Shifts of long run average cost curves: Theoretical and managerial implications

OMEGA, The Int. Jl of Mgmt Sci., Vol. 1, No. 4, 1973

Shifts of Long Run Average Cost Curves : Theoretical and Managerial Implications DAVID

A HUETTNER

Wayne State University, Detroit, Michigan (Receipea 26 March 1973)

Economists have traditionally employed one of two alternative methods when analyzing economies of scale: The long run average cost curve (LRAC curve) and the production function. Only the production function concept, however, has been extended beyond a static framework for analysis of scale economies in a dynamic setting. This paper will extend the traditional, static LRAC curve concept by developing an appropriate dynamic framework. This framework will then be used to analyze the shifts of L R A C curves through time in three major American industries: steel making, cement manufacturing, and electric power generation. The empirical and theoretical topics explored in this study raise issues of both managerial and theoretical concern. These issues include: the relationship between economic plant life and plant size; the existence of scale biases in previous studies of scale economies and current depreciation practices; the accuracy and use of construction cost indexes; and the effects of technological change over extended periods of time. The dynamic framework developed in this study serves several useful purposes. For example, it constitutes a first step toward the development of theories that fill the void between the static theory of LRAC curves and the theories of increasing, decreasing, and constant cost industries. Furthermore, many questions, such as optimal plant or firm size, should be answered in a dynamic framework if appropriate managerial or anti-trust issues are to be considered. Finally, this dynamic framework shifts the emphasis of studies of scale economies back to costs and the use of this framework should result in improved corporate planning and decision making.

INTRODUCTION ECONOmSTS have traditionally employed one of two alternative methods when analyzing economies of scale. The first of these methods, the long run average cost curve, is a physical-financial concept in that it emphasizes the relationship between plant size and total unit costs. The second method, the p r o d u c t i o n function, is a purely physical concept in that it emphasizes the physical relationship between physical i n p u t s a n d physical outputs. A l t h o u g h b o t h approaches are described in economics textbooks, economists have generally emphasized the p r o d u c t i o n f u n c t i o n a p p r o a c h in empirical studies o f economies o f scale. F u r t h e r m o r e , economists have never extended the long 421

Huettner--Shifts of Long Run Average Cost Curves run average cost curve (hereafter L R A C curve) concept beyond a static framework but have readily extended the production function concept to analyze scale economies in a dynamic framework. This asymmetry deserves further explanation. Studies of scale economies utilizing the long run average cost curve should, theoretically, lump capital and operating costs together since economies of scale are defined by the relationship between total unit costs and plant size when all costs, including fixed costs, are considered to be variable. Input prices and technology are assumed to be fixed, hence the objective is to compare alternative plant sizes producing identical products (or product-mixes) at a moment of time. The term "long run" is clearly a misnomer since the effects of the passage of time are obviously excluded from the analysis. Under the static conditions of fixed prices and technology, there is no difficulty in determining economies of scale1; but under dynamic conditions changes in total unit costs (economies of scale) may be due to changes in technology and substitution of one input for another (i.e. changes in factor proportions induced by changes in input prices). Alternatively, one might approach the problem by employing a production function and by defining increasing returns to scale as a more than proportionate increase in output resulting from a proportionate increase in all inputs, z Under static conditions of fixed prices and technology, there is no problem in determining economies of scale assuming that all plants in the sample lie on the same production function. Indeed, under these static conditions the LRAC curve may be found from knowledge of the production function and its expansion path, assuming that cost minimization exists at each point. Clearly, a change in the production function (i.e. technology) or input prices would change either the level or shape of the LRAC curve. Under dynamic conditions, assessment of the physical relationship between inputs and outputs in progressively larger plants is complicated by changes in technology and substitution of one input for another (i.e. changes in factor proportions induced by changes in input prices). In theory, then, the two approaches are equivalent and, in dynamic analysis, the basic problem is to distinguish between movements along a given production function (changes in factor proportions) and shifts to a new production function. za Shifts to a new production function are caused by technological change tUnder these static conditions, factor proportions will generally vary for each plant size but usually this does not render an assessment of economies of scale intractable since it is generally assumed that all the plants in the sample lie on the same production function. aA more sophisticated, mathematical definition of the scale economies of the production function is generally made. Usually the production function is assumed to be homogenous to some degree, to be determined by the analysis. Under these conditions, the degree of homogeneity defines the extent of the economies of scale. 2aThis equivalence is the subject of a growing body of literature on the principle of duality in the theory of cost and production. For example, see [29] and [30]. As will be noted in the fifth section, one may be indifferent at the theoretical level between the production function or LRAC curve approach, but there are many practical reasons for preferring the LRAC curve approach. 422

