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Economies of Scale and Optimal Capital in Nuclear and Fossil Fuel Electricity Production.


This paper tests for economies of scale in the electric utility industry using a five-year panel data set that includes both fossil fuel and nuclear fuel electricity generation. In addition, a variable cost function is used as opposed to a total cost function because the assumption of cost-minimizing production inputs is not met. That is, electric utilities are overcapitalized. Therefore, the optimal capital stock is estimated, which is significantly less than the actual capital stock, and an estimate of economies of scale is generated. Evidence suggests that finns are operating on the negatively sloped portion of the long-run average cost curve near the trough. This indicates either slight economies of scale or no economies of scale. (JEL L9)


Nerlove [1963] and Christensen and Green [1976] use a neoclassical cost function approach to analyze the electric utility industry to see if economies of scale exist in investor-owned electric utilities. Nerlove uses a cross-section from 1955 and a Cobb-Douglas cost function and determines that there is evidence of economies of scale. Christensen and Green use cross-sectional data and a translog cost function for 1955 and 1970. Similarly, they find strong evidence of economies of scale in 1955 but they also find that economies of scale are exhausted by 1970. These papers are the foundation of a long line of research involving economies of scale in the investor-owned portion of the electric utility industry.

Unlike Nerlove and Christensen and Green, who both use a total cost function, Nelson [1985, 1989], Krautmann and Solow [1988], Nemoto et al. [1993], and Thompson et al. [1996] use a variable cost function to test for economies of scale. A variable cost function assumes that capital is fixed in the short-run, which may result in a suboptimal capital input. The total cost function assumes that a firm uses the cost-minimizing quantities of inputs. This study assumes that the capital input is not optimal and uses a variable cost function.

Besides applying a variable cost function, the sample in this study includes utilities that use both fossil and nuclear fuels, which is a better representation of steam generation in the U.S., rather than using a sample of exclusively fossil fuel utilities. Of the aforementioned papers that use a variable cost function, only Thompson et al. [1996] includes both fossil and nuclear fuel firms in their sample. This present study differs from Thompson et al. by testing for economies of scale at the firm level. Their study tests for economies of scale at the generation level and disregards the transmission and distribution of electricity. Thus, this paper contributes to literature by using a variable cost function, a sample that represents the industry- and firm-level data.

The remainder of this paper is organized as follows. The second section will present the functional form for the empirical analysis. The third section will discuss the impact of nuclear power in electric utility research. The fourth section will present the empirical analysis, and the fifth section will summarize and present a conclusion. The data are explained in the Appendix.

Functional Form

The term "economies of scale" refers to whether the average total cost will increase or decrease as the firm increases its output along the least cost expansion path. In other words, is [partial]In TC/[partial]In Y less than 1, indicating economies of scale, or greater than 1, indicating diseconomies of scale? Similarly, it is possible to test for returns to scale using a production function. The term "returns to scale" differs from economies of scale because this refers to the change in output for an equal proportionate change in all inputs, independent of whether they lie on the least cost expansion path.

Theoretically, two conditions required for the valid use of a production

function in empirical research are that a firm chooses its level of output and that the quantities of production inputs are exogenous. These conditions are necessary because the production function indicates the maximum output for given quantities of production inputs. Thus, the firm's decision is the output quantity, and the quantities of production inputs are exogenously set by the existing technology. In the electric utility industry, these two conditions are not met. That is, firms are required to produce enough electricity to meet demand at a regulated price at all points in time, and the quantities of production inputs are a function of their prices and are not exogenous. The prices of inputs are, in most cases, set in competitive markets and are themselves exogenous. [1] Therefore, the cost function is preferred to the production function because production quantity and input prices are exogenous and firms attempt to minimize the ir cost.

The translog functional form is the most appropriate for this study. It is preferred to the Cobb-Douglas functional form because of its greater flexibility. The Cobb-Douglas functional form estimates the explanatory variables' elasticity parameters only and imposes a unitary cross-elasticity. Alternatively, the translog functional form allows different cross-elasticities, and elasticities vary with output and input prices.

Christensen and Green's [1976] regression is run as a system of equations that includes the cost function and the cost share for two of the three inputs. [2] Since then, numerous papers on the electric utility industry have used the same or a similar system of equations. This trend in literature is consistent with Guilkey et al. [1983] which shows evidence of the translog functional form performing better than the extended generalized Cobb-Douglas and the generalized Leontief function forms in tests of scale economies.

