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Major professor Date fig :4; WM / / ’ MS U is an Affirmative Action/Equal Opportunity Institution 0-12771 MSU LIBRARIES m RETURNING MATERIALS: Place in book drop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. SCALE ECONOMIES AND UNIT AVAILABILITY IN STEAM-ELECTRIC GENERATION: A NONHOMOGENEOUS CAPITAL APPROACH by Mark A. Houldsworth A THESIS Submittod to Michigan Stat. University in partial {ulfillmant of tha raquiramants for the dagraa of DOCTOR OF PHILOSOPHY Departmant of Economics 1986 ABSTRACT SCALE ECONOMIES AND UNIT AVAILABILITY IN STEAM-ELECTRIC GENERATION: A NONHOMOGENEOUS CAPITAL APPROACH bY Mark A. Houldsworth This dissertation develops a model of electricity generating unit choice that explicitly recognizes the cost effects of declining unit availability with unit size. Unit availability tends to decline with size because forced outages and maintenance outages tend to increase with unit size. Ceteris paribus. declining unit availability causes expected output to grow at a slower rate than potential output. To test the effects of declining unit availability on size. a theoretical model is first developed in such a way that expected unit output is determined by the generating units’ instantaneous rate of utilization (unit size) and the expected availability rate of the unit. Next. an engineering - economics cost function for fuel and capital costs was developed that allowed both the inference of scale (dis)economies and an examination of the engineering factors influencing these economic characteristics. In the model. capital was disaggregated Mark A. Houldsworth into dimensions of size and efficiency. Capital costs were determined by unit size. fuel efficiency. and. other engineering design information. Expected fuel costs were determined by expected fuel prices. expected output. and fuel efficiency for the unit. Combining fuel costs and estimated capital costs. the models objective was to estimate the cost minimizing level of unit fuel efficiency. Once estimated. the model was validated by comparing predicted heat rates and average costs to the observed values. As the model could not be solved. to produce parametric tests of the extent of scale economies. the estimated model was used to simulate costs and efficiency for a variety of different geographical regions and exogenous engineering design circumstances. The primary conclusion of the dissertation is that when one controls for the cost effects of unit availability minimum efficient unit size is on the order of 250 MW. Further. costs are shown to be insensitive to size once this MES is obtained. This dissertation is dedicated to my grandfather. Earl E. Sexton. ii ACKNOWLEDGEMENTS In acknowledging those who have assisted me in producing this thesis the contributions of my dissertation committee are those that are most tangible. Professor Harry Trebing provided assistance both in developing the topic and in wading through the numerous rewrites. Professor Stephen Martin frequently accommodated his schedule for my questions throughout my graduate career. Professor Peter Schmidt's early advice on some of my econometric problems saved me from barking up several wrong trees. My chairman. Professor Kenneth Boyer. patiently guided me through the various stages that are required to produce good research. I could have undoubtedly saved several rewrites by paying closer attention to his advice at earlier stages in this process. Less tangible. but no less important. are the contributions made by family and friends. The dissertation is only a culmination of a much larger educating process. and throughout this process I have benefitted immeasurably from the emotional and financial encouragement from my family. iii ACKNOWLEDGMENTS . . . TABLE OF CONTENTS LIST OF TABLES . . . . . . . . LIST OF FIGURES . . . . . . . . CHAPTER I. II. III. IV. INTRODUCTION . . . . . . MODELING THE STEAM-ELECTRIC GENERATING PROCESS: A REVIEW . . . . . . . . 2.1 Models Which Assume Firm Level Optimization 2.2 Models Optimization . . . . A MODEL OF THE STEAM-ELECTRIC GENERATING PROCESS . . . 3.1 General . . . . . . 3.2 The Model . . . . . 3.3 Er Ante Costs . . . 3.4 3.4.1 General . . . 3.4.2 Cost Function . 3.4.3 AVERAGE TOTAL COSTS AND SCALE ECONOMIES 4.1 4.2 Simulation Results . iv The Plant Cost Function Estimation of the Which do not Assume Plant Firm Level Regression Results . The g5 Ante Cost Function . i ii vi vii 13 14 30 54 54 56 59 61 61 63 68 BO .80 84 TABLE OF CONTENTS (cont'd) V. CONCLUSIONS FROM THIS STUDY . . . . . 5.1 Summary of Thesis . . . . . . . 5.2 Implications of the Results . . 5.3 Limitations of the Study and Suggestions for Further Research APPENDICES I. APPENDIX A. DATA USED IN THIS STUDY . BIBLIOGRAPHY I I I I I I I I I I I I I I I .110 110 114 116 120 127 LIST OF TABLES TABLE 1.1 Availability Rates by Unit Size . . . . . . . . . 5 3.1 Plant Cost Regression Estimates . . . . . . . . . 68 3.2 Plant Cost Elasticities with respect to unit 812. I I I I I I I I I I I I I I I I I I I I 70 3.3 Plant Cost Elasticities with respect to (a-33 for DSL - 1 I I I I I I I I I I I I I I I I I I I 71 3.4 Plant Cost Elasticities with respect to (oz-a") ‘or DSL - O I I I I I I I I I I I I I I I I I I I 72 4.1 Regression of Actual Heat Rates on Predicted H..t R.t.' I I I I I I I I I I I I I I I I I I I 81 4.2 Regression of Actual Average Cost on Predicted Average Cost . . . . . . . . . . . . . . . . . . 81 4.3 - Minimum Average Costs and Cost Minimizing 4.19 Heat Rates for Different Fuel Prices . . . 86 - 101 A-1 Comparative Equivalent Availability Rates 40!" th. PIFIOd 1972 _ 1981 e e a I e a e a e a a 121 A-2 LiSt 0‘ Plant! a e e e e a e e e a e e e e e e e 124 9‘3 Li It 0‘ D.t. e e e a e s e e e e a e e e a e e e 12: vi LIST OF FIGURES FIGURE 4.1 Average Costs Versus Unit Size . . . . . . . . . 105 vii CHAPTER I: INTRODUCTION In this dissertation we show that the unit level long- run average cost function for steam-electric generation is characterized by either diseconomies or by constant returns to scale beyond a relatively small capacity size. This result is in contrast to the conclusions reached by most previous researchers and it should be of interest for two primary reasons. First. our results derive from an inclusion of implicit costs that have been effectively ignored in previous scale studies - the implicit costs of declining capital reliability with size. Secondly. there are several pending policy issues whose resolution rest partially on the determination of minimum efficient generating unit size.1 In this regard. a successful policy strategy will necessarily depend on a characterization of the technology that is complete with respect to all implicit costs of production. Below we consider these motivations in more detail. Plant and unit level scale economies in the electric power industry have been extensively examined over the past 30 to 40 years.2 A consensus emerging from this body of research is that the expected plant utilization intensity significantly contributes to the determination of plant level average costs or output. Since larger units tend to be utilized more intensively _2 the lower average costs observed for these units partially reflects the lower average capacity costs associated with intensive utilization. But while these studies have been careful in allocating economies separately to unit size and utilization they have ignored the fact that larger units tend to be less reliable and require longer scheduled maintenance downtimes and are. hence. less available for producing output. As far back as 1955 there existed fairly complete engineering literature discussions of the factors favoring and the factors against large electricity generating unit choices. Factors favoring large unit choices include declining per kilowatt capacity costs. lower operating and maintenance costs per kilowatt-hour. and increased fue; efficiency. Factors disfavoring large unit choices include. inter alia. larger firm or system reserve requirements and declining unit availability. Larger unit choices necessitate larger reserve expenditures because when a large unit is unexpectedly forced out or derated a more severe strain is put on the system in servicing demand. Another way of saying this is that the expected value of the output of a larger unit is less than the expected value of two half-sized units. even when the availability of the units is the same. To guard against the likelihood that the firm will not be able to meet a given load the firm must keep more reserves on hand when larger units are 4 chosen. 3 Declining unit availability with size results from two factors. First. larger units are typically designed for higher pressures and temperatures and tighter turbine tolerances. In the past these characteristics have led to higher forced outage rates for larger units as compared to smaller ones. Second. maintenance durations for larger units are longer because larger pieces of equipment must be disassembled. inspected. and replaced. For the most part. each of these factors continues to be important today. The engineering literature includes all of these concerns in current plant and firm models. But while the economic literature has recently begun discussing the factors disfavoring large unit choices it is surprising that there are no unit or plant level cost or production function studies which fully recognize these Problems. In addition to the model specification problems noted above. however. there are also overriding policy interests which motivate our analysis. The issue of scale economies is becoming increasingly important in electricity generating markets. That the typical electric utility usually employs a number of generating units suggests that the generation market may not be characterized by natural monopoly. And there have been several recent suggestions to deregulate tgis industry by vertically dismembering generation assets. If firm level multiplant or multiunit generation economies are 4 6 appropriable through other institutional mechanisms then unit and plant level economies would become the controlling factor in determining effective competition in bulk power markets. And baseload plant reliability stands out as an important influence in determining these economies. Additionally. even in the current regulated environment there should be interest in the cost effects of unit reliability. Commissions are at least indirectly responsible for encouraging unit and plant choices that complement the firm. If expected unit reliability and scheduled maintenance significantly affects