Appendix on User CostJanuary 23, 2020
1. Classical User Cost
The Classical theory of value has an important concept called the USER cost, which has been overlooked.
U = A1 + (G' - B') - G
- U= An entrepreneur’s user cost
- A1 is the amount of our entrepreneur’s purchases from other entrepreneurs
- G the actual value of his capital equipment at the end of the period
- G’ the value it might have had at the end of the period if he had refrained from using it and had spent the optimum sum B’ on its maintenance and improvement.
G - (G' - B')
is the increment in the value of the entrepreneurs equipment beyond the net value which he has inherited from the previous period, represents the entrepreneur’s current investment in his equipment and can be written
I. Thus U, the user cost of his sales-turnover A, is equal to A1 - I where A1 is what he has bought from other entrepreneurs and I is what he has currently invested in his own equipment.
This is common sense.
Some part of his outgoings to other entrepreneurs is balanced by the value of his current investment in his own equipment, and the rest represents the sacrifice which the output he has sold must have cost him over and above the total sum which he has paid out to the factors of production.
If the reader tries to express the substance of this otherwise, he will find that its advantage lies in its avoidance of insoluble (and unnecessary) accounting problems. There is, I think, no other way of analysing the current proceeds of production unambiguously. If industry is completely integrated or if the entrepreneur has bought nothing from outside, so that A1 = 0, the user cost is simply the equivalent of the current disinvestment involved in using the equipment; but we are still left with the advantage that we do not require at any stage of the analysis to allocate the factor cost between the goods which are sold and the equipment which is retained. Thus we can regard the employment given by a firm, whether integrated or individual, as depending on a single consolidated decision — a procedure which corresponds to the actual interlocking character of the production of what is currently sold with total production. The concept of user cost enables us, moreover, to give a clearer definition than that usually adopted of the short-period supply price of a unit of a firm’s saleable output. For the short-period supply price is the sum of the marginal factor cost and the marginal user cost. Now in the modern theory of value it has been a usual practice to equate the short-period supply price to the marginal factor cost alone. It is obvious, however, that this is only legitimate if marginal user cost is zero or if supply-price is specially defined so as to be net of marginal user cost, just as I have defined (Chapter 3) “proceeds” and “aggregate supply price” as being net of aggregate user cost. But, whereas it may be occasionally convenient in dealing with output as a whole to deduct user cost, this procedure deprives our analysis of all reality if it is habitually (and tacitly) applied to the output of a single industry or firm, since it divorces the “supply price” of an article from any ordinary sense of its “price”; and some confusion may have resulted from the practice of doing so. It seems to have been assumed that “supply price” has an obvious meaning as applied to a unit of the saleable output of an individual firm, and the matter has not been deemed to require discussion.
Yet the treatment both of what is purchased from other firms and of the wastage of the firm’s own equipment as a consequence of producing the marginal output involves the whole pack of perplexities which attend the definition of income. For, even if we assume that the marginal cost of purchases from other firms involved in selling an additional unit of output has to be deducted from the sale-proceeds per unit in order to give us what we mean by our firm’s supply price, we still have to allow for the marginal disinvestment in the firm’s own equipment involved in producing the marginal output. Even if all production is carried on by a completely integrated firm, it is still illegitimate to suppose that the marginal user cost is zero, i.e. that the marginal disinvestment in equipment due to the production of the marginal output can generally be neglected. The concepts of user cost and of supplementary cost also enable us to establish a clearer relationship between long-period supply price and short-period supply price.
Long-period cost must obviously include an amount to cover the basic supplementary cost as well as the expected prime cost appropriately averaged over the life of the equipment. That is to say, the long-period cost of the output is equal to the expected sum of the prime cost and the supplementary cost; and, furthermore, in order to yield a normal profit, the long-period supply price must exceed the long-period cost thus calculated by an amount determined by the current rate of interest on loans of comparable term and risk, reckoned as a percentage of the cost of the equipment. Or if we prefer to take a standard “pure” rate of interest, we must include in the long-period cost a third term which we might call the risk-cost to cover the unknown possibilities of the actual yield differing from the expected yield. Thus the long-period supply price is equal to the sum of the prime cost, the supplementary cost, the risk cost and the interest cost, into which several components it can be analysed. The short-period supply price, on the other hand, is equal to the marginal prime cost. The entrepreneur must, therefore, expect, when he buys or constructs his equipment, to cover his supplementary cost, his risk cost and his interest cost out of the excess marginal value of the prime cost over its average value; so that in long-period equilibrium the excess of the marginal prime cost over the average prime cost is equal to the sum of the supplementary, risk and interest costs*.