However, using a total cost function is inappropriate in the electric utility industry. The assumption of the total cost function that input cost shares are optimal states that utilities are operating on their long-run expansion paths. That is, for the required level of output, each firm is using the most efficient quantity of all inputs, including capital. An alternative to this assumption is that firms only use the most efficient level of variable inputs, while the capital stock is assumed to be fixed in the short run. This assumption is used by Nelson [1985, 1989], Krautmann and Solow [1988], Nemoto et al. [1993], and Thompson et al. [1996] and is consistent with the unusual characteristics of capital in the electric utility industry. That is, the high capital intensity of the industry, the cost needed to change the capital structure within a firm, and the time needed to change the capital structure within the firm, especially large power plants, all contribute to a firm not operating at the cost-minimizin g level of capital.

This quasi-fixed nature of capital is implied, for example, by Tobin's q investment theory [Tobin, 1969]. In addition to the actual cost of plant expansion (or reduction), the disruption of operations causes a firm to incur adjustment costs when changing the capital stock. Tobin states that the adjustment cost function is convex, which implies that the firm has an incentive to change its capital stock slowly. Combining Tobin's adjustment cost theory with the unique characteristics of capital in the electric utility industry, it is apparently unlikely that an electric utility is ever at its optimal capital level.

Therefore, since capital is quasi-fixed, the appropriate model is the variable cost function:

ln VC = [[alpha].sub.0] + [[sigma].sub.i] [[alpha].sub.i] ln[P.sub.i] + [[alpha].sub.Y] lnY + [[alpha].sub.k] lnK + [[alpha].sub.T]T

+ 1/2 [[sigma].sub.i] [[sigma].sub.j] [[gamma].sub.ij] ln[P.sub.i] ln[P.sub.j] + 1/2 [[gamma].sub.YY] [(lnY).sup.2] + 1/2 [[gamma].sub.kk] [(lnK).sup.2]

+ [[gamma].sub.TT][(T).sup.2] + [[sigma].sub.i] [[gamma].sub.iY] lnY ln[P.sub.i] + [[sigma].sub.i] [[gamma].sub.iK] lnK ln[P.sub.i]

+ [[sigma].sub.i] [[gamma].sub.iT]T ln[P.sub.i] + [[gamma].sub.YK] lnY lnK + [[gamma].sub.TK] T lnK + [[gamma].sub.TY] T lnY, (1)

including the variable cost share equation:

[S.sub.i] = [[alpha].sub.i] + [[gamma].sub.iY] ln Y + [[gamma].sub.iK] ln K + [[gamma].sub.iT] T + [[sigma].sub.j] [[gamma].sub.ij] ln [P.sub.j],

[[gamma].sub.ij] = [[gamma].sub.ij], and i, j = L, F. (2)

A time trend is included to capture changes in technology. The cost function is homogeneous of degree 1 in prices, which implies the following constraints on parameter values:

[[sigma].sub.i] [[alpha].sub.i] = 1, [[sigma].sub.i] [[gamma].sub.iY] = [[sigma].sub.i] [[gamma].sub.iK] = [[sigma].sub.i] [[gamma].sub.iT] = [[sigma].sub.i] [[gamma].sub.ij] = [[sigma].sub.j] [[gamma].sub.ij] = 0, i, j = F, L. (3)

One contribution of this study is that it defines production technology as the array of diverse generation technologies (nuclear and fossil fuels), as did Kamerschen and Thompson [1993]. That is, all generation technologies are available to all producers who then choose the most appropriate combination. Consequently, this study does not theoretically nor empirically differentiate firms that have nuclear power in their production mix from firms that do not have nuclear power in their production mix. Thus, there is no dummy variable for firms with nuclear generation in the cost function.

Nuclear Power

Nuclear power is a significant portion of the total electrical energy generated in the U.S. (22.5 percent in 1995). Therefore, it should be included in tests for economies of scale. In addition to this prevalence in the industry, nuclear power is central to many policy issues and its exclusion in research limits the ability to draw policy or efficiency conclusions.

Except for Kamerschen and Thompson [1993] who use a total cost function, all of the firm-level research to date in the utility industry excludes the nuclear power portion of generation. The only other studies relevant to this research of the electric utility industry that involved nuclear power are Krautmann and Solow [1988] and Thompson et al. [1996]. However, the unit of observation in the Krautmann-Solow paper is the power plant, and Thompson et al. studies the generation level of production exclusively.