Omega, Vol. 1, No. 4 which is introduced as one or more shift parameters to be estimated along with the other parameters. Given the theoretical equivalence of the two approaches under either static or dynamic conditions, it is difficult to explain why economists have never extended LRAC curve analysis beyond a static framework. That economists perceive LRAC curve analysis in a static framework only is obvious; changes in the production function or prices through time should alter the level and shape of the LRAC curve, yet the theoretical and empirical literature of economists has never discussed the movement of LRAC curves through time. In fact, no diagram, chart or graph ever depicted more than one LRAC curve (for example, see [5, p. 264; 9, p. 144 and 23, p. 174]); nor have the results of production function studies through time ever been used to generate the shifts of LRAC curves through time. 3 Economists have always forced the data to fit on one L R A C curve despite problem of changes in prices and technology. 4 Instead of forcing the data to fit the static concept of LRAC curves, economists should instead develop a dynamic framework for LRAC curves and seek data to fit that framework. Prior studies of LRAC curves have been deficient in two important aspects: capital costs have been handled improperly and the requirement that cost minimization be achieved has been ignored. These points deserve fuller explanation. Capital costs have been ignored in some LRAC curve studies and instead the long run average variable cost curve (hereafter LRAVC curve) has been estimated (see the study by Johnston in Table 1). Other cost curve studies have included some capital costs (i.e. equipment costs as in the study by Olson in Table 1), but have made several assumptions to calculate capital costs per unit of output. These assumptions include equal economic plant lives for all plant sizes and equal average rates of utilization of plant capacity over the life of the plant. In the studies by Olson, Kirchmayer, and Ling in Table 1, these assumptions are implied by the computation of annual fixed charges. The production function studies must also make these same assumptions, although this has not ever been recognized. These assumptions are not only incorrect but also unnecessary since, as the next few paragraphs will show, they can be tested empirically. The major shortcoming of previous LRAC curve studies, however, is that the principle of cost minimization has been ignored. For example, the studies by Johnston, Lomax, and Olson have included plants of various vintages (technologies) constructed at widely divergent points in time under different input price conditions. These plants do not belong on the same LRAC curve since, for 3See the studies by Barzel, Dhrymes and Kurz, Galatin, Komiya, and Nerlove in Table 1. 4See studies by Johnston, Olson, Lomax, and McNulty in Table 1. Note that Olson included a shift parameter for plant vintage which implies that the LRAC curves should shift parallel to one another with no change in shape. Olson, however, did not discuss this implication and it is quite clear from his text that the shift parameter was merely an adjustment which would allow all of the plants in his sample to lie on the same LRAC curve. 423

Huettner--Shifts of Long Run Average Cost Curves cost minimization to hold, technology and prices must be fixed and one must then be free to choose the optimal input combination for each plant size. Clearly, the only correct procedure is to collect data on new plants constructed at the same point in time. When only new plants are considered, the input combinations observed for the various plant sizes will have been selected under similar price and technology conditions. 4a The results to be presented in this study have adhered to the principle of cost minimization in that they were based on a cross-sectional sample of new plants constructed at the same point in time, generally a two year period. Regression analysis was applied to each cross-section to yield the LRAC curve for that time period. Shifts in the resulting LRAC curves and changes in their shape through time will be analyzed here, but the details of the regression analysis have been omitted? Given an appropriate dynamic framework for LRAC curves, questions arise as to the pattern of shifts in these curves and changes in their shape through time. Hypotheses concerning the movements of LRAC curves through time have never been articulated by economists, but several assumptions generally made by economists and accountants imply that LRAC curves should shift parallel to one another through time with no change in their shape. Before detailing these assumptions, however, it will be necessary to introduce the concept of unit capacity cost (hereafter UCC). The development of the unit capacity cost concept will be facilitated by separating construction and operating costs instead of lumping them together. This separation not only recognizes that construction and operating costs may be determined by different sets of forces and may have divergent patterns of behaviour through time; but it also eliminates the need to make any assumptions about plant life or depreciation rates since capital costs per unit of output are not calculated. The investment required for acquiring new facilities providing additional capacity may be regarded as determined by the volume of such new capacity and by the average investment required per unit of capacity. Investmentj~xed = Capacity ×

Investment3xed Capacity

(1)

