Efficient pricing of electric power service

Resources and Energy I4 fI992f 157f74.

worth-Holland

Efficient pricing of electric power service Some innovative

solutions

William Vickrey

The author here argues that to maximize efhciency in the production and consumption of electricity, its price to the consumer should be varied in real time according to the short-run marginal social cost of providing power at various times and places, through remote control metering. To motivate privately-owned utilities to set prices in this manner he proposes the use of an escrow find to or from which would flow the difference between the responsive rate paid by the customer and the regulated retention rate established by regulatory proceedings. With consumption subject to instantaneous control through price, spinning reserves would no longer be needed and emergencies could be dealt with with fewer blackouts. How to calculate short-run marginal social cost under various circumstances is discussed in detail, and also how prices should differ from marginai cost to allow for costs involved in the provision of subsidies.

In the past, prices for electricity have generally been set to satisfy some concept of equity as between investors and various classes of consumers, on the basis of plausible but often essentially arbitrary accounting allocations of costs, with some concern for distributional impacts, but only secondary consideration given to efficient use of resources. While there is often a tacit assumption that this process does result in a satisfactorily close approximation to efficiency, efficiency tends to play a subordinate role. Actually, while if there is a failure to meet equity or distributional requirements directly there will usually be other means of redressing the balance, failure to achieve maximum efficiency cannot be made good in this way. There is thus a case for making efficiency the primary objective, and if this is done it turns out that some fairly drastic departures from present practices would be indicated. This paper will first discuss the underlying efficiency rationale for requiring prices to be set at marginal cost, and the case for meeting the resulting deficit by taxes based on the land values enhanced by the availability of electric power and other services. A technology for implementing responsive Correspondence EO:Prof. William Vickrey, 162 Warburton Avenue, Hastings-on-Hudson, 10706, U.S.A. 0165~572~92~~~~.~ $J 1992-Elsevier

Science Publishers B.V. Al1 rights reserved

NY

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marginal cost pricing is then described, an escrow fund arrangement outlined whereby the utility can be given the necessary freedom to adjust prices in real time while remaining subject to adequate regulatory control, and the ways in which short-run marginal social cost (SRMSC) is to be calculated under various circumstances are specified. Finally there is a discussion of ways of dealing with cases where the full ideal of pricing at short-run marginal social cost cannot be achieved, and one must look for constrained, or ‘second best’, solutions.

2. Responsive pricing 2.1. Efficient

marginal-cost

pricing

In an ideal Pareto efficient world, all prices would be set at short-run marginal social cost (SRMSC) so that purchasers would have proper indications to make efficient choices among the various alternatives. If this condition is not met, it would theoretically be possible to improve the lot of everyone by increasing the consumption of goods having prices in excess of SRMSC and reducing the consumption of goods for which the reverse is true, provided suitable compensation payments are made. For goods produced under constant or increasing cost conditions, competition in a free market can in principle produce this result, at least where neighborhood effects and other externalities are absent. But for goods and services with economies of scale, in many cases perhaps better termed economies of density of demand, pricing at SRMSC at an optimal level of service provision will usually require financing at least in part from sources other than sales revenues. It is a theorem of urban economic theory that in an ideal world, the urban rents generated by the local availability of goods and services at marginalcost prices will be just sufficient to yield the subsidy needed to meet the costs not covered by direct user charges at levels corresponding to SRMSC. This would be approximated if there were large numbers of cities of each type competing with one another. Land value taxation is indeed an equitable and efficient source for meeting the negative rents in local distribution networks. Landlords indeed tend to be the ultimate beneficiaries of the improvement in efficiency resulting from bringing prices closer to SRMSC. To the extent that labor and reproducible capital are freely mobile throughout the region, their returns will be determined in the medium long run by region-wide conditions, thus leaving landlords, as the owners of the fixed factor, to reap the gains from improved overall local efficiency. If the landlords correctly perceived their own long-term interests and could get together for the purpose, it would be to their advantage to agree to tax themselves to