There are reasons for excluding nuclear power in the earlier research. Kamerschen and Thompson [1993] explain that the nuclear portion of generation is often avoided in literature by stating the need for homogeneity in technology. [3] Another reason for excluding nuclear power in the earlier studies is due to the small portion of total net generation attributed to nuclear power. In 1976, when Christensen and Green published their, paper, nuclear power contributed less than 10 percent of net generation, and excluding it from the mix probably did not strongly affect their results. Consequently, they cannot be criticized for excluding nuclear power generation from their studies.

Currently, the significant contribution of nuclear power cannot be ignored in empirical studies. To do so will cause one of two errors. First, if the research uses utilities that have nuclear power plants and exclude the nuclear data, the firms' price of fuel will be miscalculated. Consider the two standard methods of calculating the price of fuel. The first method is shown in (4), where [w.sub.i] denotes the percentage of total British thermal units (Btus) and [P.sub.i] denotes the price per million Btus:

[P.sub.fuel] = [[sigma].sub.i] [w.sub.i] [P.sub.i], i = oil, coal, gas, nuclear. (4)

It is apparent from (4) that by including only the price of fossil fuels, [P.sub.fuel] will be calculated in such a manner that it does not accurately capture the firm's fuel price. Another method of calculating the fuel price is by dividing the total fuel cost by generation. The problem with this method when excluding nuclear power is that it assumes a firm will use the same distribution of fossil fuels whether or not it uses its nuclear generation capabilities. This is a problem because many firms run their nuclear plants continuously to generate power, and the difference between the nuclear generation and demand is filled by using the most convenient type of fossil fuel generation. Whereas, a firm using solely fossil fuel generation will tend to use the least cost combination of fossil fuel generation technologies. The second error is that if the research excludes utilities with nuclear power plants from the sample, the model will not capture efficiencies (or inefficiencies) in the industry that result fr om combining nuclear generation along with other generation methods.

Empirical Analysis

The regression uses a panel of 83 investor-owned utilities for 1991 to 1995 where, in 1995, at least 85 percent of a firm's output in megawatt hours is from fossil and nuclear fuel. Nuclear generation composes 24 percent of the sample's output. The regression results are presented in Table 1. [4]

As previously stated, the existence of economies of scale is determined by the percentage change in total cost relative to the percentage change in output. In general, economies of scale can be measured as:

economies of scale = 1 - [partial]ln C/[partial]ln Y. (5)

A positive value indicates economies of scale and a negative value indicates diseconomies of scale. [5] Applying (5) to the variable cost translog functional form, short-run economies of scale, or the output elasticity of cost assuming a quasi-fixed capital quantity, can be measured as:

short-run economies of scale = 1

- ([[alpha].sub.Y] + [[gamma].sub.YY] ln Y + [[sigma].sub.i] [[gamma].sub.Yi] ln [P.sub.i] + [[gamma].sub.YK] ln K + [[gamma].sub.YT] T),

i = L, F. (6)

To determine if long-run economies of scale exist, apply (5) to the total cost function, where K = [K.sup.*] (the optimal level of capital): [6]

long-run economies of scale = 1

-([[alpha].sub.Y] + [[gamma].sub.YY] ln Y + [[sigma].sub.i] [[gamma].sub.Yi] ln [P.sub.i] + [[gamma].sub.YK] ln [K.sup.*] + [[gamma].sub.YT] T/1 - ([[alpha].sub.K] + [[gamma].sub.KK] ln [K.sup.*] + [[sigma].sub.i] [[gamma].sub.Ki] ln [P.sub.i] + [[gamma].sub.YK] ln Y + [[gamma].sub.TK] T),

i = L, F. (7)

For (7) to be operational, it is necessary to calculate the optimal value of capital stock. This is accomplished by setting [partial]TC/[partial]K equal to zero, where TC = VC + [P.sub.K] (K). [7] When applied to the variable cost translog cost function:

[[alpha].sub.K] + [[gamma].sub.KK] ln [K.sup.*] + [[sigma].sub.i] [[gamma].sub.Ki] ln [P.sub.i] + [[gamma].sub.KY] ln Y + [[gamma].sub.TK] T + [P.sub.K][K.sup.*]/estimated VC = 0,

i = L, F. (8)

Table 2 shows the results of applying (6) and (7) to the regression coefficients and variables. The economies of scale averages are representative of nearly all firms in the sample period. The difference in the short- and long-run economies of scale estimates, and the high K/[K.sup.*] estimate, indicates that firms are off their long-run expansion path. Thus, this paper has empirical evidence supporting the need to solve for the cost minimizing capital stock, as opposed to assuming that firms are employing the cost minimizing level. [8]

From 1995, Figure 1 shows the cost curves for the firm with the median output of fossil fuel utilities, and Figure 2 shows the cost curves for the firm with the median output of nuclear fuel utilities. These curves show that the short and long-run cost curves are not tangent at the firm's actual output, but at a point of higher output. Thus, these firms are overcapitalized. [9] However, the firms are operating near the trough of the long run average cost curve, which indicates an efficient level of generation had they been employing the optimal level of capital.