*This depends on the convenient assumption that the marginal prime cost curve is continuous throughout its length for changes in output. This assumption is often unrealistic. There may be one or more points of discontinuity, especially when we reach an output corresponding to the technical full capacity of the equipment. In this case the marginal analysis partially breaks down; and the price may exceed the marginal prime cost, where the latter is reckoned in respect of a small decrease of output. (Similarly there may often be a discontinuity in the downward direction. i.e. for a reduction in output below a certain point). This is important when we are considering the short-period supply price in long-period equilibrium, since in that case any discontinuities, which may exist corresponding to a point of technical full capacity, must be supposed to be in operation. Thus the short-period supply price in long-period equilibrium may have to exceed the marginal prime cost (reckoned in terms of a small decrease of output).
The level of output, at which marginal prime cost is exactly equal to the sum of the average prime and supplementary costs, has a special importance, because it is the point at which the entrepreneur’s trading account breaks even. It corresponds, that is to say, to the point of zero net profit; whilst with a smaller output than this he is trading at a net loss. The extent to which the supplementary cost has to be provided for apart from the prime cost varies very much from one type of equipment to another. Two extreme cases are the following= (i) Some part of the maintenance of the equipment must necessarily take place pari passu with the act of using it (e.g. oiling the machine). The expense of this (apart from outside purchases) is included in the factor cost.
If, for physical reasons, the exact amount of the whole of the current depreciation has necessarily to be made good in this way, the amount of the user cost (apart from outside purchases) would be equal and opposite to that of the supplementary cost; and in long-period equilibrium the marginal factor cost would exceed the average factor cost by an amount equal to the risk and interest cost. (ii) Some part of the deterioration in the value of the equipment only occurs if it is used. The cost of this is charged in user cost, in so far as it is not made good pari passu with the act of using it. If loss in the value of the equipment could only occur in this way, supplementary cost would be zero. It may be worth pointing out that an entrepreneur does not use his oldest and worst equipment first, merely because its user cost is low; since its low user cost may be outweighed by its relative inefficiency, i.e. by its high factor cost. Thus an entrepreneur uses by preference that part of his equipment for which the user cost plus factor cost is least per unit of output.
*Since user cost partly depends on expectations as to the future level of wages, a reduction in the wage-unit which is expected to be short-lived will cause factor cost and user cost to move in different proportions and so affect what equipment is used, and, conceivably, the level of effective demand, since factor cost may enter into the determination of effective demand in a different way from user cost.
It follows that for any given volume of output of the product in question there is a corresponding user cost*, but that this total user cost does not bear a uniform relation to the marginal user cost, i.e. to the increment of user cost due to an increment in the rate of output.
*The user cost of the equipment which is first brought into use is not only independent of the total volume of output (see below); i.e. the user cost may be affected all along the line when the total volume of output is changed.
User cost constitutes one of the links between the present and the future.
In deciding his scale of production an entrepreneur has to exercise a choice between using up his equipment now and preserving it to be used later on. It is the expected sacrifice of future benefit involved in present use which determines the amount of the user cost, and it is the marginal amount of this sacrifice which, together with the marginal factor cost and the expectation of the marginal proceeds, determines his scale of production. How, then, is the user cost of an act of production calculated by the entrepreneur?
We have defined the user cost as the reduction in the value of the equipment due to using it as compared with not using it, after allowing for the cost of the maintenance and improvements which it would be worth while to undertake and for purchases from other entrepreneurs. It must be arrived at, therefore, by calculating the discounted value of the additional prospective yield which would be obtained at some later date if it were not used now. Now this must be at least equal to the present value of the opportunity to postpone replacement which will result from laying up the equipment; and it may be more*.
*It will be more when it is expected that a more than normal yield can be obtained at some later date, which, however, is not expected to last long enough to justify (or give time for) the production of new equipment. To-day’s user cost is equal to the maximum of the discounted values of the potential expected yields of all the tomorrows.
If there is no surplus or redundant stock, so that more units of similar equipment are being newly produced every year either as an addition or in replacement, it is evident that marginal user cost will be calculable by reference to the amount by which the life or efficiency of the equipment will be shortened if it is used, and the current replacement cost. If, however, there is redundant equipment, then the user cost will also depend on the rate of interest and the current (i.e. re-estimated) supplementary cost over the period of time before the redundancy is expected to be absorbed through wastage, etc. In this way interest cost and current supplementary cost enter indirectly into the calculation of user cost. The calculation is exhibited in its simplest and most intelligible form when the factor cost is zero. e.g. in the case of a redundant stock of a raw material such as copper, on the lines which I have worked out in my Treatise on Money, vol. ii. chap. 29. Let us take the prospective values of copper at various future dates, a series which will be governed by the rate at which redundancy is being absorbed and gradually approaches the estimated normal cost. The present value or user cost of a ton of surplus copper will then be equal to the greatest of the values obtainable by subtracting from the estimated future value at any given date of a ton of copper the interest cost and the current supplementary cost on a ton of copper between that date and the present. In the same way the user cost of a ship or factory or machine, when these equipments are in redundant supply, is its estimated replacement cost discounted at the percentage rate of its interest and current supplementary costs to the prospective date of absorption of the redundancy. We have assumed above that the equipment will be replaced in due course by an identical article. If the equipment in question will not be renewed identically when it is worn out, then its user cost has to be calculated by taking a proportion of the user cost of the new equipment, which will be erected to do its work when it is discarded, given by its comparative efficiency.