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subsidize electric power rates so that electric power service would be available at rates closer to SRMSC. It can not properly be said that this arrangement would be inequitable to those using their land for parking lots or tennis courts, who make no direct use of electric power service. Those making use of land in the area where power is available should no more be excused from paying for the service availability inevitably packaged with their property than one could expect to go to a car rental agency and expect to be granted a discount for the cost of the headlights because one is renting only during daylight hours, or for the windshield wipers if the weather is clear. If efficient choice is to be motivated, one choosing to purchase a package should pay for the social costs of the entire contents even if one intends to throw some of it away. The proprietor can indeed expect to be able to charge more for parking and tennis playing because of the convenient location surrounded by property occupants who use utility services, and thus he does indeed benefit indirectly. If he pays less than his full share of the cost according to the space occupied, he will be getting away with acquiring a benefit without contributing to its cost. This is especially damaging in the case of parking lots, where there is thus still another hidden subsidy to the automobile. A similar argument can be used for using land value taxes to finance the non-marginal part of the cost of telephone service, mail pick-up and delivery, fire protection, libraries, museums, parks, transit lines and so on. It is important to note that the benefits are not confined to property in the vicinity of the power lines: even those living in areas not directly served gain from the entire urban ambience that is enhanced by the provision of utility services at efficient prices. Economies of scale in transmission presented a more difficult problem, in that the benefits of pricing this element at SRMSC are widely distributed and there is no obvious source particularly apt to finance the subsidy. One possible source would consist of the excess rents accruing to scarce generating sites over their alternative uses, especially but not exclusively hydro. In the case of Tennessee Valley Authority, for example, the economic rents from its hydro-electric sites increased over time as the growth of demand requires recourse to less and less favorable sites and even to thermal plants; thus, these rents become available to cover the negative rents involved in the transmission and distributing lines. There is, however, no reason to expect the positive and negative rents to balance. In some countries wholesale distribution of power is over a national grid, which would ideally lead to financing in part from national tax revenues. 2.2. lmpkmeatation

of P = SRMSC: Responsive (‘spot’) pricing

In the past, the costs of sophisticated metering, bureaucratic

inertia and a

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failure to appreciate the efficiency advantages of keeping prices in line with costs have led to complacent acceptance of extremely crude methods of charging for electric power. Excessive concern with equity, indeed, has led to the imposition of standards for accuracy in metering that cost far more than they are worth. Technology has been available for some time, however, that would permit price to be caused to track SRMSC extremely closed at modest cost. For example, one method that would be sufficiently low in cost to warrant its application to most commercial and industrial customers, as well as a large fraction of residential customers, would involve retrofitting pulse generators on existing meters; the pulses could then be fed to a counter in an electronic package containing the counter, registers, a transceiver, a local signal generator and possibly a clock. Most of the electronics involved could be contained on a specially designed computer chip. The pulse generator could take the form of a mirror mounted on the shaft of existing meters, aligned with a light source and a photoelectric cell in the electronic package. The pulses thus produced would be fed to an electronic counter Whenever a rate change is to take effect, a signal is broadcast, either by carrier current over the power lines or through telephone lines, that would cause the counter reading together with the new rate level, and possibly also the time, to be transferred to a register. A signal indicating the current rate level would also be made available to customers at a local signal outlet. During the intervals between rate changes, meters would be polled in sequence causing one or more register records of the counter reading at the time of rate change and possibly the corresponding new rate to be transmitted to a central computer for eventual analysis and billing. Customers would be able to adapt by choosing for themselves the prices and circumstances at which various units of equipment will be turned off and on. Automatic switches of varying degress of complexity can be set to respond to the price signals, in many cases within a fraction of a second, in others after a delay sufficient to allow completion of functions in process. This type of responsive pricing can have a salutary effect on service reliability. In the event of an outage, sufficient demand can often be shed through a price increase to maintain service to essential uses, often converting what would have been a disastrous blackout into a minor inconvenience. To be assured that an adequate response can indeed be elicited during an emergency it may be desirable to hold occasional dry runs or fire drills in which a price increase is signalled over a small area without actually charging the higher price in order to observe the response. If the response is inadequate it may be necessary to find some other way of motivating consumers to set their switches appropriately. If a blackout nevertheless does occur, responsive pricing can smooth recovery, permitting load to be picked up gradually rather than having to