It is worth noting that the trough of the nuclear fuel long-run average cost curve is at a much greater level of output than the trough of the fossil fuel long-run average cost curve. This is consistent with the idea that economies of scale exist through a high level of output for firms that include nuclear generation in their mix. The higher average cost for the nuclear fuel utility is representative of the industry. That is, utilities with nuclear generation have an average cost that is 43 percent higher than that of fossil fuel utilities.

This is likely due to the decreased efficiency of fossil fuel production that exists when nuclear production is added to the mix. That is, firms employ nuclear production as baseload technologies and use fossil fuel production to meet demand peaks. This causes fossil fuel production at high average cost levels, which more than offsets the low average cost of nuclear production. Firms that employ fossil fuel generation as their baseload technology are able to adjust their capital such that they operate near the trough of the long-run average cost curve. Thus, the average cost of electricity generation is higher at the firm level when nuclear generation is included in the mix.

Further analysis indicates evidence of a trend of increasing inefficiency in the industry. Table 3 shows that the mean and median overcapitalization estimate is increasing throughout the sample period. Thus, firms are moving further from their expansion path. Since firms receive a rate of return that exceeds the cost of capital, they have an incentive to overcapitalize [Douglas and Rhine, 1999].

The results also show that over the sample period, the industry is moving away from a downward-sloping long-run cost curve toward a flat cost curve. Table 4 shows a consistent decrease in the long-run economies of scale estimate. Thus, the cost curve is flattening out over time. This indicates that firms are learning how to lower the costs of generation for a wide range of output. That is, the high average cost of using fossil fuel plants to meet demand peaks is being reduced.


Using a variable cost function and an industry representative sample, the empirical analysis suggests either slight economies of scale or no economies of scale. That is, firms are operating on the negatively sloped portion of the long-run average cost curve near the trough. However, they possess more capital than the cost-minimizing level. This is true even when recognizing that firms must overcapitalize to some degree to compensate for the electricity demand forecasting error.

Within the current environment of deregulation, competition among utilities at the generation stage will give firms an incentive to reduce costs by not overcapitalizing. Thus, the trend of increasing overcapitalization, which exists throughout the sample period, will likely slow or reverse with deregulation as firms attempt to capture customers. Also, as firms continue to learn how to reduce costs of generation (flatten out the long-run average cost curve), costs will be reduced and electricity prices will consequently fall.

(*.) St. Mary's College of Maryland--U.S.A. The author is grateful to Stratford Douglas for his helpful comments. Any errors are the responsibility of the author.


(1.) Similarly, realizing that the input prices are determined in the market, it is unlikely that there is any correlation between the stochastic portion of the prices and the error term of a cost function. Alternatively, it is more likely that a correlation exists between the stochastic portion of the input quantities and the error term of a production function since firms choose their input quantities.

(2.) For the regression to be operational, one cost share equation must be dropped from the system. Also, the total cost and the remaining input prices must be divided by the price of the input from the dropped cost share equation (see Christensen and Green [1976]).

(3.) Christensen and Green [1976] and Nelson [1989] state the desire for homogeneity in production technology.

(4.) In Table 1, the high t-statistics and a high adjusted [R.sup.2] are not unusual for this type of regression. This is due to the flexibility of the translog functional form, which results in the functional form fitting the data. The high [R.sup.2] can also, in part, be contributed to multicollinearity. However, the existence of multicollinearity does not bias the estimates.

(5.) Economies of scale is a long-run concept. However, the cost curve, where capital is not at the cost-minimizing level, is the short-run cost curve. Consequently, the existing literature somewhat misleadingly defuses the output elasticity of cost with respect to short-run output, changing the short-run economies of scale.

(6.) This form is used by Nelson [1985, 1989], Krautmann and Solow [1988], and Nemoto et al. [1993].

