Appendix on User Cost Past and Present

2:

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.

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*.

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.

3.

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.

Author’s Footnotes

11. 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.