face the surge resulting from a large number of motors starting up simultaneously when power is restored. Responsive pricing can greatly reduce capital requirements, Not only can it shave peaks, but it can eliminate the need for spinning reserves; response to price can be quicker than any ramping of generators. Generating units can be more efficient or less costly if they are not required to be capable of rapid ramping. Voltage and frequency regulation can be improved, since adjustment to shocks through pricing can be more rapid than through generator ramping. 2.3. Regulatory can~roi with responsive pricing To work efficiently, responsive pricing must be freely adjustable by the utility according to conditions of the moment. This precludes direct control by a regulatory body, but if pricing is completely uncontrolled there would be serious danger of abuse and ineflicient deployment of capital. Control over responsive pricing can be exercised by separating the responsive price charged to customers from the price received by the utility that could be specified by normal regulatory processes, and arranging for the difference to be paid into or out of an escrow fund. Whenever marginal cost to the utility is less than the specified retention rate the utility will have an incentive to reduce the responsive price to consumers at least down to the retention rate, since for each additional unit sold as a result of a reduction in the responsive rate there will be a profit equal to the excess of the retention rate over marginal cost, If there is a substantial balance left in the escrow fund, this incentive will persist as the responsive rate is reduced to below the retention rate down to marginal cost. Indeed if the escrow fund has grown so large that this is the only way it can be drawn upon within a relevant horizon, there could even be a motive for lowering price below marginal cost, since this would immediately yieid to the utility the margin of scheduled price over marginal cost on the additional sales induced by the lower responsive price. This would be rare, however, as in the long run there would usually be more profitable ways of drawing on the escrow fund at other times. Whenever marginal cost to the utility is above the specified retention rate, there will be an incentive to raise the responsive rate so as to curtail consumption and the loss from such sales, up to the point where the reduction in output lowers marginal cost to the retention rate level. If capacity is inadequate, so that marginal cost is predominantly above the scheduled rate, the escrow fund will continue to grow, and the utility will eventually have an incentive to expand capacity to drive marginal cost down so that prices can pro~tably be lowered to where the escrow fund can be drawn on.

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While some of the reliability provided by responsive pricing can be provided by interruptible power contracts, responsive pricing would in general be a far superior alternative. Since customers would retain control over the way their usage is curtailed, many more customers would be willing to participate, and the repose to an emergency would be more efficient than where the cut is determined centrally by the utility. Since the arrangement would be universally available, there would be no room for discriminatory practices. Indeed it has been alleged on occasion that interruptible power rates have been merely a device for granting rate concessions to favored customers, as when a lower rate is justified by a hypothetical interruptibility which in fact almost never occurs. 3. Measuring marginal social cost In implementing a responsive price mechanism, it will be important to measure the marginal cost of providing power because the responsive price should track the marginal costs. Thus this section discusses various aspects of the marginal cost of providing electricity. SRMSC of electric power at a given instant and location has two main components: the cost to the utility on the one hand, and the cost in terms of impaired quality of service to other customers on the other. With responsive pricing, the likelihood of an absolute outage resulting from overload will be negligibly small, outages then being mainly the result of storm, accident, or other eventuality not related to the level of consumption. The cost of providing added power to the customer when capacity is being fully utilized is the depriving of another customer of power; if this is done by raising the responsive price, this price is the measure of that cost. Where we have in effect a vertical segment on the supply or marginal cost curve, the appropriate price is one which is greater than the marginal cost of producing the last unit, but less than the marginal cost (possibly infinite) of producing the next unit, and such as to equate consumption with the output at which this discontinuity occurs. In a more conventional environment one would have to evaluate the marginal increment in loss of load probability, MLOLP, resulting from an increment in consumption, and multiply by the expected damage resulting from such an incident. Such estimates are, to be sure, highly subjective and variable. But one puts more food on the table by shooting at the flying ducks than at the floating decoys, even though one would secure more hits on the latter. 3.1. SRMSC

in terms of current and future elfects

Calculation of SRMSC, even where service impairment is not in question, is more a matter of engineering than of accounting or statistics, more a

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matter of evaluating efffects on present and future situations than of allocating costs incurred in the past. The marginal cost of fuel is to be calculated in terms of the price at which the inventory of fuel is expected to be replenished in the future, not the price at which it was purchased, in spite of the cries of profiteering that arise when fuel prices rise sharply and the efficient policy is followed. Delaying the recognition of the cost increase only exacerbates the eventual burden of adapting to the change. To the extent that the useful life of equipment is affected by usage, this wear and tear element is part of marginal cost. Usual methods of depreciation, however, fail to reflect this cost with any accuracy. Proper evaluation would be in terms of the present value of the acceleration of the replacement of an item of equipment and its successors as a result of a given results from the deterioration of usage. In many cases this acceleration insulation and is a function of the operating temperature which in turn may be a sharply increasing function of load, as well as of ambient temperature. In the extreme case where the life of a piece of equipment can be defined in terms of a number of hours of active use or number of kilowatthours processed, and there is no technological progress, optimal husbandry of equipment dicates that equipment be assigned so as to give the heaviest duty to the newest units, with the oldest units called into use only during peaks. In this way the recovery of the capital cost of each unit will be brought forward and the total amount of unrecovered capital cost minimized. This pattern of assignement will be even more urgent if the newer units are more efficient. With such optimum equipment husbandry, the marginal cost assignable at a given time over the daily or weekly cycle will vary in proportion to the present value of a dollar due at the end of the useful life of the oldest unit in use at that time. The result corresponds neither to conventional allocations of capital charges uniformly over usage units, nor to the allocation of part or all of the capital charges to the peak period, however defined. Some feeling for the reasonableness of this result may be obtained by imagining that equipment could be rented by the hour in a competitive market, assuming that the equipment could be transferred costlessly from a depot to place of use and back.

