approximately with the number of consumers; those which vary approximately with the maximum rate at which current is taken; and those which vary approximately with the amount of current used. This division into "consumer," "demand" and "output" expenses is often further simplified by leaving out the consumer expense as a separate category, and, indeed this was the form used by the earlier pioneers in the development of rate theories.12 The details of the process of apportioning the expenses into these classes are matters of practical accounting, beyond the scope of the present study.

The first two steps in the making of a cost-schedule, then, are first, to divide the expenses, and second, to settle on a way of determining the individual consumer's share of the capacity expenses. This may be done, as already outlined, by measuring the consumer's maximum demand, and charging him a fraction of the total capacity expense equal to the ratio his maximum demand bears to the sum of the maximum demands of all consumers, or, expressed mathematically:

total capacity expense X individual's maximum demand

sum of individuals' maximum demands.

This might be modified by introducing the same factor in both numerator and denominator, as follows:

But if on account of the single consumers' peak demands coming at different times, the sum of them all were, for instance, four times as great as the peak demand made at any time on the central plant, then the second fraction reduces to 14, and the whole expression to the following:

13

measured, for lack of suitable meters or because it would not pay to install them, other ways of calculating responsibility become necessary.1 Here the maximum demand can be actually measured only for considerable classes of consumers, and the amount to be borne by the class as a whole can be found in the same way as that shown above for individuals. Then this must be divided among the members of the class, either equally, or else in proportion to their connected loads, on the assumption that, within the class, the maximum demands are in proportion to the total capacity of their "services" or individual fixtures for use of light or power.

A third possible way, simpler but less just than the above, is to go on the assumption that the capacity costs should be shared in proportion to connected loads, without regarding the fact that some classes of consumers regularly use at certain times the whole, or nearly the whole, of their connected load, while others never use more than a fraction of it at any one time.14

Residences, for instance, never as a class put as heavy a strain on the plant in proportion to the capacity of their fixtures as do other classes of consumers. Thus in making tentative calculations for the city of St. Louis, the trial rates which were obtained on a basis of connected load were, for residences, over ten times as high per kilowatt-hour as for the municipal consumption, and between four and five times as high as the rate for business light. On the basis of their actual shares in responsibility for the peak demand, residence rates were less than three times as high as municipal, and only about seventy per cent higher than business rates.1

15

From this showing of discrepancy and of discrimination caused by using as a base the entire connected load, such discriminations bearing heavily on the residence consumers whose connected load gives an exaggerated measure of their real demand on the plant's capacity, it would seem that so far as practicable the more important classes of consumers should have their burdens based on measurements of their actual class demands. Within the classes, the connected load would seem to be the best practicable basis for distributing the class-burden to individuals, except in cases where

I.

"Report St. Louis Public Service Commission, op. cit., Appendix B, pp. 3-17. 14 Report of St. Louis Public Service Commission, op. cit., Appendix C, Table

15 See table cited above.

these would be so nearly alike that a mere equal sharing of the burden would do at least approximate justice.

The above treatment gives a bare outline, without going far into the mathematical formulae involved, of the currently accepted methods of locating responsibility for capacity expenses. This theory is not universally agreed in, however; in fact it has been vigorously combated in the recent report to the St. Louis Public Service Commission by the commission's chief engineer.16

These documents present, in contrast to the cause or responsibility theory elaborated above, the use or benefit theory of adjusting these burdens. First, it is claimed that none of the above methods give an accurate measure of responsibility for investment, and, secondly, that such responsibility is not the only proper measure by which these costs should be divided. On the contrary, the principle of value of service dictates, first, a general policy of charging according to benefit received, measured by amount consumed (which would lead to uniform rates per kilowatt-hour), and second, miscellaneous concessions based on expediency (or what the traffic will bear). Actual rates, then, cannot be calculated by any one formula, but should be compromises between cost-formula rates, uniform or use-formula rates, and rates governed by mere expediency, such "as may be arrived at by judgment alone."