costs. uninformed decisions will result when not taking availability into account. When investigating scale economies it is the relationship between scale and availability that is important. As we have noted above. the relationship between these two is inverse. Statistics on equipment availability which have been published regularly by the Edison Electric Institute since the late 1950's have all indicated declining unit availability with size. Table 1.1 illustrates this relationship with availability rates. equipment forced outage rates. and scheduled outage rates by unit size. 5 TABLE 1.1 7 Availability Rates by Unit Size 8 Equivalent Schedule Equivalent Forced Out Out k Availability Rate Rate 100 - 199MW .852 .059 .094 200 - 299MW .827 .080 .096 300 - 399MW .758 .122 .131 400 - 599MW .745 .132 .139 600 - 799MW .679 .199 .149 Since it seems plausible that managers are capable of forming expectations about unit availability and since availability would seem to affect the unit choice decision our instant problem is to explore how availability affects costs.9 Standard empirical results show that increases in unit size. ceteris paribus. lead to reductions in per kW 10 costs. Holding constant availability rates. then. average capacity costs should decline with output. In varying degrees. however. declining availability with size has the opposite affect on average costs. The cost effects of availability are most serious in baseload units. As baseload units are. by definition. economically preferred on a round-the-clock basis. the lack of availability over any period translates directly to the cost 6 penalty associated with operating units with higher short- run marginal cost. For non-baseload units. which may be designed to cycle with daily and seasonal loads. increasing forced outages would continue to increase expected average capacity costs. but planned outages may be scheduled for periods when the unit is idle. Since many of the anticipated outages do not affect the expected output of the unit. availability rates are less important in determining costs. Couched in other terms. the concern motivating an analysis of availability rate effects is utilization intensity. It is clear that one may produce the same output with a larger unit at low utilization or a smaller unit at relatively higher utilization. And indeed one can find ex post utilization intensities as low as 10-20 percent for high marginal cost peaking or cycling units. But in addition to the variability of utilization intensity there also tends to be a postive relationship between unit size and utilization. Larger units are more likely to be baseload or near baseload units with large utilization intensities relative to the smaller utilization rates expected for smaller peaking units. Consequently. ignoring utilization in unit or plant cost studies would seriously bias the cost effects of increasing unit size. One way that several authors have of controlled for differences in utilization is to introduce the ex post plant factor directly into the cost or production ,7 11 function. A robust result of these models employing the plant factor is that scale economies due to size are much smaller. if they exist. and ”economies" due to increased utilization are much more important. But while these authors have made important contributions to understanding plant and unit level cost functions there are problems with using plant factor as a proxy for ex ante utilization intensity. Expected utilization intensity. or plant factor. can be broken into two components: desired utilization and expected availability. Expected availability has been discussed above but we should take a closer look at desired utilization. For well known reasons. electricity production is distinct from processes which produce physical outputs. Firms are required to serve a peaky load schedule with an output which is economically non-storable. As a result of these demand and technology constraints. firms rationally choose some plants for which the desired utilization intensity is relatively small in trying to meet the firm's total annual load at the smallest cost. These are typically small. low capital cost-high fuel cost. peaking plants. At the other extreme are the higher capital cost- lower fuel cost plants designed to run continuously throughout the period. The intended utilization for these plants is one. Between these two extremes are cycling plants designed to run for intermediate lengths of time. 8 The question now arises as to what the effect is of mixing baseload and non-baseload units in a sample and controlling for ex 3253 utilization but not desired utilization. A first problem here is that there may be units with the same size and 25 £225 plant factor having different costs because of different desired utilization levels. Non-baseload units are designed with less efficiency because there is less incentive_gx ante to substitute fuel efficiency related capital for fuel when designing a unit if the desired utilization of the capacity over the period is small. Non-baseload units are designed with reduced turbine tolerances and lower steam and temperature conditions.12 And this translates to a substitution of fuel for efficiency related capital relative to the design characteristics of baseload units. But in addition to the differences in unit design for baseload and non-baseload of the same size. declining availability should more seriously affect baseload units as size grows. For non-baseload units. increasing planned outages with size may. depending on the level of desired utilization. be scheduled for periods when the unit is not needed. If increasing planned outages can be placed entirely during periods during which the unit is not desired then these planned outages will have no effect on ._x ante output of the unit. For baseload units. however. every increase in either expected scheduled outage or 9 expected forced outage directly inhibits ex ante output for the plant. There is little that we can say here with respect to the effects on average costs for different levels of desired utilization. Ceteris paribus. declining unit availability should lead to increasing average capacity costs for baseload units. The higher efficiencies associated with increasing unit size. on the other hand. should lead to declining average fuel costs for these units. For non-baseload units declining unit availability should have a relatively smaller impact on ex ante average capacity costs because. again. _35 3353 output for these units should be less affected by declining availability. But while the effects on average cost of different levels of desired utilization is unclear it is apparent that both desired utilization and availability combine to determine scale economies. Our study proceeds as follows. A review and critique of existing studies will be provided in Chapter II. In Chapter III we begin by developing the theoretical structure of our model. The approach developed to measure scale economies is nontraditional to a degree. The traditional neoclassical cost minimizing view of production is expanded to envelope specific engineering characteristics of capital. The result is a model that describes the electric power generating technology in terms of both its physical and economic attributes. 10 Total plant costs in the model will be comprised of annual capital costs and annual running costs. Chapter III continues from a theoretical development of the model to estimation and presentation of the plant cost function that will be used to determine the capital cost component of total plant costs. The plant cost function will be presumed to represent a generating unit manufacturer's schedule of investment costs for different plant characteristics. Chapter III will conclude with estimates of this plant cost schedule. Chapter IV begins with a discussion of how we use the model developed in Chapter III to determine the minimum average cost for plants in our sample. After discussing the solution to the model we then provide evidence that our model predicts observed average costs reasonably well. To take the next step in attempting to infer the extent of scale economies our modelling construct requires that we use the model to simulate cost minimizing efficiency levels and associated average costs for different plant sizes and relative factor prices. The presentation of the results of this simulation exercise will conclude Chapter IV. Finally. a summary of our study will be provided in Chapter V. CHAPTER I: ENDNOTES 1 We use the terms unit and plant interchangeably throughout. A generating plant is made up of one or more boiler-turbine-generator (BTG) units. While the focus of this analysis is on unit level scale economies the analysis that follows does allow for multi-unit economies to account for those instances when multiple units are included in a single plant. 2 Nordin (1947). Barzel (1964). Dhrymes and Kurz (1964). Cowing (1974). Huettner (1974). Fuss (1978). and Stewart (1979) are some of the more frequently cited studies in the literature. For an excellent survey of econometric studies of this industry see T. Cowing. and V. Kerry Smith. "The Estimation of a Production Technology: A Survey of Econometric Analyses of Steam-Electric Generation. Land Economics. 54. 2. May. 1978. 3 L. Kirchmayer. A. Mellor. J. O‘Mara. and J. Stevenson. "An Investigation of the Economic Size of Steam-Electric Generating Units." Transactions. American Institute of Electrical Engineers. August 1955. 600-609. 4 There are two independent reasons why larger unit choices cause larger reserve requirements. First. larger unit choices imply larger average unit size for the firm. Holding availability rates constant. larger average unit sizes imply the need for larger reserves (imagine the reserve requirement if the firm sought to service all demand withe a single unit). The second effect is then the declining availability with unit size. For a more complete discussion see Galabrese (1947). Also. a good theoretical discussion of these effects is found in Burness.et al. (1985). 5 A sampling of this literature would include Berry (1982). Golub. et. al.. (1983). and Huettner and Landon (1976). 6 A possible mechanism would be the bulk power broker considered in Huettner and Landon (1976). 