By: John T. Wenders Ama Agyeiwaa Ferkah Eco 435

INTRODUCTION  The traditional theory of peak-load pricing argues that peak period users should bear marginal operating costs and all of the marginal capital costs, and off-peak users should be charged prices which cover only marginal operating costs.  Economists have extended peak load pricing theory to include the effect of a regulatory constraint, with the conclusion that the regulated utility will set off-peak prices at the same level as an unconstrained monopolist and set peak prices below the level that would be set by an unconstrained monopolist  The implication of this analysis is that the regulated firm will, therefore, expand productive capacity beyond the level that would be set by the unconstrained monopolist, possibly even beyond the level that would maximize social welfare

PURPOSE  This paper shows that off-peak marginal cost prices almost always should include some marginal capacity costs and that the profit maximizing regulated electric utility may set price above marginal cost at the peak and below marginal cost during the off-peak in order to encourage the expansion of capital-intensive base load generating capacity.  Looks at fixed peak pricing problem (the exclusion of the possibility that marginal cost pricing may shift the peak).  Assumes maximization of economic welfare in the market for electricity, which is implemented by maximizing the sum of consumer and producer surpluses.

LONG-RUN CAPACITY ADJUSTMENTS  Assume 1 - peak load capacity 2 - intermediate load capacity 3 - base load capacity Bi - annual marginal and average capital cost for each technology, and it is assumed that B3> B2 > B1 bi - marginal and average energy cost of producing a KW of electricity for one year, and it is assumed that b1 > b2 > b3.  Thus, base load capacity has high capital costs and low energy costs  peak capacity has low capacity costs and high energy costs.  Intermediate capacity lies somewhere in between these extremes.  It is assumed that b1 + B1 > b2 + B2> b3 + B3.

Cont. TABLE 1 ANNUALIZED CAPITAL AND ENERGY COSTS BY PLANT TYPE  This gives a rough estimate of the magnitudes involved from data supplied by Tucson Gas and Electric Company TYPE OF LOADTYPE OF PLANTBibi BASECOAL STEAM$100.00$ INTERMEDIATEOIL STEAM$ 40.00$ PEAKINTERNAL COMBUSTION $ 20.00$240.90

Cont. FIGURE 1 ANNUAL LOAD DURATION CURVE This curve is a descending arrangement of the hourly demand for electricity during a year. Thus, at least KW3 amount of capacity is needed for t2 hours in the year, while at least KW2 is needed for only t1 hours. t* represents the number of hours in a year = t1 and t2 divide the year into three periods, each of which make up a fraction of the year defined by W1 = t1/t*, W2 = (t2 - t1)/t*, W3 = (t* - t2)/t*.

Cont.  Suppose this utility has built KW3 units of base load capacity, and is contemplating increasing this capacity by one KW. As an alternative, it must consider the cost of one additional unit of intermediate capacity. MC3 = B3 + (t2/t*)b3 MC2 = B2 + (t2/t*)b2.  If MC3 < MC2, base load rather than intermediate load capacity should be added, and this should continue up to the point where MC3 = MC2, t2/t* = WI + W2 =(B3 - B2)/( b2 – b3 )  Since W1 + W2 + W3 = 1, W3 = 1 - (B3 - B2)/( b2 – b3 )  W1, W2, and W3 depend only on the relative capital and energy costs of the three alternative capacities and do not depend in any way on the shape of the load duration curve. This curve could be flatter or steeper without altering the size of the w's.  But the amount of each kind of capacity will vary with the load duration curve

MARGINAL COST PRICING WITH HOMOGENEOUS CAPACITY

MARGINAL COST PRICING WITH MIXED CAPACITY The dashed vertical lines indicate the break points in load duration among the three supply periods and correspond to the optimal t1 and t2 derived in the first part of this paper. Peak capacity operates only during the first or peak pricing period, intermediate load capacity operates during both the first and second pricing periods, and base load capacity operates during all three pricing periods

Cont.

TABLE 2 Table 2 shows the prices which will be charged during each of the three pricing periods

Contrast these results with those of Bailey and White  When demands are independent, BW find that off-peak prices are the same as for an unconstrained monopolist. The results of row three in Table 2 show that both off-peak prices are reduced below those of the unconstrained monopolist.  BW emphasize that the regulatory constraint results in a lowering of peak price below the unconstrained monopoly level and that peak price might even be lowered below the welfare maximizing level. The results in Table 2 show that BW's results may be obtained in our model. However, since off-peak prices will be lower in our model- and quite possibly below the welfare maximizing level-the necessity for the lowering of peak prices is reduced  Finally, BW emphasize the possibility of a reversal between peak and off-peak prices. Since our model has shown that off-peak prices will be lower, and peak prices higher, than those obtained with BW's model, the possibility of peak/off-peak price reversals is similarly reduced.

CONCLUSION  The traditional theories of peak load pricing and the regulated firm both assume homogeneous production capacity. The above analysis has demonstrated that when it is optimal to employ capacities with different capital and energy costs, the conclusions of both these theories are modified considerably, and these modifications are particularly relevant to the application of these theories to the electric power industry