(7.) Since a logarithmic cost function is used, applying the chain rule to [partial]TC/[partial]K results in:

([partial]exp(In VC)/[partial]In VC)([[partial]lnVC/[partial]lnK)([partial]lnK/[partial]K),

which is equal to (8).

(8.) The estimated K/[K.sup.*] should not be interpreted as an absolute and accurate measurement of overcapitalization. Alternatively, it should be viewed as evidence of the existence of overcapitalization, suggesting that the actual level may be very high.

(9.) The curves are generated using the actual capital stock for the short-run cost curve and the optimal capital stock for the long-run cost curve.


Christensen, L.; Green, W. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, 84, 1976, pp. 655-76.

Cowing, T.; Small, 3.; Stevenson, R. "Comparative Measures of Total Factor Productivity in the Regulated Sector: The Electric Utility Industry," in Tom Cowing; Rodney Stevenson, eds., Productivity Measurement in Regulated Industries, New York, NY: Academic Press, 1981, pp. 161-77.

Douglas, S.; Rhine, R. "Disallowances and Overcapitalization in the U.S. Electric Utility Industry," unpublished manuscript, 1999.

Energy Information Administration. Financial Statistics of Selected Investor-Owned Electric Utilities: 1996, December 1997.

Guilkey, D. K.; Knox Lovell, C. A.; Sickles, R. C. "A Comparison of the Performance of Three Flexible Functional Forms," International Economic Review, 24, 1983, pp. 591-616.

Kamerschen, D.; Thompson, H., Jr. "Nuclear and Fossil Fuel Steam Generation of Electricity: Differences and Similarities," Southern Economic Journal, 60, 1993, pp. 14-27.

Krautmann, A.; Solow, J. L. "Economies of Scale in Nuclear Power Generation," Southern Economic Journal, 55, 1988, pp. 70-85.

Moody's Investors Service. Moody's Public Utility Manual, various.

Nelson, R. "Returns to Scale from Variable and Total Cost Functions," Economic Letters, 18, 1985, pp. 271-6.

_____. "On the Measurement of Capacity Utilization," The Journal of Industrial Economics, 37, 1989, pp. 273-86.

Nemoto, J.; Nakanishi, Y.; Mandono, S. "Scale Economies and Over-Capitalization in Japanese Electric Utilities," International Economic Review, 44, 1993, pp. 431-40.

Nerlove, M. "Returns to Scale in Electric Supply," in Carl F. Christ; Milton Friedman; Leo A. Goodman; Zvi Griliches; Arnold C. Harberger; Nissan Liviatan; Jacob Mincer; Yair Mundlak; Marc Nerlove; Don Patinkin; Lester Telser; Henry Theil, eds., Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld, Stanford, CA: Stanford University Press, 1963, pp. 167-98.

Thompson, H.; Hovde, D. A.; Irwin, L.; Islam, M.; Rose, K. "Economies of Scale and Vertical Integration in the Investor-Owned Electric Utility Industry," report, 96-05, National Regulatory Research Institute, 1996.