7 Edison Electric Utility Institute. Equipment Availability for the Ten-Year Period: 1967-1976. EEI no. 77- 11 12 64.New York. 1977. All references made to availability in the text refer to equivalent availability. Equivalent availability is a measure of unit availability that accounts for partial as well as full outages. For a complete discussion of the availability information used in the analysis the reader should refer to Appendix A. 8 Also given in the Edison Electric data are the major causes of forced outages. The primary cause of forced outages is boiler problems. For the 100-199MW group the forced outage rate for the boiler alone 2.9 percent and the forced outage rate for the turbine alone was .9 percent. For the SOOMW and larger group the forced outage rate for the boiler was 10.8 percent and the forced outage rate for the turbine was 3.5 percent. Remaining outages were attributable to the condenser. the generator. and other equipment. 9 The formation of availability expectations based on the EEI data may seem simplistic. However. in my discussions with Mr. David Bedford. Vice-President of Operations with the Public Service Company of New Mexico. he indicated that these were the statistics they used in their in-house models. 10 See for instance Huettner (1974). Cowing (1974). and Stewart (1979). The reason for this is commonly attributed to the "six-tenths" rule. As the volume of a sphere grows its’ surface area increases by approximately "six-tenth" of that increase. Since capacity is more nearly related to "volume" and costs are more nearly related to the surface area. per kW plant costs should decline with capacity This is more fully developed in Chapter III. 11 Plant factor is defined as the ratio of actual output to potential output at rated capacity over some period. 12 Improving the efficiency of a particular unit essentially involves improving the temperature and pressure conditions of the steam cycle. Primarily. this involves the addition of reheat stages or feedwater heaters. Both involve bleeding off steam from an intermediate turbine blade. In the reheat stage the bled steam is simply reheated and reintroduced at the next turbine blade. The feedwater heater. however. takes the steam and reintroduces it to the boiler. Since both enhance steam enthalpy the cycle efficiency is improved. See Roth (1970. pp. 48-58) for a moderately technical discussion of the steam cycle. CHAPTER II MODELING THE STEAM-ELECTRIC GENERATION PROCESS: REVIEW Below we critically evaluate studies that. have investigated unit or plant level electricity generation scale economies. Due to the capital intensity of this industry. and to the consequent large amount of good data on this industry. electricity generation studies have become a nesting place for new developments in cost and production theory. Consequently. there is a large number of studies to review. But. in addition to the large number of studies there are also many different methodologies. There are a number of ways one might stratify these studies. We have divided these studies into two groups: those which have employed an assumption of firm level optimization and those which have not. The former group includes a variety of cost. production. and profit function studies. The latter group is something of a catch-all group including simple cost-output relationship as well as some studies from the engineering and engineering-economics literature. With respect to this separation of studies we should keep in mind that the definition of economies of scale is a narrow and precise one. Economies of scale occur for any output region wherein long-run average costs decline with output.1 A prior assumption embedded in the long-run average cost curve is that all factors are employed in a least cost manner in producing each output quantity. Consequently. any 13 14 study which attempts to measure economies of scale without adhering to a firm level cost minimizing principle is technically invalid. What we have said. however. should not be taken to mean that studies which do not relate to cost minimizing principles are without merit. All of the studies have contributed to the body of knowledge concerning the economic description of this technology. Moreover. many of the hypotheses which have found their way into cost minimizing analyses evolved from some of the less formal cost studies. We take up first the group of firm optimizing models. 2.1 MODELS WHICH ASSUME FIRM LEVEL OPTIMIZATION Yoram Barzel provides a careful study of the steam- power plant production function and changes in industry technology.2 He is also one of the first to acknowledge the misspecification that occurs when one ignores plant utilization intensity.3 He notes. "The distribution of output over time in the steam power industry is not entirely up to the firm. Consequently. output is a function not only of the size of the plant but also of the extent to which this plant is utilized."4 The first methodological problem Barzel takes up is dismissing the production function empirical approach. Here he argues that since a production function approach would require including the plant factor and plant size on the RHS. and since output is identically related to plant size 15 and utilization intensity. "...the production function leads to an identity relation between the dependent and independent variables in the production function."5 The alternative taken then is the input demand function approach. Here. Barzel develops three input demand functions for fuel. labor. and capital. Since most of our concerns appear in his fuel and capital equations we take them up explicitly. With a sample of plants which were newly constructed between 1941 and 1959 Barzel estimates the following fuel demand function. log Y = E b 109 x (1.1) f i i i Where. Y 8 fuel input (Btu/year). f x 8 plant size (kw). 1 x = anticipated average load of plant. measured by the 2 observed load factor in the first full year of operation. x - within-plant index of x . over time 3 2 x 8 fuel price and vintage variables. 4-19 The inclusion of x in the equation is Barzel’s way of 3 attempting to capture a short run scale effect in addition to the long-run scale effect which x and x combine to 1 2 pick up. The within plant index of x . x . is merely an 2 3 16 index of the actual load factor in later years divided by the expected plant factor. x . Since the variable x is presumed to be the expectid load factor it reffects the_gx_gntg scale effect for utilization. But since short- run load factors may vary from the expected load factor and hence affect fuel costs in later years. x picks up this short-run utilization effect. 3 Since our concerns here are entirely with ex ante scale effectse we concentrate our attention on the variable x . Certainly the inclusion of both x and x removes some 2of the bias on the size variable. gut thesarguments we have made throughout apply here as well. Since x captures information on both desired utilization and2 expected availability. b may be biased. Implicit in the approach is 2 an assumption that either the availability rate or desired utilization is the same for all plants. If it is the former. which seems more likely. then b will be biased to the 2 extent baseload and peaking plants are mixed in the sample. Barzel's capital input demand equation is: 4 18 log P = E b log x + 2 b x . (II.2) k i=1 i i i=5 i i Where 9 P = total undeflated value of plant. k X = capacity size. 1 -17 X ll labor price. X ll fuel price. X = load factor. X a vintage dummies. 5-18 In the capital input demand equations Barzel uses the ”total undeflated value of plant” for the dependent variable. Arguing that different generators of the same size may embody different equipment he rejects capacity as a measure of the "quantity" of capital. And dismissing the validity of price indexes because of their broad coverage he eliminates all "quantity" measures excepting that chosen. A distinguishing feature of the analysis is Barzel's inclusion of the load factor in the capital equation. Barzel explains the inclusion of this variable by saying that. "The higher the load factor at which a plant is expected to operate. the more desirable it becomes to obtain equipment that can cope with the heavier strain. and consequently the higher the cost of equipment."6 This is the same point that we made in Chapter I above. The coefficient on the load factor term is both positive and significant at the 99 percent level but. unfortunateIY. Barzel must use the 35 Egg; plant factor as a proxy for what he is attempting to capture. As we have noted. the desired utilization rate is the appropriate determinant for plant 18 costs. and. because of declining availability. the-g! egg} plant factor may nonsystematically understate desired utilization. Dhrymes and Kurz7 developed input demand functions for fuel. capital. and labor from a limited - substitution generalization of a CES production function: Of Ok 1/u O =- min [g(L). (a F + a K ) J. (11.3) f k In (11.3) a minimum of g(L) is required to produce Q. It is obvious that the firm may not optimize with respect to labor in this production function. Fuel and capital. however. are substitutable in an ex ante sense. Since it was not possible to develop the three demand functions explicitly in terms of output and price ratios a two-stage technique was used to derive the nonstochastic portion of K. K*. A linear Taylor series was used to derive the nonstochastic portion of K. a s In K = a + 2 a ln 1 + a 1n O (i=k) (11.4) 0 i=1 i i k Where. I - p /p . i i k Since 0 is presumed exogenous this expansion is approximate. Next. the input demand functions were estimated over 362 plants which began operation over the period 1937-1959 19 and for 13 vintage-capacity size cells. The five size categories were 0-40 MW. 41-120 MW. 121-2OOMW. 201-449MW. and 45OMW and larger. The four vintage groups were 1937-45. 1946-50. 1951-54. and 1955-59.8 Scale economies were found in each of the cells with the rate of returns to scale falling with size in all but the smallest size groups.9 The Dhrymes and Kurz methodology appears sound. However. we have two concerns with underlying assumptions in the model. Our first concern is with the construction of the service price of capital. In deriving the service price of capital the authors first derive the plant level price of electricity with what is referred to as a "residual method". First. let10 1r= TR -TC. F F The subscript. F. indicates the firm level and total costs. TC. are defined such that 1 measures the return to total capital of the firm. Next. we let a = equity/asset (Book) ratio. Then. we represents return to stockholder capital for the firm. Now if this value is divided by net generation at the firm level one gets a measure of the firm generation level price of electricity. To derive their service price (cost) of plant capital one first multiplies the electricity price calculated above by net plant generation. giving the return to stockholder capital at the plant level. Subtracting plant operating 20 expenses and dividing by net plant output one then gets P . the capital rental price (cost) per megawatt hour. k Our primary concern with the measurement of P here is that using firm level data in the calculatio: of the electricity price assigns the same price of electricity to all plants in the firm. This is noted by the authors. "Note that this method has the consequence of assigning the same price to all plants of a multi-plant firm.