3.2. Effects of inflation and lumpy investment In a context of inflation, conventional methods of accounting and rate of return setting result in a front-end loading of costs that is at odds with efficient pricing. For example with 10% inflation and an allowed rate of return of 15% based on nominal market rates corresponding to a real rate of interest of approximately 4.5x, straight line depreciation on a $1,000,000 asset with a life of 20 years will have first year capital charges of $150,000 in

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interest plus $50,000 depreciation, a total of $200,000, and $7,500 plus $50,000 or $57,500 in the last year, as compared to what the charges would be in the absence of inflation of $l~,~ and $52,000, respectively. A treatment more in line with efficient pricing would be to charge the change in market value as depreciation in conjunction with the market rate of interest. If the asset depreciates to $950,000 in real terms, under inflation of 10% this becomes $1,045,000, a negative depreciation in nominal market value of $45,000 which when combined with the interest of $150,000 gives a net capital charge of $105,~, more in line with the result in the absence of inflation. Alternatively, one could combine the real depreciation of $50,000 with real interest of $45,000 to get $95,000. Thus one can either combine real depreciation with real interest, or market depreciation with market interest and get appropriate results. Combining market interest and real depreciation, however, results in a serious distortion. This distortion is particularly important for nuclear power plants where capital charges are an especially large part of total costs. Nevertheless, all three methods give comparable total discounted value of returns to investors. Nuclear plants also give rise to problems associated with the addition of capacity in relatively large lumps. Efficiency in such cases calls for rates to be raised prior to the coming on line of the new unit, keeping demand within previously existing capacity for a longer time and permitting the new investment to be deferred. Immediately after the new capacity comes on line rates should be reduced to permit its full economic use. Responsive pricing would tend to lead to such a result: prior to the availability of the new unit funds would flow into the escrow fund, to be liquidated by the reduced rates applied after the new capacity becomes available. 3.3. Costs of low power factor Where low power factor is charged for, the present charges are typically highly arbitrary and bear little relation to marginal cost. Power usage is actually a vector with two components at right angles to each other, the power-delivering kilowatt (KW) component and the ‘wattless’ reactive kilovolt-ampere (RKVA) component. The total power to be delivered to a given node is calculated by summing the KW and the RKVA of the various customers separately, and the appropriate manner of charging is to charge for these components separately. The cost of supplying RKVA to a customer at given time and place is largely inde~ndent of the power factor of that customer: it is just as great for the customer with a power factor of 0.9 as for one with a power factor of 0.5. Costs associated with delivering RKVA are, however, calculated in terms of the system KVA, which is equal to the hypotenuse of the right triangle with legs consisting of the system KW and the system RKVA. The capacity

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of generators and transformers are specified in terms of KVA, while the mechanical input to the generator is specified in terms of KW delivered to customers plust the KW lost in transmission and distribution. The variable part of these losses in turn also vary as the square or slightly more of the KVA. Capacity constraints of course affect costs only during peak periods, while transmission and distribution losses are relatively low in off-peak periods. Accordingly, if charges for RKVAH are made at all, they should be even more sharply concentrated on peak hours than charges for KW. On the other hand, if the system power factor is high the effect of adding RKVA on the system KVA and hence on the system cost will be relatively slight. For example if a system node is originally at 100KW and 5 RKVA, combining to give 100.12 KVA, has another 5 RKVA added to bring the total to 100.5KVA, this results in an increment of only 0.38 KVA, whereas if the same 5 RKVA were aded to a system load of 100KW and 40 RKVA the system load is increased from 107.8 KVA to 109.5KVA, an increase of 1.7 KVA. Accordingly, if power factor charges are imposed at all, they should be concentrated on occasions when loads are near peak and system power factor is low. When charges are made, they should be made for all customers whose charges would be sufficient to warrant the metering costs, regardless of the customers’ own power factor.