The latter term will be referred to as unit capacity cost (UCC). Despite its obvious relevance to changes in investment requirements, this concept has received no direct attention in economic theory although the concept is used 4aThe similarity of price conditions is particularly useful for the usually troublesome

price of capital. Since financial inputs are obtained in national markets, there is some assurance that these plants were financed under similar market conditions. As will be seen later, this similarity of market conditions in combination with the unit capacity cost concept eliminates the need to compute a numerical value for the price of capital, such as the weighted average cost of capital. 5For details, see [17]. Also see the Appendix to this study. 424

Omega, Vol. 1, No. 4 quite frequently in engineering literature and by some economists. 6 It should be emphasized that the concept of UCC differs from that of economies of scale. The latter concerns changes in average total unit costs with increases in plant capacity. UCC relates only to the ratio of total net fixed investments to capacity and hence tells us very little about capital costs per unit of output--since interest rates, depreciation practices, and the structure of financing must also be considered--and much less about unit variable costs. Clearly, there need not be any consistent relationship between decreasing unit capacity cost and economies of scale. The concern of investment theory with more traditional capital cost concepts such as depreciation charges per unit of output suggests that the relationship between this traditional concept and UCC be elaborated more completely. The relationship between plant life, UCC, depreciation charges per unit of output and utilization of plant capacity can be explored by assuming that the entire plant investment is depreciated linearly over the economic life of the plant£ Under these assumptions, the total annual depreciation charge will be the same in each year and depreciation charges per unit of output in year i will be Annual Depreciation Unit Capacity Cost Plant Capacity × Physical Outputi -- Economic Plant Life Physical Outputi

(2)

It should be noted that the accounting definition of depreciation charges per unit of output in year i may differ from that of equation (2) depending on whether the accounting estimate of plant life is the same as the economic plant life. s The last term in equation (2) is simply the reciprocal of the rate of utilization of plant capacity in year i. The advantage of using the UCC concept in an analysis of scale economies is that it requires no assumptions about economic plant life or depreciation practices yet still allows a partial examination of the relationship between plant size and capital costs. Furthermore, when this concept is used in a cross sectional analysis of new plants there is no need to estimate numerical values for the price of capital. As noted earlier, hypotheses concerning the movements of LRAC curves through time have never been articulated, but several assumptions generally made by economists and accountants imply that LRAC curves should shift parallel to one another through time with no change in their shape (for a review of the literature, see [17]). For example, the frequently used assumption that economic plant life is the same for all plant sizes implies that the LRAVC curves 6For a more detailed explanation of the use and development of this concept see [17]. The earliest comprehensive development of this concept is contained in [12] and [13]. 7This analysis ignores more rapid methods of depreciation and also assumes that both structures and equipment will be depreciated at the same rate. U.S. income tax laws allow variations other than those explored here, but this does not detract from the value of the analysis. SPhysical plant life is much greater than either economic or accounting plant life, at least for the production processes included in this study.

425

c

Huettner--Shifts of Long Run Average Cost Curves should shift parallel to one another with no change in their shape through time. Certainly, the LRAVC curve for new plants constructed at any point in time may be regarded as the lower bound for the unit variable costs of any plant operating at that point in time which produces identical products. Furthermore, the economic lives of plants producing similar products should be determined mainly by operating costs.9 If the LRAVC curves for the new plants, constructed at a point in time, shift upwards more rapidly through time for small plants than for large plants, then the unit operating costs for any small plant must have increased more rapidly through time than those of any large plant. Small plants should clearly have a shorter economic life under these conditions. Another assumption frequently used by economists in both theoretical and applied studies of scale economies is that construction and operating costs can be adjusted for price changes through time by use of an appropriate cost or price index. 1° This not only presupposes that appropriate indexes exist, but it also assumes that one index is appropriate for all plant sizes. The use of these indexes implies that the unit capacity cost curves and LRAVC curves shift parallel to one another with no change in their shape through time. The above discussion indicates that proper use of LRAC curve analysis will raise issues of both theoretical and managerial interest. For example, the issues raised concerning cost indexes and the usual assumptions underlying depraciation calculations will indicate that previous studies of economies of scale have underestimated these economies and that managerial decisions based on traditional accounting data should be biased in favor of small plants. Furthermore, knowledge of the past patterns of shifts in LRAC curves should be of use to corporate planners and forecasters for investment planning and plant size decisions, and of use to economists interested in filling the void that presently exists between the theory of LRAC curves and the theory of increasing, decreasing and constant cost industries. Finally, the above discussion indicates that the LRAC curve framework may be of more use for certain types of problems than the physical framework emphasized by production functions. For example, questions regarding minimum efficient plant size are of concern to both corporate planners and anti-trust economists. These questions can best be answered in a LRAC curve framework, even though this framework does not lend itself easily to questions requiring the classification of changes through time into categories of substitution effects, scale effects, and technological change effects. In fact, this study will argue that such classifications are artificial, particularly with respect to scale and technological change, and that preoccupation with these classifications has diverted economists' attention from more important issues. 9Sincethe plants are producingsimilarproducts (and in this studyhomogeneousproducts), shifts in demand should have little influence on relative economic plant lives. Geographic shifts in demand would be the major exception to this statement. 1°See the studies by Galatin and Komiya in Table 1. 426