“11 This seems implausible and would seem to deny that these electricity prices calculated on a plant basis would no doubt reveal higher electricity prices for non-baseload units than for baseload units. And. by extension. this bias would affect P . Our seco:d concern is that there is no accounting for different utilization levels in the analysis. That scale economies with output are discovered is unsurprising since larger output levels will be correlated with larger plants and larger‘gx Egg; utilization intensities. But since many of the plants are likely to be intended for different utilization it is unlikely that they all belong on the same long-run cost function. The principal concern of Roth12 is the separation of technology and scale effects. In contrast to other studies. which employ a vintage proxy. or cost or production function estimation for different time periods. Roth isolates technologically homogeneous populations of plants and investigates scale effects within these populations. Seven 21 technologically homogeneous populations are established considering furnace type. number of bleedpoints. number of reheat cycles. pressure-temperature. and generator cooling type. Input demand functions are derived from a profit function which includes varying forms of the CBS and Cobb- Douglas production functions. One must question. however. whether or not it is appropriate to derive plant level input demand functions from a firm level profit function. Viewing the problem from a cost function perspective. it is not necessarily the case that firms seek to minimize unconditional plant level cost for a given output. Rather. firms seek to minimize plant level costs conditioned on whether the output level is incurred at peak load or baseload. or somewhere in between. If baseload and non- baseload plants are mixed (and they are). then the firm level profit function is not appropriate for deriving input demand functions for the plant. That Roth includes baseload and non-baseload plants in his sample is revealed above. But in addition. there is no control for plant factor or different levels of utilization. He notes. "A smaller proportion of the variation in capital input was explained by output and the number of machines. Presumably because differences in plant factors across plants account for some variation in the installed capacity required to generate a given annual output with a given 13 number of units." That plant factor may vary 22 systematically with unit size is not considered. And. given this 'missing variable'. it is not surprising that Roth finds that "increasing returns to scale is characteristic of steam-electric generation at the plant level."14 15 Thomas G. Cowing provides one of the early examples of how one might characterize the steam-electric technology with an engineering process approach. As contrasted with the more general neoclassical characterization of technology the engineering process approach blends technical information - or specific engineering variables - with the traditional economic variables in describing a particular technology.16 In this he estimates input demand functions for the two presumed characteristics of capital: size and efficiency. The reduced form equations that were estimated are given below. * In E (p.v) = B + a ln p + bv (11.5) 1 * ln 2 (p.v) = B + c ln p + dv 2 * E = design efficiency for unit (Btu/kwh). Z = unit size. 23 ratio of present value fuel price to price of capital. ‘0 ll vintage index. < II In the model. E and Z . (that is. observed unit design efficiency and size) are presumed to be respective first order solutions to a capital and fuel cost function. With capital costs being determined in an hedonic machinery cost function and fuel costs being determined by unit efficiency and the plant factor. this function is written as PV = zG(z.e.v)p + zP /E. (11.6) m k f Where. T, -rt P = S p (t)1(t)e dt + o + p = expected fuel price in period t. and f l(t) = expected plant factor. Here. 6 is the hedonic average plant cost per unit of capacity. 2. And P is “...a kind of expected present value Price of fuel."17 + That Cowing finds significant scale economies is related to the way in which utilization. l(t). enters his model.18 Rather than exploring an independent scale effect for utilization the utilization effect is embedded in the Price ratio on the RHS of (11.5). Thus the ex §g£g_ scale effect would seem to be a reflection of both unit size and utilization effects. 24 As is the case with all of the studies we have reviewed. Cowing does not control for variations in intended utilization or expected availability rates. But there is one more potential problem which we should make note of. The observation used for E*. the unit heat rate. was the published design heat rate for the unit. In our own sample we found that for 24 plants which had published design heat rates the mean design heat rate was 8955.6. while the mean g5 £253 heat rate for these same plants was 10358.6.19 Moreover. only one plant in our sample had an 55 Egg} heat rate which was less than the design heat rate. We do not have access to his data. but these figures would suggest that the design heat rate may be a poor proxy for the expected heat rate. Cowing’s engineering process approach is appealing because it provides a fuller description of the steam- electric technology at no expense to the optimizing spirit of the neoclassical approach. However. the problem of identifying the separate cost effects of availability and desired utilization remains. The only example of a plant level scale analysis which uses a translog cost function is provided by Fuss.2o Fuss specifies expected 55 post costs with a generalization of the Diewert cost function. v v v v n v v v EC (P ’Ile9p sEY )= 2 b P h (EY ) (11.7) t It nt t i=1 ii it i t v v v 1/2 v +82b (P P ) h(Ey) i.j—1.....n i=j 13 it it t Where. v p = expectation of the price of the ith factor it formed at time v. What distinguishes this formulation from the usual v Diewert cost function is the substitution of h (Ey ) and v i t h(Ey ) for the typical output variable. These two terms are t defined as v 61 v v v 6i v h (y ) = (l ) Y = (y /Y ) Y . (11.8) i t t t t t t and v v 0 v h(y ) = (l ) Y . respectively. t t t Where. 1 = plant factor (actual output/potential output). t v Y = designed output at time t. t V y = actual output at time t. and t 0.0 = parameters to be estimated. Apparently Fuss is attempting here to fold into the expected output variable an accounting for unintended utilization. In defining the potential output for the plant. EY . however. Fuss states. "The expected yearly t 26 output at time t. EY . is assumed to be equal to the rated capacity (on a yeatly basis) times the expected proportion of the year the turbine-generator is hot and connected to load."21,22 This has the effect of overstating the actual utilization intensity on an annual basis. With this adjustment a small peak load plant and a large baseload Plant may well have the same utilization intensity. The majority of scale effects are therefore forced back into the single dimension of capacity effects. Fuss goes on to estimate 35 eggs and .gx agtg_ input demand functions for the four factors: structures. equipment. fuel and labor. But since his primary interest is in testing the putty-clay hypothesis. scale effects are lumped in with vintage effects and no attempt is made to sort them out.23 Nevertheless. from a strict neoclassical cost function standpoint the approach is sound and would be appealing if utilization economies were handled better or if there was an attempt to limit the study to baseload units. Stewart extends the class of cost function studies which take explicit account of engineering variables. The first problem he takes up is the development of an appropriate output notion. Given a non-uniform load curve and non-storable output Stewart imagines a system planner who selects a plant for a specific increment of the load curve. In this. the plant choice reflects an instantaneous rate of power. K. and the duration of operation over the period. The load increment for the plant being defined. 27 expected cumulative output for the plant is given as O I 8760bK. Where. 8760 = hours in year b 8 expected plant factor. and K = capacity (kW). Next. Stewart follows Cowing by defining capital in dimensions of efficiency (BTU/kWh) and size. The Problem for the planner is then to take a known load increment which is defined by K and b. and choose a cost minimizing efficiency level for the unit. For known load increment and expected relative factor prices the cost minimizing heat rate. is given as * a = g(K.b.P .r). (II-9) .f Where. * a = cost minimizing heat rate (BTU/kWh) "D II fuel price. and f 25 cost of capital. 1 ll Given the cost minimizing heat rate Stewart writes the _x ante fuel and capital cost function as (11.10) * TC (K.b.P .r)-g(K.b.P .r)8760bKP + rP (g(K.b.P .r).K)K. + f + k + Where. P (.) = the per kW cost of capacity. k 28 Here we should note that while decreases in the heat rate (increases in efficiency) reduce ex 3255 fuel expenditures they come at the expense of increasing Plant cost expenditures which make the increase in efficiency Possible. This results in a neoclassical condition where a unique cost minimizing heat rate obtains. The cost of plant function is estimated for a cross section of 58 gas turbine and steam-electric units which began operation during the 1970-1971 period. Using a log- log specification Stewart finds per kilowatt plant costs declining at a decreasing rate with declining efficiency. as expected. Given the cost of plant estimates. the load increments and expected factor prices. Stewart then solves numerically for the cost minimizing heat rate. a* . and the associated minimum average costs.26 Confirming the reasonableness of the model by comparing predicted heat rates and average costs with actual values he then uses the model to simulate average costs for a grid of sizes and plant factors. Surprisingly. an important finding here is that there are diseconomies of scale due to size for all steam-electric plants and for each plant factor. However. Stewart points out that the diseconomies indicated result largely from the positive coefficient on size in the Plant cost function.27 Since the partial with respect to size is not significantly different from zero little faith can be placed on the diseconomies indicated. 