3.4. SRSMC

of hydro power

Calculation of marginal costs where there are hydro plants presents special features that can produce paradoxical results in some cases. At one extreme, if for example at 3 a.m. during spring runoff water is spilling while hydro generating capacity is more than adequate to meet demand, marginal cost is essentially zero. When generator capacity is fully utilized, supply side marginal cost can be thought of as the range between the marginal cost of the last unit and infinity as the marginal cost of the next unit that is effectively impossible to produce; price is set where demand intersects this vertical supply cuve and can be thought of as representing demand side marginal cost reflecting the value of the last unit produced to consumers, or alternatively as the cost of adding to supply from alternative sources. In a period prior to an expected spill such that it is clear that the reservoir will not be depleted to its minimum level in the interim, short-run marginal cost of water would still be zero except in cases where a reduction in the reservoir level significantly reduces the capacity of the turbo-generator units and this capacity is fully used at least some of the time in the interim. In such cases the SRSMC of water through the turbines consists of the loss of generation from the lowering of the reservoir level during periods of full use of generating capacity, after allowing for the additional drawdown of

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reservoir level requires to maintain electrical output at times capacity is not fully utilized. In periods where the reservoir remains at its minimum level, generation is determined by the inflow into the reservoir, to be sold at whatever price the market will bring as determined by consumer demand and the marginal cost of alternative supplies. In periods where it is expected that the reservoir will reach its minimum level before it spills, there is then a given expected supply of water to be disposed of over this period. A shadow price is to be set for this water and for the energy generated with it, that will just result in the energy generated being disposed of at a value corresponding to the marginal value of the energy to customers or the marginal cost of energy from alternate sources. The shadow price of water within this period may decline over time to allow for the effect of a drawdown of the reservoir on the power potential of subsequent drawdowns, and the shadow price of power relative to that of water will vary with the reservoir level. Uncertainty concerning future water inflows and demand levels further complicates the calculation of current SRMSC at any given time. A more precise analysis will be given in an appendix. Since the capital cost of an additional penstock-turbine-generator unit in an existing hydro installation is generally substantially less than that of a thermal plant of comparable capacity, it will usually be economical to install at least sufficient generating capacity in a hydro plant to permit the low season water availability to be fully used in meeting the peak daily or weekly demand, minimizing the thermal capacity required to meet the balance of demand, with the thermal capacity operated on base load during these periods. In times of higher water availability the hydro units would be shifted sufficiently to base load operation to permit full utilization of the available water. While without responsive pricing it would often be desirable to maintain at least some hydro units operating as a spinning reserve even during off-peak hours in the dry season, this would no longer be necessary with responsive pricing. If with hydro units all on base load there is still some spillage, it may be worth while to install additional hydro units not required to meet the system peak, merely to economize on fuel by increasing the utilization of water otherwise spilled. If the price of fuel rises, it may become economical to install additional hydro generating capacity that will be useful for a shorter spillage period. Paradoxically, as a result there will be times when the marginal cost is lower than previously because of the increase in fuel cost. 3.4. Environmental costs SRMSC of course includes costs of impacts on the environment,

of which

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one principal element is the impact of the atmosphere of fossil fuel consumption. As far as carbon dioxide is concerned, it is possible to assume that practically all carbon contained in fuel eventually winds up as carbon dioxide in the atmosphere; at the moment there seems to be no prospect of a technology for keeping carbon dioxide out of the atmosphere at reasonable cost. Perhaps the best way of bringing this cost into account would be to place a tax on the carbon content of all fuels, whether used in power production or in other ways. How to determine the level of this tax is of course a vexing problem, but whatever rate is fixed, it is proper that it be the same for electric power as for other uses. For emission of nitrogen oxides there is perhaps no good alternative to an actual measurement of stack emissions, given the many ways in which such emissions vary with the conditions of combustion. The same approach is also appropriate for sulphur oxides, even though in this case there is a possibility of relating emissions to the sulphur content of fuel. The relation is not so precise as with carbon, however, as some sulphur can be removed in scrubbers, or in fluidized bed combustion. It would be possible to measure sulphur in the resulting solid wastes and subtract it from the sulphur in the fuel to get a net emission to the atmosphere, but if stack emissions must be monitored for nitrogen oxides in any case, adding monitoring for sulphur would seem to be the more economical method. A lesser impact is that from heating of condenser discharges; in many cases this can be considered of negligible importance. Another hydrological externality can be the impact of fluctuations in reservoir levels on recreational and other amenities. More complicated problems arise when water discharges are involved in navigation, irrigation, water supply, or fish conservation, which would involve an analysis too complicated to include here. While environmental questions are involved in plant siting and the construction of new hydro projects, these decisions are not made by large numbers of individual customers but by decision makers that can and should take the environmental considerations into account in ‘terms of a cost-benefit analysis of the project as a whole. Once these decisions are made, SRMSC is to be calculated taking these decisions as given. Environmental considerations have become an extremely emotional issue in the case of nuclear power. Much of the difficulty arises from lumping together the experience with civilian power production with that of military nuclear operations where a tradition of secrecy and exemption from civilian oversight, combined with the greater tolerance of the military towards risk to human life and health have produced a number of very unsavory situations. The actual experience with civilian nuclear power, however, has been relatively good, at least in western countries; injuries and fatalities have been far less than those associated with the production of a comparable amount of