4~ I'O ",-d

Time series No study of 17 U.K. firms that had no capacity changes between 1928-47

Time series No study of 365 U.K. firms that had capacity increases between 1928-47 Yes

No

Time series Yes, sample Yes, only study of 365 stratified for capital U.S. plants into four input built between technological 1937-5911 eras

Yes, inter- Yes cept dummy variable used lz

1960 cross section of 220 U.S. plants built between 1941-59

Plant Factor considered*

Plant vintage considered

Data used

No

No

Yes, only for labor input

No

Rated None used capacity of firm

Rated None used capacity of firm

Nameplate Profits capacity of allocable to plant generating

Nameplate Fixed capacity investment of plant

Fuel or Measure Measure Construction of capacity of capital type considered

11Only two units were larger than 200MW and 19 plants larger than 400MW. 12The intercept dummy variables estimates were very erratic, alternating from positive to negative values.

Short run average variable cost curve estimated

Johnston [18]

Neo-classical Leontief production function estimated

Dhrymes and Kurz [10]

Long run average variable cost curve estimated

Log linear production function estimated

Barzel [4]

Johnston [18]

Type of study

Author

Marginal cost is constant

L R A V C curve is L shaped

Economies of scale largest for labor and smallest for fuel; no technological change for labor input

Economies of scale largest for labor and smallest for fuel; scale effects larger than effect of technological change

Conclusions

T A B L E 1. S U M M A R Y OF EXISTING ECONOMIC STUDIES OF ELECTRIC P O W E R GENERATION

4~

q3

t~

O0

Type of study

Plant vintage considered

1949 and 1953 cross section of 145 U.S. firms 1955 cross section of 145 U.S. firms

No

No

No

No

No

None

Interest a n d Economies of scale for all depreciation inputs charges allocable to generating

Constant returns to scale for administrative costs

L R A V C curve declines

U n i f o r m returns to scale for capital, labor a n d fuel

Nameplate Deflated capacity of Equipment each unit t6 Cost

None

Returns to scale for all inputs

Nameplate Deflated capacity of Fixed plant investment

Rated capacity of firm

Conclusions

Measure Measure of capacity of capital

N o n e needed Book value N o n e of plant

No

No

Fuel or Construction type considered Yes, fuel type

Plant Factor considered*

Time series Yes, inter- Yes study of 152 cept d u m m y U.S. plants 1~ used TM 1920-53 Time series Yes, sample N o study of 340 stratified U.S. plants into four built between technological 1938-5618 eras 1947 cross No Yes section of 37 U.S. firms

Data used

13Only two plants were larger than 300MW. 14The intercept dummy variables estimated were very erratic, alternating from positive to negative values. l~Land and structures costs omitted but equipment costs included. 16Each plant is composed of one or more b o i l e r - t u r b i n e - g e n e r a t o r units. 17Only 12 plants were larger than 400MW. ~8Only 15 plants were larger than 400MW and no units were larger than 210MW.

Lomax [22] Long run average variable cost curve estimated McNulty Long run [24] average administrative cost curve estimated Nerlove Cobb Douglas [25, pp. production 409-439] function estimated

Galatin [11 ] Log-Leontief production function estimated Komiya Log-Leontief [20] production function estimated

Author

(CONTINUED)

TABLE 1.