29 Stewart’s conclusions read. in part. "The major source of cost reduction at the unit level comes from increases in the plant utilization factor. not from increases in the size of the unit. and the cause of declining average primarily a result of the ability of plants with cost is higher utilization rates to spread capital expenses over a greater volume of output. That econometric studies have consistently found average cost declining with cumulative output is not surprising. given that larger plants are 28 generally operated at higher plant factors. As with previous studies. Stewart presumes that the Plant factor observed in 1972. the year after plant installation. is the ex ante utilization rate. We know that the intended utilization rate is greater than or equal to this _55 post plant factor. But we do not know by how much when no attempt is made to exclude non-baseload plants. That is. by mixing non-baseload and baseload plants together in the same sample the utilization effect seems picking up the effect of becoming a baseload plant than what is traditionally thought of as a 'scale’ And the question arises as to whether gas turbine Power and steam-electric baseload power are the same As in Cowing (1974). the engineering variables the cost function complement the information obtained from only relative factor price and Unfortunately. however. Stewart's mixing of gas to be rather effect. peaking product. used in normally output. turbine peaking plants with plants intended for larger utilization 30 intensities leaves his results open to criticism. Nowhere are the differences in desired utilization more pronounced than they are across this sample. And failure to control for these differences merges the scale effects of baseload units with those of peaking units. 2.2 MODELS WHICH DO NOT ASSUME FIRM LEVEL OPTIMIZATION Lomax provides the earliest example of a study which does not explicitly assume firm level optimization.29 He also appears to be the first author to acknowledge the importance of plant utilization in determining plant level average costs. He argues. "It is most important in investigating the laws of true returns to scale for electricity generation to be able to allow for varying load factor because there is a natural tendency in big undertakings with large numbers of consumers for irregularities in demand to be smoothed out to some extent and the load factor improved.”30 Accordingly. Lomax estimated the following regression for all steam-electric power stations in England which were operated for 6600 hours or greater during 1947. North-West ln Y = C - .12 1n X - .41 In X2 (11.10) 1 1 South-East 1n Y = C - .15 In X - .70 In X 2 1 2 31 Where. Y = costs per unit generated. in pence X = capacity of generator (kW) 1 X = load factor. and 2 31 C = constant term. i That Lomax failed to use some kind of input demand approach is perhaps related to the fact that the article was published in the year preceding Shephards' seminal book presenting the duality between cost and production functions.32 It is interesting. though. that even at this early writing Lomax seems keenly aware of the fact that larger plants tend to be baseload and hence used more intensively. One sees these concerns when he notes. "It should be pointed out. furthermore. that the two independent variables being highly correlated it is very difficult. statistically. to separate out their effects."33 Lomax’s results are consistent with other researchers who find relatively more important ’economies' in utilization. He notes. “This rate of decrease in costs as size increases for unchanged load factor is probably less than would be generally expected. The big undertakings in this country have the high load factors and long hours of generation so that actual costs in large statiogz are appreciably lower than size alone would imply. This statement is consistent with our observation that scale 32 economies should be investigated for only a class of plants which has the same intended plant factor. Kirchmayer. et a1. is discussed here as only one example of the numerous engineering cost studies which investigate plant size choices with plant and system cost 35.36 simulations. It is not a statistical study and therefore not suitable for any testing of scale hypotheses. Our review of the article is justified. however. because of the explicit consideration Of the engineering suboptimizations implicit in the production function or cost function approach. Kirchmayer’s method was to assume an existing 2000MW system and investigate costs when the system is expanded to a size of 10.000MW for different plant size choices. A host of unit level and firm level considerations were considered! "Factors such as the size of the system. forced outage rate. rate of load growth. installed cost of larger generating units. the effect of a maintenance program. and the effect on the transmission system of the use of larger generating units have been taken into account."37 While the results of the analysis are certainly conditioned on cost considerations specific to their time frame their conclusions read. in part. as follows. 1. If the investment cost of large units continues to decrease with size and the forced outage rate for large units remains at the present level [2 per cent (Z) or lower]. the most economical pattern of system expansion is to add units of between 10% and 7% of the size of the system studied. 33 2. If above any size the investment cost in dollars per kw remains constant. there will be very little incentive to use units above this size. 3. Any increase in the forced outage rate of large units will slow up the move to these large units. It is their third conclusion above that partially motivates our analysis. Komyia sought to determine declining input requirements in generation over the 18 year period 1938 to 1956.38 Tentatively he acknowledged three possible sources for the decline in input requirements: scale economies. technological growth. and factor substitution. After dismissing the Cobb-Douglas production function for poor Performance he retreated to a Leontief framework investigating production function shifts and scale economies. His device for sorting out these effects was a set of three input requirement functions given below. Y = a + b x (1) (11.12) f f f 1 Y = a + b x + b x (2) c c c 1 n1 2 Y = a + b x + b x (3) l l l 1 n1 2 Where. Y = fuel input per generating unit when operated at f full capacity. Y = log of equipment cost per unit. 34 Y a log of average number of employees during year 1 per generating cost. x ll log average size of generating unit. and X = log of number of units in the plant. A sample of 235 plants which were newly constructed in the period were further subdivided into four vintage cells. and also by coal and non-coal types. The vintage groups were 1938-45. 1946-50. 1951-53. and 1954-56. A general finding was that there were significant reductions in input requirements with scale across the vintage groups. Additionally. he found a significant reduction in input requirements in the post-war vintage groups as compared to pre-war plants. holding scale constant. His adjustment of fuel input to full capacity utilization was unfortunate. however.39 For when he makes this assumption he discards the possibility of investigating utilization intensity effects. And no attempt is made to use a proxy for ex ante utilization. While there is some evidence that forced outages were much less of a problem for the period considered it is unlikely that all 235 plants were intended for full utilization.4O A final concern we have with Komyia’s analysis is that it seems premature to reject substitution possibilities because of poor performance from the Cobb-Douglas functional form. The unexpected parameter signs and the general lack of statistical significance could have resulted from a 35 simultaneous equations problem or from the restrictive substitution elasticities imposed by the Cobb-Douglas functional form. And there existed several references to the substitution possibilities of efficiency related capital 41 for fuel in the engineering literature. Another engineering analytic investigation of 42 electricity scale economies is developed by Ling. Ling's objective is to use an analytic-engineering model to simulate costs for some typical electric utility. He begins with a base system size of 2500MW made up of ten 5MW units. twelve 100MW units. and four 2OOMW units. Then the following assumptions are imposed. 1. Investment. operating and maintenance costs are as in Kirchmayer et. al. 2. Fuel cost is 25 cents per MBtu. 3. System Peak load is 1950 MW. 4. Maintenance outage is equal to 20 weekdays and unit forced outage rate is equal to 2 percent. 5. Fixed charge on investment is equal to 12 percent. The assumption of a constant outage rate for all unit sizes. which departs from our analysis. may have been appropriate for the technological vintage Ling works with. And he provides a discussion of why the assumption is plausible for his analysis.43 Ling then goes on to allow the system to expand along the same expansion path as in Kirchmayer. Provided. however. is relatively more sophisticated analysis of costs. 36 Station heat rates were determined by pressure. temperature and unit size. And individual plant factors are "chosen" under a developed merit loading model.44 With this information a system-wide total cost function is developed as a function of station heat rates. station plant factors. system load. and fuel costs. And. as expected. simulated average operating costs decline with both system size and system load factor.45 Olson estimated an ex .gggt Along-run average cost function for 52 coal fired units and 24 non-coal units built between 1956 and 1965.46 Presented is a simple multiple regression of average costs on the independent variables of the form log $/kWh = 2 b log x . (11.13) 1 1 1 Where. x = constant 0 x = unit size x = number of units in plant 2 x e 1/plant factor. and 3 x - x = vintage dummies. 4 12 The three non-vintage variables all took appropriate signs and some level of significance. And both unit size scale economies and utilization economies are inferred. 