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power from coal. Indeed it can be said that the accident at Three Mile Island did indeed result in casualties, but they occurred in Appalachian coal mines producing the coal for power to replace that no longer available from the nuclear plant, not in the Susquehanna valley. Cost overruns and difficulties in disposal of spent fuel are to a considerable extent a result of an exaggerated fear of the unknown; known deaths and injuries in coal mines may be deemed a risk accepted by miners, thought of as a less important hazard than the specter of a remotely possible nuclear holocaust inflicted on unconsenting bystanders. The risk of continued reliance on fossil fuels pushing the greenhouse effect past some critical point of no return may be thought of as at least as threatening as that of a major nuclear disaster.

4. Other issues concerned with responsive pricing We now come to consider the fact that we live in an imperfect world in which the full efficiency resulting from setting all prices equal to short-run marginal social cost may not be attainable. Taxes have distorting effects; responsive pricing may not be economically applicable to many customers, especially small ones; there may be resistance to departing too abruptly from traditional tariff forms; and the existence of a subsidy or variations in the manner in which it is determined may have adverse effects on managerial efficiency. These circumstances may call for modifications in the way principles of marginal cost pricing are applied, but not for ignoring them. 4.1. Second-best pricing One major consideration is the fact that governments nearly always need to use other taxes or revenues that are not, as is the land tax, free of adverse effects on the efficiency of the economy. The added ‘excess burden’ associated with obtaining a unit of additional revenue from a given source can be termed its ‘marginal social cost of public funds’ (MSCPF). Minimizing the total social cost of obtaining a given total amount of net revenue would involve equalizing these MSCPF’s over all the various sources. Among the sources are possibilities of raising prices of services provided by government agencies, or subject to government subsidy, above SRMSC; such an excess of price over marginal cost can be thought of as an excise tax. Whenever a price p is raised above marginal cost m resulting in the amount sold falling from the optimum level Q to a suboptimum 4, there is for each unit of use given up a loss of social surplus consisting of the excess of the value to the consumer p over the cost m ranging from near zero for the first unit given up to (p-m) for the last unit given up, or altogether (p- m)(Q -q)/2. Thus this loss varies roughly as the square of the deviation of price from SRSMC, and total inefficiency will be minimized by pricing

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each service provided or subsidized by government at least slightly above SRSMC. More precisely, if demands for the various services are independent of one another and there are no externalities or neighborhood effects to be taken into account, efficiency can be maximized by applying a rule first developed by Frank Ramsey in 1928 according to which the excess of price over marginal cost as a percentage of the price should vary inversely with the elasticity of demand for the particular service or commodity. Another formulation is to make the price such that the amount of each commodity or service actually purchased is a constant fraction of what would have been purchased had the price been set at current marginal cost and the demand curve were a linear one. A third formulation, which may be easier to apply in situations involving interrelated demands, is in terms of equalizing a ‘leakage ratio’, a concept developed by Bernard Sobin. This ratio is the proportion by which the net revenue actually realized from a price increase falls short of (‘leaks away from’) what would have been obtained had there been no change in the quantities sold of the given service and complementary or substitute services. Leakage is in effect a measure of the increase in excess burden resulting from an increment in the price. Where there are externalities, whether as neighborhood effects or as impacts on markets outside the revenue constraint, these must be included in the leakage, and the leakage ratio must be computed in terms of the net revenue increment within the revenue constraint. In comparing the marginal cost of net revenues for the utility with the marginal cost of public funds, it would be appropriate to allow for the effect on tax revenues of the stimulus to the economy and the iimprovement in efficiency brought about by the closer approach of rates to SRSMC. If the tax system captures a large proportion of the land rents, the subsidy may be largely self-financing in the medium long run out of increased tax revenues at constant tax rates.