Where the equipment is not obsolescent but merely redundant for the time being, the difference between the actual user cost and its normal value (i.e. the value when there is no redundant equipment) varies with the interval of time which is expected to elapse before the redundancy is absorbed.
Thus if the type of equipment in question is of all ages and not “bunched’ so that a fair proportion is reaching the end of its life annually, the marginal user cost will not decline greatly unless the redundancy is exceptionally excessive. In the case of a general slump, marginal user cost will depend on how long entrepreneurs expect the slump to last. Thus the rise in the supply price when affairs begin to mend may be partly due to a sharp increase in marginal user cost due to a revision of their expectations.
It has sometimes been argued, contrary to the opinion of business men, that organised schemes for scrapping redundant plant cannot have the desired effect of raising prices unless they apply to the whole of the redundant plant. But the concept of user cost shows how the scrapping of (say) half the redundant plant may have the effect or raising prices immediately. For absorption of the redundancy nearer, user cost and consequently increasesthe current supply price. Thus business men would seem to have the notion of user cost implicitly in mind, though they do not formulate it distinctly. If the supplementary cost is heavy, it follows that the marginal user cost will be low when there is surplus equipment. Moreover, where there is surplus equipment, the marginal factor and user costs are unlikely to be much in excess of their average value. If both these conditions are fulfilled, the existence of surplus equipment is likely to lead to the entrepreneur’s working at a net loss, and perhaps at a heavy net loss. There will not be a sudden transition from this state of affairs to a normal profit, taking place at the moment when the redundancy is absorbed. As the redundancy becomes less, the user cost will gradually increase; and the excess of marginal over average factor and user cost may also gradually increase.
IV In Marshall’s Principles of Economics (6th ed. p. 360), a part of user cost is included in prime cost under the heading of “extra wear-and-tear of plant”.
But no guidance is given as to how this item is to be calculated or as to its importance.
In his Theory of Unemployment (p. 42) Professor Pigou expressly assumes that the marginal disinvestment in equipment due to the marginal output can, in general, be neglected=
“The differences in the quantity of wear-and-tear suffered by equipment and in the costs of non-manual labour employed, that are associated with differences in output, are ignored, as being, in general, of secondary importance”.
The notion that the disinvestment in equipment is zero at the margin of production runs through a good deal of recent economic theory. But the whole problem is brought to an obvious head as soon as it is thought necessary to explain exactly what is meant by the supply price of an individual firm.
The cost of maintenance of idle plant may often reduce the magnitude of marginal user cost, especially in a slump which is expected to last a long time.
Nevertheless a very low user cost at the margin is not a characteristic of the short period as such, but of particular situations and types of equipment where the cost of maintaining idle plant happens to be heavy, and of those disequilibria which are characterised by very rapid obsolescence or great redundancy, especially if it is coupled with a large proportion of comparatively new plant. In the case of raw materials the necessity of allowing for user cost is obvious;— if a ton of copper is used up to-day it cannot be used to-morrow, and the value which the copper would have for the purposes of to-morrow must clearly be reckoned as a part of the marginal cost. But the fact has been overlooked that copper is only an extreme case of what occurs whenever capital equipment is used to produce. The assumption that there is a sharp division between raw materials where we must allow for the disinvestment due to using them and fixed capital where we can safely neglect it does not correspond to the facts; — especially in normal conditions where equipment is falling due for replacement every year and the use of equipment brings nearer the date at which replacement is necessary. It is an advantage of the concepts of user cost and supplementary cost that they are as applicable to working and liquid capital as to fixed capital. The essential difference between raw materials and fixed capital lies not in their liability to user and supplementary costs, but in the fact that the return to liquid capital consists of a single term; whereas in the case of fixed capital, which is durable and used up gradually, the return consists of a series of user costs and profits earned in successive periods.
- Mr. Hawtrey (Economica, May 1934, p. 145) has called attention to Prof. Pigou’s identification of supply price with marginal labour cost, and has contended that Prof. Pigou’s argument is thereby seriously vitiated.