37 However. in addition to mixing baseload and non-baseload units the average cost variable is constructed in an unusual way. Each firm is presumed to purchase fuel at the same cost per Btu and a fixed charge rate of 12 percent is applied to each unit. Since unit specific fuel prices and firm specific fixed charge rates were available this seems an unnecessary simplification. Since Olson's cost regression is not derived analytically from any firm level objectives it is difficult to interpret his estimated regression as a long-run average cost function. It would. therefore. be technically incorrect to interpret scale economies from his results. Nevertheless. Olson's results do support other studies which have found significant and important utilization scale economies. Huettner attempts to estimate scale economies by estimating average capacity and average fuel cost equations directly.47 Using a stepwise regression technique and considering variables such as capacity. fuel type. plant efficiency. and plant construction he develops multivariate regressions for both average capacity costs and average fuel costs in which only the reciprocal of size and a fuel type dummy appear on the RHS. This functional form is then used to examine costs for 13 vintage time periods from 1923 to 1968. One result of the analysis is that. "minimum efficient 48 plant size is slightly over 300 megawatts." But. since 38 the structures and equipment equations costs are measured with cost per kilowatt. as opposed to cost per killowatt hour. the analysis cannot be thought of as a traditional scale economy analysis. and this is acknowledged by the author. It is Huettner's argument. though. that this approach may be more useful in investigating efficient plant choices because the useful lives of different plants are unknown and the implicit assumption of equal plant lives made by most may cause a "scale opposed bias." He argues. "While boilers and electrical equipment generally wear out physically at a relatively slow rate and do not rapidly decline below efficiencies attained when new. the more historically relevant parameter is economic life...Obviously. a more efficient unit has a longer economic life in years and. because of merit order dispatching practices. is likely to spread its capital charges over still more kilowatt hours of output...Because of the correlation between unit size and efficiency. there is a good possibility that capital charges based on accounting data have a scale-opposed bias." But larger. more efficient units are operated at higher temperatures and pressures. and. as we have noted. are subject to higher forced outage rates. And so physical obsolescence may well be an important consideration. In any event. Huettner provides no convincing evidence that systematically different depreciation charges are appropriate. 39 Two points are in order with respect to Huettner’s methodology. First. the estimation of individual average cost regressions for capital and fuel costs assumes that capital and fuel may not be substituted. This seems unreasonable and the comments we made above on the Komyia 50 analysis apply here as well. Secondly. more flexible functional forms were available at the time of this research (1974). And the reliance on a simple linear functional form seems curious in this light. But in spite of these methodological problems we should note that Huettner does refer to one of our primary concerns. With respect to the differences between baseload and non— 51 baseload plants Huettner notes. Generating plants may also be classified as base- load plants. cycling plants. and peak-load plants. Base-load plants are designed to operate at maximum fuel efficiency without being shut down for long periods of time. This may increase UCC (unit capacity costs) above that of cycling plants. which are designed to operate at the highest fuel efficiency consistent with rapid warm-up and cool- down during frequent shut downs. Cycling plants might tend to have a lower UCC due to looser tolerances on equipment as for example on the turbine blades. Before being screened out by the stepwise regression technique Huettner attempted to capture this load type effect by including the plant heat rate as an explanatory variable in the capacity cost equation. But while this is a step in the right direction. the plant heat rate is likely to be a poor proxy for desired utilization. The plant heat rate depends not only on the level of desired utilization. 40 but also on the availability and temperature of the condensing water and on the heat content of the fuel. Without controlling for the other determinants of plant efficiency it is unsurprising that the stepwise technique failed to retain this variable. Galatin is interested in separating scale effects and technology effects in a multi-unit production function when one explicitly recognizes the instantaneous nature of electricity Production. Since the level of fuel efficiency for a given plant depends on the instantaneous rate of output. and since Galatin is faced with the same annual FPO plant data used in all of the U.S. studies. his objective. "is to derive a functional form for the ex post production function which. as well as making economic sense. enables annual data to be used to estimate an essentially instantaneous process.“ Essentially Galatin is confronting one form of the “aggregation problem.” Here. two aggregated functional forms are presented which use annual data and which are based on a constructed disaggregated production function. -1 a = «(X /X ) + 0X + u + v (11.14) it it 1K 1K it -1 -1 a = a(X /X ) -+ 0(X ) + u + v (11.15) it it iK iK it Where 9 a = heat rate (Btu/kWh) for the ith machine it during period t. 41 X = output of the ith machine in the tth it period. and X = capacity of the ith machine. iK Equations (11.14) and (11.15) were estimated using ordinary least squares over a sample of 812 observations on 158 plants. The observations were stratified by coal and non-coal types and by six technological vintage groups beginning with 1920 and ending with 1953. Since (11.15) yielded generally higher R-squares over the different vintage-fuel type cells it was selected as "the ex post production function." With all of the estimated coefficients positive and generally significant across the vintage-fuel type cells Galatin next uses these estimates to infer scale economies. The positive estimate for a suggests declining fuel input per kilowatt hour with increasing capacity utilization for fixed size. From this Galatin argues "there are intra- capacity economies in the use of fuel. for if output increases in more than proportion to fuel input this implies that the average input of fuel input per unit of output decreases as full capacity is approached."54 In addition to the "intra-capacity“ economies the positive estimate for 0 implies that ”the fuel input per unit of output decreases the larger is the machine. Thus scale economies exist over the full range of the sample.“ While the degree of economies varies for different groups 42 around the sample Galatin’s results point to economies of both utilization and size throughout. Galatin's concern for capturing the instantaneous nature of production. while notable. may have distracted him from equally important aspects of this technology. A first problem with the analysis here is that while Galatin develops a solid theoretical model of the industry early in the analysis the final functional form chosen bears almost no relationship to this model. The functional form develops solely from an interest in using aggregated data to represent an instantaneous production technology. Our second concern is the same one we have had elsewhere. Both intra-capacity and inter-capacity economies may well depend on the desired level of unit utilization. There is no reason why the effect of size or actual utilization on unit heat rate should be the same for both baseload and non-baseload plants. The single analysis in which availability rates were considered is provided by Lewis Perl. Perl's methodology involved first estimating hedonic cost equations for capital. and operating and maintenance costs over 245 coal plants built between 1965 and 1980. Plant capital costs were related to size. area wages. architectural firm dummies. and other variables. Operating and maintenance costs were regressed on plant size. the number of units in the plant. area wages. and regional dummy variables. 43 These costs were then inserted into a model which calculates a levelized cost of electricity. Levelized costs of electricity are a ”constant annual charge for electricity which yield the same present value as actual annual charges over the life of a plant." The formula for the levelized cost is: n i 2 RR (1+1) m LC = i=1 i x 1/(1+r) (11.16) n i i 2 G (1+1) /(1+r) i=1 1 Where. RR = revenue requirement in year i. G - generation in year i. n = book life of the plant. m a number of years from current date to start of operation. I a nominal discount rate. and r - inflation rate. The revenue requirements in (11.16) are composed of "interest on debt. a return on equity capital. income and property taxes fuel costs and non-fuel operating and maintenance costs."58 Fuel costs for the model were derived from the National Economic Research Asssociates World Coal Model which estimates and forecasts equilibrium coal prices for different geographical regions in the U.S. and Europe. 44 The plant output figure. G.. used in the model are given by a sub-model which predict; equivalent availability based on plant size. age. vintage. and a number of plant characteristics. Here. Perl makes an assumption similar to one we make below. 