4.2. Formulation

of subsidies

Unless the government concerned is saddled with an unusually inefficient tax system with a correspondingly high marginal cost of public funds, Ramsey pricing is likely to indicate that a subsidy is still in principle called for. In spite of this, if in the absence of subsidy the marginal cost of net revenues resulting from applying the Ramsey rule to the utility as an independent unit is not too much greater than the government’s marginal cost of public funds from other sources, it may be worthwhile to eschew subsidization for the sake of preserving the financial autonomy of the utility enterprise for the sake of whatever increased incentive for efficient management this may provide.

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If a subsidy is provided for, a lot will depend on the way the subsidy is formulated. A subsidy defined in terms of costs, while theoretically correct, is likely to encourage carelessness in cost containment and even the inflation of costs, particularly of management overheads and perquisites. There may also be a megalomanic tendency to want to design on a grandiose scale, goldplate the service to forestall complaints over service quality, and generally add fancy bells and whistles to be paid for out of a ‘deep pocket’. Another influence is the fact that utility managements are likely to associate with business executives and other relatively well-to-do persons whose preferences tend to run in the direction of high-quality-high-cost service. A subsidy based on revenues is somewhat better, but also tends to create a bias in favor of higher prices, and higher costs to justify them. A subsidy in terms of service offered may tend to promote the provision of unused or lightly valued services. Although without direct theoretical justification, a subsidy calculated in terms of actual utilization, set at a level that is roughly compatible with efficient pricing, may be the best of a number of imperfect alternatives. A composite measure of utilization of a number of different services, using fixed weights roughly proportional to marginal costs, might be a suitable basis for calculating the subsidy. 4.3. Demand charges

Where responsive pricing is used there would be no need for demand charges of the usual type. A case can be made for a demand charge or customer charge based on the size of the fuses or the circuit-breaker settings at the customer’s meter, as a measure of the cost to the utility of being ready to meet the impact of the load the customer might throw on the system, as well as the impact on the quality of service to neighboring customers. One might even consider a charge based on the degree to which the customer makes abrupt changes in his power demand. Actual demand charges are a long way from reflecting SRSMC, and in many cases tend to induce considerable ine~ciency. A typical demand charge of $10 per KW per month measured on the basis of a KWH consumed during a 15 minute period is equivalent to a charge of $40 per KWH for power consumed during the critical 15 minute period. Worse, if this charge is subject to an 11 month 90 percent ratchet, the eventual cost to the customer of a KWH consumed during a critical period can be as high as $436. At these charges it often pays the customer to engage in costly load control programs, without there being any assurance that the reduction in load will occur during the system peak and lower the utility’s costs to any comparable extent. Ratcheting appears to be more a way of preserving utility revenues in the event of a business downturn at the expense of customers, whereas most utilities are better able to weather a recession than many of its customers.

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There would be something to be said for basing demand charges only on demand peaks occurring during periods when a system peak is likely, but this would require a more expensive form of metering. A still more expensive scheme is to charge customers for their consumption during the actual system monthly peak; if customers are to react rationally to such a rate, they must be provided with a telemetering of the system load. It leads to an interesting form of game playing in which customers seeing the system load approaching the peak are motivated to reduce their load, but thereby shift the peak to some other time. If the usual form of demand charge is retained, charges based on the maximum consumption in any two- or four-hour period would probably correlate better with the system peak than the 15minute demand. 4.4. Optimum uniform pricing and long term commitments Where prices cannot be varied instantaneously, a different approach is required. The marginal cost that is relevant for the setting of a price in advance which will necessarily cover a variety of usages with varying SRMSC’s is not any variety of ‘long-run marginal cost’ but rather an average of expected SRMSC’s of the various subcategories of usage. The weights to be used in this average are not the total amounts used in each category but rather the amounts that would be added to usage in each subcategory as a result of a small reduction in the common price. In effect one is asking whether the package of usages that would be added by a reduction in price is worth its cost. It is sometimes argued that prices should be set at some version of longrun marginal cost in order that consumers may intelligently make long-run commitments such as those involved in the installation of durable equipment. This can be handled in the context of short-run marginal cost pricing by allowing for the making of contracts for the purchase of power at specified times over a specified future period at pre-established prices, with or without indexing to a general price level or the cost of fuel. Incentives for efficient adjustment can be retained if provision is made for the purchase of additional power at the current marginal cost rates, and alternatively for the relinquishment or sale back of contracted for power at these same current rates. The main difticulty would be in assuring that such contracts would not involve undue discrimination or favoritism. 5. Conclusion

Marginal cost pricing is not merely a minor adjustment to rates, but a major change in rate-making philosophy that makes full use of modern pricing technology, puts efficiency in first rank and considerations of

