respectively, that there would be no point of price equilibrium at which transactions could take place. In this case our terms would cease to be applicable, since output would no longer have a definite market value, prices would find no resting-place between zero and infinity. Experience shows, however, that this, in fact, is not so; and that there are habits of psychological response which allow of an equilibrium being reached at which the readiness to buy is equal to the readiness to sell. That there should be such a thing as a market value for output is, at the same time, a necessary condition for money-income to possess a definite value and a sufficient condition for the aggregate amount which saving individuals decide to save to be equal to the aggregate amount which investing individuals decide to invest.
Clearness of mind on this matter is best reached, perhaps, by thinking in terms of decisions to consume (or to refrain from consuming) rather than of decisions to save. A decision to consume or not to consume truly lies within the power of the individual; so does a decision to invest or not to invest. The amounts of aggregate income and of aggregate saving are the results of the free choices of individuals whether or not to consume and whether or not to invest; but they are neither of them capable of assuming an independent value resulting from a separate set of decisions taken irrespective of the decisions concerning consumption and investment. In accordance with this principle, the conception of the propensity to consume will, in what follows, take the place of the propensity or disposition to save.
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