31;. that if a unit is available it is producing output. For the analysis. Perl assumed a plant life of 30 years. a nominal discount rate of 8.6 percent. an inflation rate of 7 percent. and fixed other variables in the model. Next he varied the plant sizes and calculated levelized costs assuming an actual plant life time running from 1985 to 2014. A general conclusion reached by Perl was that. "The cost of electricity is about the same whether the unit size is 200 megawatts or 1.000 megawatts. This reflects the offsetting influences of size on availability factors and construction costs. Construction costs per kilowatt are higher for the smaller units but availability factors are also higher."59 While the Perl analysis is enlightening with respect to the effects of unit reliability we have two principal concerns. The first concern, relates to the way in which unit efficiency enters the analysis. Total electricity costs in the model are comprised of operating costs and plant costs. Further. the parameter estimates in his plant cost regression will be consistent and unbiased only on the condition that there are no left out variables which are correlated with the RHS variables. But in Perl’s plant cost 45 equation there appears no proxy for the level of plant efficiency. That the level of plant efficiency exerts an independent and substantial influence on plant costs has been hypothesized and accepted by several researchers. Thus. it would seem that the plant size coefficient may well be biased here. The level of unit efficiency is included as a determinate of operating costs. but the way it is included is unsatisfactory. In this model. plant heat rates are determined by way of a regression in which heat rates have been related to plant age. vintage. and a number of other plant characteristics. The level of plant efficiency is. therefore. determined by the characteristics of a plant. Since this plant efficiency choice is not subjected to any cost minimizing rules it is easy to see how the model may assign either more or less than the cost minimizing level of efficiency and that a distorted picture of long-run average costs may follow. The second general concern we have with the Perl analysis is that no theoretical structure is developed. Consequently. no hypotheses are developed that can be accepted or rejected. The analysis is interesting due to the number of engineering influences it accommodates. But the conclusions remain subject to concern because they are not subject to rejection. 46 Summary In summarizing the literature that has been reviewed two general observations seen worthwhile. First. scale analyses of this industry which have either ignored 61 62 utilization or folded utilization into an output variable have uniformly found plant scale economies throughout. However. we would contend that the economies discovered in these analyses must be shared between the effects of plant size and the level of utilization. Secondly. studies which have recognized the utilization dimension of capital heterogeneity and have attempted to capture the independent effects of size and utilization have without exception found substantial and significant economies of utilization. If a general consensus were to emerge from this body of research it would seem to be that to adequately characterize this technology one must first control for the salient dimensions of capital heterogeneity. While there may be disagreement. two of the more important dimensions appear to be plant utilization and plant efficiency. With respect to plant utilization we have seen only two studies which have attempted to relate costs to desired utilization.63 Unfortunately. both of these studies employed proxies which inadequately described desired utilization. 47 64 The last study reviewed acknowledged the necessary decomposition of .55 post utilization into its two components: unit reliability and desired utilization. But the principle of cost minimization was not employed in this analysis. What seems to be needed at this point is a model which presumes cost minimizing behavior that separates the effects of desirability and availability and that allows for capital heterogeneity. We begin developing a model along these lines in Chapter III. CHAPTER 11: ENDNOTES 1 An alternative definition of scale economies is that developed by Baumol. .3; a}. in the contestable markets literature. Here. scale economies occur for output regions wherein ray average costs decline with output along a ray defining a fixed output proportion in multiple output space. See W. J. Baumol. ”Contestable Markets: An Uprising in the Theory of Industry Structure." American Economic Review. Vol. 72. no. 1 (March. 1982). p. 6. 2 Y. Barzel.“The Production Function and Technical Change in the Steam-Power Industry." Journal of Political Economy. 72 (April. 1964). 3 Throughout the article Barzel uses "load factor" instead of the correct ”plant factor.” Load factor is defined as the ratio of actual output for the firm to the output which would be realized if output were produced continuously at peak demand. 4 Barzel. op. cit. p.134. 5 Ibid. 6 Ibid. 7 P. Dhrymes and M. Kurz. "Technology and Scale in Electricity Generation.” Econometrica 32 (July. 1964). 287- 315. 8 Ibid. p.298. 9 Ibld’ P-310. 10 See pp. 312-13 for a discussion of this calculation. 11 Ibid. p.313. 48 49 12 J. Roth. An Econometric Approach to Technological Change and Returns to Scale in Steam-Electric Generation. Ph.D. dissertation. Michigan State University. East Lansing. 1971. 13 Ibid. P.138. 14 Ibid’ I'D-163- 15 T. Cowing. "Technical Change and Scale Economies in an Engineering Production Function: the Case of Steam- Electric Power." Journal_gf Industrial Economics. 23 (Dec.. 1974). pp.135-52. 16 Ibid. For a fuller discussion of the approach see pp. 135-36. 17 Ibid’ P-144- 18 Returns to scale (p. 147) in the model are given by d/d-bs 19 Design heat rates were found in Power. 1970-79. 20 M. Fuss. "Factor Substitution in Electricity Generation: A Test of the Putty-Clay Hypothesis." in Production Economics: A Dual Approach to Theory and Applications. eds. M. Fuss and D. McFadden. Amsterdam: North Holland. 1978. 21 Ibid. p. 194. 22 Note that this is the same adjustment Galatin (op. cit.) made. 23 See Fuss' discussion of the difficulty of sorting these effects out (pp. 195-96). 50 24 J. Stewart. "Plant Size. Plant Factor. and the Shape of the Average Cost Function in Electric Power Generation: A Nonhomogenous Capital Approach." Bell Journal of Economics. 1979. PP. 549-65. 25 The reader will note that as in Cowing (1974) Stewart ignores labor cost in his analysis. 26 The functional form of the plant cost function did u not permit an explicit solution for a . 27 See the Stewart's (op. cit.) footnote 23. P. 562. 28 Ibid. p. 564. 29 K. Lomax. "Cost Curves for Electricity Generation." Economica. 19. 1952. 30 Ibid. p. 195. 31 It is unfortunate that at this earl writing the popularity of publishing t-statistics and sample size along with the regression coefficients had yet to catch on. 32 R. Shepherd. Cost and Production Functions. Princeton: Princeton University Press. 1953. 33 Lomax. op. cit.. p. 195. 34 Ibid. p. 197. 35 Kirchmayer. et al.. op. cit. 36 See for instance 8. Z. Haddad and R. French. "The Economics of Reliability and Scale in Generating Unit Size Selection." Proceedings of the American Power Conference.42. 1980 pp. 680 - 86. N. Hall .N. Tibberts. and M. Adams. 51 "Analysis of Interrelationships Among System Loads. Capacity Requirements and Generating Unit Availability." Erogggdingg WW 41. 1979. pp. 1035 — 42. C. W. Watchorn. "Elements of System Capacity Requirements.” American Institutg_of Electrical Engineers - Transactions. 70. 1951. pp. 1163 - 85. 37 Kirchmayer. op. cit.. p. 600. 38 R. Komyia."Technical Progress and the Production Function in the U.S. Steam Power Industry." Review of ‘Economics_§nd Statistics. 44 (1962). 156-66. 39 Ibld’ p. 158. 40 See Kirchmayer. et al.. op. cit. 41 The same criticism was made by Roth. op. cit. 42 S. Ling. _Economies of Scale in the Steam-Electric .E9fl§£_fi2flefiating_industry; Amsterdam: North Holland. 1962. 43 Ibid. p. 20-21. 44 Ibid. p. 39-41. This indicates the endogenous nature of plant factor from a system perspective. That other unit or plant level studies seem to be merely controlling for plant factor effects seems to ignore the fact that intended utilization is determined at the system level. 45 That average costs decline with system size results from the fact that larger systems can include more larger plants. With no availability penalty for larger units this is precisely what one would expect. 46 C. Olson. _Cost Considerations for Efficient Electricity Supply. East Lansing: Michigan State University' Public Utilities Institute. 1970. 47 D. Huettner. .Elant Size. Technological Change. and Investment Reguiremengs. New York: Praeger Press. 1974. 52 48 Ibid. p. 103. 49 Ibid. 50 Komyia. op. cit. 51 Huettner. op. cit.. p. 53. 52 M. Galatin. Economies of Scale and Technological Change in Thermal Power Generation. Amsterdam: North Holland. 1968. 53 Ibid. p. 100. 54 Ibid. p. 120. 55 Ibid. 56 Lewis Perl. "The Current Economics of Electric Generation from Coal in the U.S. and Wester Europe." Presented at the International Scientific Forum on Reassessing the World's Energy Prospects. National Economics Research Associates. Paris. 1982. 57 Ibid, P. 2. 58 Ib1d’ P. 12. 59 Ibid’ p- be 60 See for instance Cowing. op. cit.. and Stewart. op. cit. 61 Dhrymes and Kurz. op. cit. and Roth. op. cit. 62 T. Cowing. op. cit. 63 Bazrel. op. cit.. and Huettner. op. cit. 64 Perl. DP. cit. 53 CHAPTER III A MODEL OF THE STEAM-ELECTRIC TECHNOLOGY In this chapter we develop a model of the steam- electric generation process which incorporates observations set out in Chapters I and 11. Section 111.1 provides a general discussion of the methodology employed. Sections 111.2 through 111.4 develop the model. and section 111.5 provides estimates of the plant cost function. 3.1 GENERAL The model developed below describes the steam-electric production technology in terms of both engineering and economic factors. This is in contrast to the neoclassical approach commonly used by economists to describe production relationships. but the approach does offer certain advantages. The analytical vehicle normally used by economists to represent production relationships is the neoclassical production function. A key characteristic of the neoclassical production function is its general applicability across different technologies. Defined to relate the maximum technologically feasible output with the level of inputs. the neoclassical approach maintains a prior assumption that the process under investigation is previously optimized with respect to engineering factors. As such. the engineering peculiarities of different 54 55 technologies are ignored. _and the analytical focus is limited to economic characteristics. The engineering-economics approach. on the other hand. folds engineering and economic factors into the same analysis. Where the neoclassical approach is general. the engineering-economics approach employs engineering information that is specific to the technology being studied. As a result. the final form of the model will be uniquely appropriate for the technology it is developed for. An obvious advantage of the engineering -economics approach is that it provides a more complete description of the technology. While preserving the economic characteristics of the technology. the engineering - economics approach provides a much richer description of the production process under investigation. In addition to the scale1 and substitution effects normally estimated in a production study. one may also investigate the influence that specific engineering factors have on the technology. Moreover. the added descriptive ability of the engineering-economics approach is especially valuable when investigating production relationships for a regulated industry such as electricity generation. Informed regulatory oversight depends not only on the verification of economic characteristics but also on why these characteristics exist. In this regard. the engineering-economics approach will be seen to be ideally suited to the task of exploring 56 both the economic and the engineering factors that structure the steam-electric production process. 