Plant Factor considered*

No

No

Yes

Rated A n n u a l fixed capacity of charges on each unit investment computed as 12% of original investment

Rated A n n u a l fixed capacity of charges o n each unit investment computed as 12% of original investment

Rated Annual capacity of depreciation each unit 16 charges computed as 12% of cost of equipment

Fuel or Measure Measure Construction of capacity of capital type considered

The most economical pattern of system expansion is to add units of between 7% and 10% of the size of the system. The L R A C curve declines**

The most economical pattern of system expansion is to add units of between 7% and 10% o f the size o f the system. The L R A C curve declines**

Economies of scale on a unit basis but not a plant basis; effect of plant factor larger than scale effect: technological change not significant

Conclusions

*Plant factor is a concept similar to the annual rate of utilization af capacity: P F =

Annual kilowatt hours produced Capacity × 360 days × 24 hours. **Note that both of these studies assumed a forced outage rate of 2 per cent since this was normal for the range of plant sizes used in the early 1950s. Recent data on total forced outrage hours indicate that forced outage rates are now higher the larger the unit and that 12"5 per cent was the average forced outage rate for 600-2000MW generating units built during the 1960s. As b o t h of these studies point out any increase in the forced outage rate of large units would reduce the cost advantages of the larger generating units.

Engineering No. estimates of Kirchmayer, et al.

Yes

L R A C curve estimated for a generating system

Ling [21]

1965 cross Yes, inter- Yes section of 76 cept d u m m y U.S. plants variable built between used a, 1956-6517

Plant vintage considered

Yes

Long r u n average cost curve estimated 15

Olson [26]

D a t a used

Kirchmayer L R A C curve Engineering N o et al. [19] estimated estimates for a generating system

Type of study

Author

TABLE 1. (CONTINUED)

4~

Huettner--Shifts of Long Run Average Cost Curves The next section of this paper will briefly review some of the prevailing views of the effects of technological change and increased plant size on unit capacity costs and unit operating costs. The third and fourth parts of this paper will present the results of a study of unit capacity costs and unit operating costs of 400 U.S. electric generating plants. The unit capacity cost analysis will also include the results of an analysis of the U.S. construction costs of 36 steel making plants and 120 cement plants. 19 The final sections of this paper will review the theoretical and managerial implications of this analysis. Before turning to these tasks, however, it should be noted that electric power generation will be emphasized in this study for two reasons. Firstly, both operating and construction costs are available at the plant level and sufficient numbers of new plants are constructed each year to permit the cross-sectional analysis described above. Secondly, electric power generation has received considerable attention in previous economic studies, hence the traditional assumptions, conclusions and methodologies are easily documented. The important characteristics of these studies are summarized in Table 1. A review of these characteristics indicates that each of these studies is deficient in one or more respects in that: eight violated the principle of cost minimization; eight made either no allowance or only partial allowance for differences among plants due to fuel or construction type; four used an inadequate measure of capacity-the nameplate capacity rating (see the Appendix); five made no allowance or only partial allowance for different rates of utilization of plant capacity; all five of the studies of plant level economies were based on samples containing few generating plants above 400 megawatts (hereafter MW) in size; and finally, none of these studies considered the possibility that economic plant life may differ either among plants or through time. The long run average cost studies of Table 1 concluded that, for increased plant or firm size, administrative cost per un.it of output remained constant but both average variable costs and average total costs declined. The production function studies found that all inputs were subject to economies of scale, but these economies were very large for labor, moderate for capital, and smallest for fuel. In addition, Barzel's production function study concluded that the scale effect far overshadowed the effect of technological change [3]. Finally, Olson's study of long run average costs found that scale economies occur at the unit level but not at the plant level. 19a Furthermore, he found that the effects of increased plant utilization far outweighed the scale effects? 9b The last two studies reviewed in Table 1 are based on engineering estimates rather than on actual cost data. Both of these studies differ from the preceeding ten in that they emphasize scale economies of a generating system rather than 19 Operating costs for both the steel making and cement plants were not available. 19a A plant is composed of one or more turbine-boiler-generator units. tgb Since electric power generation is a high fixed cost operation, one would expect utilization of capacity to be an important factor. It has been shown, however, that variable costs of generating plants are very insensitive to plant utilization. See [17]. 430

Omega, Vol. 1, No. 4 those of individual generating plants or units. Both studies concluded that the long run average system cost curve declines and that the most economical pattern of system expansion is to add generating units of between 7 and 10 per cent of the size of the system. Unfortunately, the engineering estimates used in both of these studies were based on the technological relationships of the early 1950's. Many of the conclusions of the twelve studies reviewed above need retesting not only because of the limitations noted, but also because of the need to update conclusions based on samples of generating plants built 20, 30, and even 40 years ago.