RF

G

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distributional equity become secondary. Even matters of financial solvency have better solutions than a routine raising of rates to meet a revenue requirement. Equity, distributional, and financial objectives can be met in a number of alternative ways, but if rates fail to produce efficient results there is no way to make this up elsewhere. Responsive pricing is the only way in which full efficiency can be approached. For privately-owned utilities an escrow fund mechanism can be the means whereby the freedom of the utility to vary prices on short notice can be reconciled with the need for regulatory constraints against excessive exploitation of the monopoly position. Ideally the closest possible approach to maximum efficiency will probably call for a subsidy of some sort, even when prices are increased above SRSMC in accordance with a second-best or Ramsey principle. The advantages of preserving the financial independence of the utility and the incentives to good management that are enhanced by such independence may combine with Ramsey margins in the context of a highly suboptimal tax system to lead to being satisfied with the level of efficiency achievable without subsidy. What is clear, in any case, is that there is a strong case against the placing of special tax burdens on utilities, and even for exempting utilities from general taxes where this can be done without introducing distortions from another angle. In the case of publicly-owned utilities it is clearly desirable to avoid treating the utility as a money cow, as has been done in some instances. Appendix A: Short-run marginal cost of hydro power

Let R

W(t) U(r) &I% KM(H) KE(H1 M(t)

F(w, tl

V(r)

be the capacity of the reservoir, be the amount of available water in the reservoir, be the rate of utilization of the water, is the rate of electrical energy production, =dE/dU be the effective head or marginal hydro-electric conversion rate as a function of water volume and power output, is the maximum capacity in kilowatts of the turbo-generators, is the output of the generators at maximum efficiency for given H, is the marginal cost of power, is the net rate of inflow into the reservoir after allowing for evaporation, seepage, and top level usage for irrigation, fish ladders, etc., is the scarcity value of water utilized at time t.

There will be four reservoir states, spilling - S, full - F, part full - P, and empty - E, to be combined with three generator states, capacity K, part load G, and idle, 0, combining to produce a total of 12 plant states. Of these SO,

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spilling but not generating, is nearly always uneconomical, and four others, FK, FO, EK, and EO involve two constraints and will exist only momentarily as transition states between others, leaving 7 states to be considered. In the simple case approximated by some high head plants, variations in H are insignificant and F is independent of W. The seven significant conliguration types can then be analyzed as follows. SG. Water spilling and generation less than capacity: then M =O; a Ramsey price may be greater than 0, but must be such as to limit demand to less than generator capacity KM. SK. Water spilling and generation at capacity: Here M is discontinuous from ML=0 to MU =infinity. If the hydro plant is the sole supplier, price must be such as to produce a demand equal to KM, otherwise price will be determined by reference to marginal cost in alternative sources. FG. Reservoir full but not spilling; generation therefore equal to net inflow: E =H * F
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spillage will be much the same. In condition PG, instead of V being constant, if it is positive it will, upon optimization, decrease over time in a manner that can be determined as follows. A drawdown of dW at time t yielding a value of V(t) * d W will decrease the head by dH, so that in order to maintain generated output over a subsequent period dt there will be a further additional drawdown. If these drawdowns are then made good so as to restore the reservoir level to that which would have obtained without the drawdown dW, by a reduction in use dX at time t + dt, then in order for the total value of water use to remain at a maximum, the value of the drawdown at t must equal that of the restoration at t + dt, or V(t) * d W = V(t + dt) * dX. The value of dX can be determined in turn by considering that over the interval dt, E = U * H is to be constant, so we have dE = U * dH + H * dU = 0, and over the interval dt, dU = -(U/H) *dH. Then since dX=dW-dU *dt, we have V(t)*dW=V(t+dt)*[dW+(U/W)*dH*dt] dV/dt = I/ * (U/H) * (dH/d W).

and 64.1)

If V is zero it will remain zero over this phase, but otherwise will decrease exponentially at the rate (U/H) * (dH/d W). During the other four phase types the value of V will be determined mainly by the requirement of meeting one of the constraints F, E, K, or 0, eq. (A.l) serving as a bound which, if about to be transgressed, will trigger a transition to another phase type. The above assumes perfect foresight as to the variations in inflow F and power demand. In practice one would have to consider a number of alternative future scenarios and their probabilities, with the value V to be imputed to water being an average of what would occur under the various alternatives and their respective probabilities. As the likelihood of a condition permitting V to fall faster than the exponential limit (A.l) occurring prior to the next spill decreases, V will approach zero.