Tobin, J. "A General Equilibrium Approach to Monetary Theory," Journal of Money, Credit, and Banking, 1969, pp. 15-29.
                         Estimated Coefficients
Parameters                      Estimates
[[alpha].sub.O]                   2.795     (14.304)
[[alpha].sub.Y]                   1.827     (71.924)
[[alpha].sub.K]                  -0.829    (-23.826)
[[alpha].sub.T]                   0.038      (3.860)
[[alpha].sub.L(price)]           -0.973    (-70.808)
[[alpha].sub.F(price)]            1.973     (70.808)
[[gamma].sub.YY]                  0.153     (37.284)
[[gamma].sub.KK]                  0.141     (32.184)
[[gamma].sub.TT]                  0.001      (0.967)
[[gamma].sub.TK]                 -0.001     (-7.748)
[[gamma].sub.TY]                  0.010      (9.021)
[[gamma].sub.YK]                 -0.146    (-35.349)
[[gamma].sub.F(price)F(price)]    0.207     (97.909)
[[gamma].sub.L(price)L(price)]    0.207     (97.909)
[[gamma].sub.YL(price)]          -0.176    (-57.934)
[[gamma].sub.YF(price)]           0.176     (57.934)
[[gamma].sub.KL(price)]           0.166     (52.972)
[[gamma].sub.KF(price)]          -0.166    (-52.972)
[[gamma].sub.L(price)F(price)]   -0.207    (-97.909)
[[gamma].sub.TF(price)]           0.010      (8.684)
[[gamma].sub.TL(price)]          -0.010     (-8.684)
Notes: t-statistics are in parentheses.
For the adjusted [R.sup.2], the cost function is
0.991 and cost share is 0.745.
                       Average Economies of Scale
                               All Utilities  Nuclear Utilities
Short-Run Economies of Scale
  Sample Mean                   .274              .305
  Sample Median                 .275 (.006)       .306 (.007)
  1995 Median                   .278 (.006)       .311 (.007)
Long-Run Economies of Scale
  Sample Mean                   .007              .005
  Sample Median                 .006              .005
  1995 Median                   .005              .004
  Sample Mean                   7.46              9.04
  Sample Median                 6.45              7.94
  1995 Median                   6.67              8.38
Megawatt Hours (in thousands)
   Sample Mean                  18,071,032        26,135,252
                               Nonnuclear Utilities
Short-Run Economies of Scale
  Sample Mean                       .246
  Sample Median                     .246 (.005)
  1995 Median                       .249 (.005)
Long-Run Economies of Scale
  Sample Mean                       .008
  Sample Median                     .007
  1995 Median                       .006
  Sample Mean                       6.07
  Sample Median                     5.35
  1995 Median                       5.50
Megawatt Hours (in thousands)
   Sample Mean                      10,923,201
Notes: Standard errors are in parentheses.
K/[K.sup.*]  1991  1992  1993  1994  1995
Mean         7.0   7.5   7.5   7.3   7.9
Median       6.4   6.2   6.4   6.6   6.7
                           Economies of Scale
Long-Run  1991   1992   1993   1994   1995
Mean      .0076  .0071  .0066  .0060  .0056
Median    .0073  .0067  .0066  .0056  .0052


Variable cost is a function of [P.sub.fuel], [P.sub.labor] subject to Y, K. [P.sub.fuel] is calculated by dividing total fuel costs by output. Output per utility is measured in megawatt hours of generation, obtained from the Energy Information Administration [1997, Table 43]. The labor price is determined by dividing the total labor cost by the number of employees, where the total labor cost is equal to salaries and wages charged to electric operation and maintenance; and the number of employees is equal to the number of full-time employees plus one-half the number of part-time employees. All labor data are obtained from the Energy Information Administration [1997, Table 41].

To determine capital expenditure, the method presented in Cowing et al. [1981] is slightly modified. The capital expenditure presented in Cowing et al. is the product of the deflated capital stock and the capital service price. The capital stock is calculated by dividing the yearly net additions to the electric utility plant (NA) by the Handy-Whitman index (HW), obtained from Moody's Investors Service [various], and adding it to the previous year's capital stock:

[CS.sub.i] = [CS.sub.i-1] + [NA.sub.i]/[HW.sub.i], i = 1972 ... 1995. (A1)

The base year capital stock is calculated using a triangularized weighted average of the Handy-Whitman index, where K is the book value of the plant in service in 1972:

[CS.sub.1972] = K/[[[sigma].sup.20].sub.j=1](j/,[[[sigma].sup.20].sub.j=1]j) [HW.sub.j], j = jth year (1953 through 1972). (A2)

Contrary to Cowing et al. [1981], the sum of the base year capital stock and the net additions to capital stock is then multiplied by the 1995 Handy-Whitman index so that the capital stock is in current U.S. dollars. The calculation for the service price is shown in (A3), where CC is the cost of capital and DE is the depreciation rate:

[P.sub.k] = (CC + DE). (A3)

Cowing et al. multiplied the sum of the cost of capital and the depreciation rate by the Handy-Whitman index. This is not done because the capital stock is multiplied by the Handy-Whitman index. The cost of capital is the weighted average of the cost of debt and the estimate for the required return on equity for the utility. The weight for debt includes bonds and preferred stock. The cost of debt is calculated by averaging the yield of newly issued public utility bonds for each month. The required return on equity is calculated using the capital asset pricing model, and the depreciation rate is 3 percent. The net additions to capital stock are obtained from the Energy Information Administration [1997, Table 381, the beta used in the capital asset pricing model is obtained from Value Line, the estimated market return is a 48-year average (1947-95) of the return of the Standard and Poor's 500 stock index, and the risk-free rate of return is a 48-year average of three-month t-bills.

[Graph omitted]

[Graph omitted]
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Date:Jun 1, 2001
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