PLANT SIZE AND TECHNOLOGICAL CHANGE: SOME PREVAILING VIEWS The effect of increased plant size on unit costs is clearly established in economic theory but is of little practical value since the LRAC curve tells us only that total unit costs will decline as plant size increases and that, beyond some optimal plant size, total unit costs will increase. The effect of plant size on the various unit cost components (i.e. unit capital, labor and material costs) is, however, rarely discussed in economic theory (see, however, the discussion in [12]). The effect of increased plant size on unit capacity costs is based on the engineering argument that the cost of equipment, such as tanks, tubes, kilns and reaction vessels, is proportional to its surface area while its capacity is proportional to its volume. The resulting rule for investment in equipment of larger capacity is: I'-

"-It

Icap2 [ where cap2 > capl

(3)

x~ = tj. L~ap~J The exponent x was originally assumed to equal its theoretical value of 0"6 but subsequent articles have assumed that each process has its own characteristic exponent and also extended the rule to total plant costs as well as equipment costs (for example, see [2, 7, 8, 15]). An alternative statement of equation (3) is that unit capacity cost must decline if x < 1. A review of the above noted engineering studies has produced no x greater than 0"9. The above paragraphs indicate that economic and engineering theory have, in some instances, clearly established views regarding the effects of plant size on some unit cost components in a static framework. The preceding section noted the absence of any such established theories in a dynamic framework, however. It is somewhat disconcerting to note that economic theory is even less illuminating in terms of established theories of the effects of technological change on total unit costs or any of its components. 19c Classifications of 19eFor a review and development of the reactions in price and quantity attributable to technical advance alone see 128]. 431

Huettner--Shifts of Long Run Average Cost Curves technological change into such categories as capital saving, labor saving, neutral, and so on, may be useful for some purposes, but these efforts have not produced definitive statements as to the effects of technological change on unit costs through time. Some studies of technology have concluded, however, that most technological change is gradual, almost imperceptible at any point in time, yet it results in a major change in technique after a number of years (for example, see [16, 27]). This view will be explored in the remaining sections by considering two aspects of technology or technological change. Firstly, the various production processes of an industry, such as Bessemer, open hearth and basic oxygen, will be identified and each will be considered a different technology. This will allow an examiation of the effects of new process innovations (new technologies) on UCC and on operating costs. Secondly, each technology (production process) will be studied through time and some inferences made as to the effect of technological change on UCC and operating costs. Incidentally, a review of the empirical studies listed in Table 1 indicates that the empirical results follow the pattern noted above for economic theory. The empirical studies generally conclude that economies of scale do exist in electric power generation but there is substantial disagreement as to the importance and magnitude of the effects of technological change.

SHIFTS IN UNIT CAPACITY COST CURVES T H R O U G H TIME Tables 2, 3, and 5 present plant level data on unit capacity costs for each of the industries studied. The capacity and cost data in these tables are actual figures, not estimates. Note, also, that all UCC data are unadjusted for price changes. In fact, throughout this study no attempt has been made to adjust any cost figures by a price index or a construction cost index, z° Examination of Table 2 indicates very little support for the view that UCC declines as plant size increases, except for steel making plants using the electric process. Stepwise regression analysis confirmed this view since capacity was a significant explanatory variable only for electric process plants. Table 2 provides only two instances in which the UCC of a given production process can be observed through time but in both instances, UCC increased substantially through time, from $6 per ton to $25 per ton for the open hearth process and from $15 per ton to $27 per ton for the electric process. The great differences in UCC by type of steel making process are also readily apparent and the sequence 2°No adjustment by a geographic price index has been made either. This procedure is fairly common and, for example, none of the studies reviewed in Table 1 used a geographic price index for either construction or operating costs. Note also that UCC can be disaggregated further into land and structures cost per unit of capacity and installed equipment costs per unit of capacity. For an analysis of these subcomponents, see [17]. 432

Omega, Vol. 1, No. 4 o f steel m a k i n g process i n n o v a t i o n s is o f p a r t i c u l a r interest since it indicates t h e p o w e r f u l i m p a c t process i n n o v a t i o n s can have o n U C C a n d hence i n v e s t m e n t requirements. A t the t u r n o f the century, the o p e n h e a r t h process was r e p l a c i n g t h e Bessemer p r o c e s s despite the t h r e e f o l d increase in U C C . T h e electric process was the next i n n o v a t i o n , b u t its limited use k e p t its l o w e r U C C f r o m h a v i n g a m a j o r i m p a c t on i n v e s t m e n t requirements. T h e b a s i c oxygen p r o c e s s w i t h its s u b s t a n t i a l l y l o w e r U C C a n d its wide a p p l i c a b i l i t y has h a d a m a j o r i m p a c t o n i n v e s t m e n t r e q u i r e m e n t s d u r i n g the p a s t ten years. T h e succession o f

TABLE 2.