3.2 THE MODEL The general problem for the firm in this model can be described as follows. An exogenous baseload output level is first given to the firm. Given this load. the firm has the problem._gx gate, of choosing equipment to service the load at minimum expected total cost.2 The loads considered by planners in this model are restricted to baseloads so that we do not confuse the relative impacts of unit availability and desired utilization. By definition. a baseload is a load that is of a constant level throughout the period of investigation. Consequently. restricting output to take the form of a baseload presumes that the desired utilization of the chosen equipment will be one. and the influence of unit availbility can be isolated. More specifically. the baseload output for the boiler- turbine-generator (BTG) unit will be defined over an instantaneous rate of power and a utilization intensity. While the instantaneous rate of power for the unit is defined by the size of the HTS unit the anticipated utilization factor for the unit will be defined by the expected availability rate. a(k). Combining these conditions 57 r\ we have a direct relationship between expected output. 0. and unit size. This relationship is: a = 8760a(k)k. (111.2) Where. 8760 = number of hours in a year. k = instantaneous rate of power for the unit. kW. a(k) = expected availability rate for the unit. Regarding substitution possibilities in the model. we assume a putty-clay world where capital and fuel are combined to produce electricity. The level of unit efficiency is presumed to be variable and endogenous in the blueprint stage. But once the unit is built we assume that the conversion rate of fuel into electricity is fixed and unalterable. Under these conditions. expected_gx 3923 total fuel and capital costs are: (111.3) SRTC(a .k .P .r) = a 8760k a(k )P- + rP (a .k )k . 0 0 f O 0 0 f k 0 O 0 Where. 3 a = ex post unit heat rate (Btu/kWh). O P = expected fuel price ($/Btu). .{2 r = expected service price of capital (interest and depreciation). and P (a.k) = per kilowatt plant cost. k 58 While the model given in (111.3) provides a general description of the major engineering and economic features of BTG costs it is limited with respect to a number of less important cost components. Labor. materials. administrative. and other costs are ignored. These cost components are excluded for two reasons. First. while unit level economies may be affected by these other inputs their influence is likely to be inconsequential. Cost shares typically run 50 percent fuel. 40 percent capital. and 10 percent labor. So (111.3) should capture the most important cost components. Further. none of the studies reviewed in Chapter 11 above attributed overall unit or plant level economies to inputs other than fuel and capital. Secondly. substitution possibilities between capital and labor and the left out inputs are negligible even in the long-run. Consequently. the implicit substitution elasticities estimated within the context of the model (111.3) should be free of bias. Further. the model abstracts from the effects of time. r is assumed to represent the service price of capital in a single year. A sufficient condition for r to be constant with respect to time would involve assuming (1) that the unit size is derated for depreciation regularly with time. and (2) that unit availability and efficiency is constant with respect to time. Under these conditions the service quality of capital would be constant. In reality the issue is much more complex. Unit efficiencies and availability do 59 4 not significantly decline with time. But. in later years. economic depreciation caused by changing relative fuel prices or technology improvements may reduce the desired utilization of the unit. All things considered. the focus on a single year may indeed misrepresent the information one might obtain with a longer-term analysis. but the more complete model would require the formation of expectations regarding future economic depreciation. and this is outside the scope of the analysis presented here. 3.3 _5 ANTE cosrs While the expected short-run technology is characterized by fixed coefficients the firm is faced with the ex ante problem of choosing the level of unit efficiency which minimizes the expected accounting costs of serving the given baseload. The plant cost - efficiency possibilities the firm is faced with are given by the plant cost function. P (a.k). The plant cost function. in our context. is consideted to be an hedonic plant cost pricing schedule which is known to the firm. Briefly. we can characterize the expected efficiency plant cost tradeoff as follows. We expect 3P (a.K)/aa<0 because less efficient units require less efficiency related equipment. We also expect aRP (a.k)/aa2>0. For fixed plant size we expect plant costs k 5 to decline at a decreasing rate with declining efficiency. 60 For the given baseload requirement. ex ante total costs are determined by the unit heat rate: (111.4) TC(a.k .P .r) = a8760ka(k)P + rP (a.k )k. f f k Developing the ex ante cost function we first minimize (111.4) with respect to the heat rate: aTC/aa = B760ka(k)P + 6P (a.k)/aakr = O f k or (111.5) S760a(k)P = -aP (a.k)/aar *. f k a Since increasing the heat rate (decreasing efficiency) should result in lower per kilowatt unit costs the RHS of (111.5) should be positive. Intuitively. this is a typical neoclassical result which implies that the energy efficiency of a planned plant. ceteris paribus. should be reduced so long as the resulting amortized costs are greater than the incremental fuel costs. The second order condition is given in (111.6): 62TC/aa2 = 62P (a.k )/aa2r. (111.6) k 0 The second order condition holds so long as 62P (a.k )/aa2>0. Plausibly. this would be the result if k 0 61 the cost penalty for improving efficiency were greater for relatively efficient units as compared to relatively inefficient units. Implicitly then we have the cost a minimizing heat rate. a . as follows: a a I h(P .k.r). 4: Using the assumptions above and (111.4) the ex ante cost function becomes: 1* LRTC (k.r.P ) = 8760h(k.P .r)ka(k)P + (111.7) 4 + 4 P (h(kgp .r) .k)kr. k 4 Since a unique relationship is preserved between unit size. k. and output. the ex ante cost function. as expected. is shown to be a function of output and prices. 3.4 THE PLANT COST FUNCTION In section 111.3 we completed the development of the theoretical model describing the steam-electric technology in terms of fuel costs and capital costs. In this section we explore the determinants of capital costs and present estimates of the plant cost function. P (a.k). k 3.4.1 General Mentioned above. the plant cost function. P («.k). k represents a pricing schedule of plant costs for different 62 Plant characteristics. We assume that this schedule is known to the firm. As this function captures not only technical and economic information in the equipment manufacturing production process but also market structure conditions in the equipment industry some assumption about market structure effects is required. Here. we make the weakest assumption possible. gig. that equipment prices are proportional to production costs in the equipment manufacturing industry. While an assumption of perfect competition in the equipment industry would be sufficient for our purposes it would also be both unrealistic and stronger than needed. A weaker. yet sufficient. assumption is that there is no price discrimination with respect to any characteristics of the purchasing electric utility. With respect to our expectations on how plant costs should respond to changes in efficiency and unit size we discuss first the expected cost effects of efficiency. Improving unit efficiency involves. primarily. the introduction of strengthened materials which allow higher temperature and pressure conditions. and the addition of regenerative pre-heaters and/or reheat units.6 Since each of these physical additions require a capital expenditure we expect 6P (a.k)/ aa<0. However. as the unit becomes more efficientk we expect that additional efficiency will come at the expense of a more than proportionate increase in plant costs. That is. we expect aZP (a.k)/aa2>0. k 63 With respect to the effect of size on per kw plant costs engineers frequently employ a "six-tenths" rule. This simply relates to the analogy that as volume increases for a sphere the surface area increases by approximately “six- tenths“ of the increase in volume. Since electric capacity is more nearly related to unit volume. and costs are more nearly related to the surface area. increases in capacity should lead to reductions in per kilowatt costs. That is. 0P (a.k)/ak<0. However. we expect this relationship to be k stronger for smaller plants than for larger plants. aZP (a.k)/ak3>0. k Finally. we expect the cross partial elasticity to be governed by two opposing forces. Ceteris paribus. we expect that a one percent reduction in the heat rate will be relatively more expensive for a smaller plant than for a larger plant. aZP («.k)/aaak>0. This is because the expenditures for efficienc: improvement are spread over a smaller base in a smaller plant. However. we agree with Stewart (1979. p.556) that the fabrication requirements may be more complicated and expensive in a larger plant. 62Pk(a.k)/aaak<0. The sign of the cross partial elasticity should depend on the relative importance of these two affects. 3.4.2 ESTIMATION OF THE PLANT COST FUNCTION For estimating the plant cost function we have selected 7 a translog functional form. The reasons for its selection if". tn: ef‘ tht 93' m .rs W :5 \ Cs 64 are twofold. First. and more importantly. is the fact that the translog specification allows all of the size - efficiency effects discussed above to occur. And secondly. the translog form can be viewed as a second order Taylor 8 approximation to any continuous plant cost function. The equation to be estimated is: (111.8) lnP = B + B 1n + B 1n