This proposition, as will be seen, corresponds closely to the position taken in an earlier paragraph of the present paper, namely, that expediency should properly be considered when the peak load does not tax the full capacity of the plant, and that the weight given it should normally be in proportion to the extent of the plant's idleness. If this be one of the chief considerations which "judgment" would weigh, then the writer can agree fully to the proposition of the St. Louis report. But when the plant is, at times at least, running at full capacity, the argument against the "responsibility" principle at once loses force. It is even possible to argue that expediency itself dictates the use of "cost" rates. To make this plain, let us suppose as the St. Louis report does, that the hours of the day are separated as if they were different persons, and the peak hour is charged with all the capacity costs and the others with none. This supposition was made in order to show the unfairness of such charges, and it is effective 1 Report of St. Louis Public Service Commission, op. cit., Appendices B and

C.

16

to the purpose. But how about the expediency of such a policy? What would be the practical effect of it if it could be carried out? Would not the natural result be to cause the peak hour to be avoided as much as possible, and other hours chosen until the peak was virtually no longer a single hour or fraction of an hour, but instead there was a fairly steady rate of use, covering a considerable part of the day and without any short-time maximum worth mentioning? Instead of a peak there would be a plateau wide cnough to bear without crumbling the weight of the capacity expenses. And would not this result in more efficient use of the plant without arbitrary personal discrimination; and is not this the highest kind of "expediency"? In short, would not a perfect cost system be also a perfectly expedient one, if the necessary data could be gathered? Certainly cost is the basis of expediency, and certainly any approach to uniform rates must seriously hamper development of both of these principles. To this extent the writer is in disagreement with the St. Louis report.

The further criticism that none of the methods described gives an accurate measure of responsibility, would seem to be too purely a logical counsel of perfection, resting on a premise which itself falls short of the perfect standard. This premise is that, in following the cause theory, the capacity costs should be divided according to share in the peak load on the central plant. To this the writer cannot agree, because (as mentioned above), much of the capacity expense is for the various mains and branches of the distributing system, and the peak loads on these do not correspond to the peak of the central plant, either in time or in ratio to the average rate of use. Any assignment of these costs on one simple basis is necessarily a compromise between the various peak demands of the various groups which determine the amount to be invested in the different parts of the plant. And the compromise represented by the more generally accepted methods would seem to be as good as practical utility calls for.

Finally, we come to the third step in making a rate system. Having divided costs and laid them separately at the doors of individuals, it remains to decide just what form the rates shall take in practice. The simplest system would seem to be to charge each cost directly to the base that measures it. Thus the consumer would pay the direct consumer expenses as a lump sum, and a further lump sum to cover his share of the capacity expenses, while the output expenses would be covered by a uniform rate per kilo

watt-hour. This characterises the general type commonly known as "readiness to serve" systems, so called because of the charge made for the provision of capacity which is held ready to serve the consumer's probable demand, separate from the charge for current actually consumed.

While this is the logical system, it meets with certain practical objections. The customers object to a charge that seems to be added to the price they pay for their current; while the law often furnishes obstacles by forbidding meter rents and similar charges that do not in themselves entitle the consumer to any current.17 As a result, another system of charging finds much favor in practice, a system in which the capacity charge is concealed in the output charge. To do this justly, the rates must be so arranged that few consumers will use so little as to escape their share of the burden, while those who use current many hours a day and regularly, shall not thereby be made to pay more towards capacity costs than others whose peak responsibility is the same, but who use less current.

This could only be perfectly secured by loading all the capacity costs onto the first few kilowatt-hours consumed, so that it would fall practically as a separate fixed charge. The method actually used is to fix on a number of hours daily use of the consumer's maximum demand, representing the average daily consumption of the class of consumers who use the current fewest hours, and to make the rate for this amount of consumption high enough to cover the capacity costs. Beyond this point, the rate falls to a level representing output expense merely. Or perhaps a compromise system is introduced, on the principle advocated by the St. Louis commissioner, and some of the capacity costs are laid upon the second stage of the rate, and not all of them raised from the first.

The result of this system is, in appearance, a sliding scale of charges, but it is governed by very definite principles, and must not be confused with mere reductions for quantity used, regardless of the liability of the consumer to take more, or less, of that quantity at the peak.18 The latter practice is "not likely to be in keeping with the costs of service or conducive to the successful cxtension of business."

"In re Application Stoughton Municipal Electric Light System, 3 W. R. C. R., 484, 502.

18 In re Menominee & Marinette Light & Traction Co., 3 W. R. C. R., 778, 831.