TREND OF STEEL MAKING PLANT UNIT CAPACITY COST BY PLANT SIZE GROUPS AND TYPE OF PROCESS*

Steel making plant size groups (millions of tons) 0 to 0.59 New Bessemer Plants 1903-12 New open hearth plants 1911-20 1952-58 New electric arc plants 1942-49 1958-71 New basic oxygen plants 1963-71

0.60 to 1.29

1.30 to 2.79

$6/ton $25/ton

$26/ton

2.79 to 4.29

$2/ton $5/ton

t;15/ton $27/ton

$20/ton $15/ton

$14/ton

*Unit capacity cost in g/ton of annual steel making capacity. TABLE 3. TREND OF CEMENT PLANT UNIT CAPACITY COST BY PLANT SIZE GROUP*

Gray cement plant size groups (millions of Bbl)

Year

0 to 1"99

2"00 to 3"99

4.00 to 13.99

1914-1927 1938-51 1952-57 1958-59 1960-62 1963-64 1965-69

2"9 2"6 4.6 6"8 7.5 7.2 6"5

--6.9 6'4 6.9 4.5 6'0

----4"4 2"9 6"3

*Unit capacity cost in $/Bbl of annual gray cement capacity. 433

Huettner--Shifts of Long Run Average Cost Curves TABLE 4.

LEAST SQUARES ESTIMATES OF THE UNIT

CAPACITY

COST OF NEW

PLANT

SIZE GROUP

GRAY CEMENT PLANTS BY AND TYPE OF PROCESS*

Gray cement plant size groups (millions of Bbl) 0 to 1.99

2.00 to 3.99

4.00 to 13.99

Wet process: 1914-1927 1938-51 1952-57 1958-59 1960-62 1963-64 1965-69

2"58 -8.76 6"97 8-67 9-35 --

--5"75 6"97 5-90 5"92 6"31

----4.98 4"84 6"31

Dry process: 1914-1927 1938-51 1952-57 1958-59 1960-62 1963-64 1965-69

2,58 3'94 8.76 7.75 10"55 9"35 --

--5'75 7'23 7"78 5.92 7.04

m N m m m

*Unit capacity cost in $/Bbl of annual gray cement capacity.

TABLE 5. TREND OF FOSSIL STEAM PLANT UNIT CAPACITY COST BY PLANT SIZE GROUPS* F o s s i l s t e a m p l a n t size g r o u p s ( M W )

Year 1923-29 1930-39 1940--45 1946-49 1950 1951-52 1953-54 1955-56 1957-58 1959-60 1961-62 1963-65 1966-68

0 to 49

50 tO 99

100 tO 199

200 tO 399

400 to 999

1000 to 1999

Average all size groups

124 112 114 230 165 153 180 218 211 202 ----

122 116 93 141 129 130 162 148 169 161 141 133 --

114 111 83 112 119 138 131 135 142 168 162 142 123

120 --131 -139 127 124 107 142 126 123 101

-----117 125 128 125 141 140 118 105

-------124 --110 120 103

117"3 111"I 106-3 189-5 147"6 141"4 154"2 148-9 150-2 164"7 148-4 131.1 110"5

*Unit capacity cost in 434

S/KW.

Omega, Iiol. 1, No. 4 TABLE 6. LEASTSQUARESESTIMATESOF THE UNIT CAPACITYCOSTOF SUBCRITICALCOALFIRED GENERATINGPLANTSWITH CONVENTIONALINDOORCONSTRUCTION* Subcritical coal plant size groups (MW)

Year

0 to 49

50 to 99

100 to 199

200 to 399

400 to 999

1000 to 1999

1923-29 1930-39 1940-45 1946-49 1950 1951-52 1953-54 1955-56 1957-58 1959-60 1961-62 1963-65 1966-68

117 100 104 193 160 184 218 173 233 236 ----

121 110 93 163 135 156 158 155 164 190 267 168 --

122 113 91 155 129 150 143 148 147 178 202 144 140

123 --151 -148 136 144 138 172 170 132 119

-----146 131 142 133 168 151 125 108

-------141 --144 123 103

*Unit capacity cost in S/KW. process i n n o v a t i o n s in steel m a k i n g has clearly c h a n g e d investment r e q u i r e m e n t s d u r i n g the p a s t 50 years, zl F o r a n y given time p e r i o d in T a b l e s 3 a n d 5, one w o u l d expect t h a t the U C C o f each size g r o u p w o u l d be progressively lower in each succesively larger p l a n t size g r o u p . This e x p e c t a t i o n was fulfilled in 37 o f the 52 possible cases, b u t the f r e q u e n c y a n d m a g n i t u d e o f the decline was m o r e p r o n o u n c e d in the smallest size g r o u p s suggesting t h a t the benefits o f r e d u c e d c a p a c i t y cost v a n i s h r a p i d l y as p l a n t size increases b e y o n d the smallest size ranges. This view is c o n f i r m e d b y the results o f a stepwise regression analysis shown in T a b l e s 4 a n d 6. T a b l e s 3 a n d 5 implicitly a s s u m e t h a t all c e m e n t o r generating p l a n t s are similar, hence subtle differences in p l a n t characteristics have been ignored. F o r example, T a b l e 3 includes b o t h wet a n d d r y process c e m e n t plants. Stepwise regression analysis a l l o w e d c o n s i d e r a t i o n o f several p l a n t characteristics a n d i n d i c a t e d t h a t there is a significant difference in the U C C o f wet a n d d r y process c e m e n t plants. 2z Similarly, stepwise regression analysis o f fossil steam g e n e r a t i n g p l a n t s i n d i c a t e d t h a t significant differences exist, for example, between c o a l fired p l a n t s a n d p l a n t s fired b y oil a n d gas. 22a Incidentally, a variety o f f u n c t i o n a l f o r m s were tested d u r i n g the stepwise regression analysis b u t the best results were o b t a i n e d with unit c a p a c i t y cost as an inverse f u n c t i o n o f p l a n t capacity. P l a n t c a p a c i t y 2tBlast furnace capacity requirements have been ignored in this analysis although each process does differ markedly in its dependence on blast furnace capacity. 22Dry process cement plants are more expensive to build since they require concrete storage silos for in-process inventory. Wet process plants use less expensive steel tanks for storage of in-process inventory. zza As noted earlier, the reliability of fossil units diminishes as unit size increases. The UCC figures in Table 4 tend to overstate the cost benefits of larger units since these units should increase reserve capacity requirements when integrated into a system. 435

Huettner--Shifts of Long Run Average Cost Curves TABLE 7. LEAST SQUARES REGRESSION FOR THE UNIT CAPACITY COST OF NEW GRAY CEMENT PLANTS BY TYPE OF PRODUCTION PROCESS*

1965-69 1963-64 1960-62 1958-59 1952-57 1938-51 1914--27

Wet process

Dry process

UCC UCC UCC UCC UCC

UCC UCC UCC UCC UCC UCC UCC

= = = = =

6.31 4.20 + 5.15/cap 4.52 q- 4.15/cap 6.97 4.25 + 4.51/cap

U C C = 1.22 q- 1.36/cap

= = = = = = =

6.31 4.20 6-40 6.97 4-25 3.94 1.22

+ + + + +

2-19/cap 5.15/cap 4"15/cap 0.78/cap 4.51/cap

+ 1.36/cap

~2

try

n

0.48 0.39 0.85 0.20 0.15 0.40 0.97

1.61 2.21 1.61 1.83 2.80 1.55 1.04

21 15 17 18 31 11 7

*All regression coefficients were significant at the 90 per cent level or higher. Note: tr~ is the variance due to deviation from regression; R 2 is the sum of squares due to regression divided by the total sum of squares in analysis of variance. ~2 is R 2 adjusted for loss of degrees of freedom. TABLE 8. LEAST SQUARES REGRESSION FOR THE UNIT CAPACITY COST OF SUBCRITICAL COAL FIRED PLANTS WITH CONVENTIONAL INDOOR CONSTRUCTION*

Year 1966-69 1963-65 1961-62 1959-60 1957-58 1955-56 1953-54 1951-52 1950 1946--49 1940--45 1930--39 1923-29

Regression equation for unit capacity cost

~2

UCC UCC UCC UCC UCC UCC UCC UCC UCC UCC UCC UCC UCC

0.66 0.24 0.76 0.66 0.62 0.49 0.50 0.33 0.68 0"64 0.17 0.49 0.06

= = = = = = = = = = = = =

99.6 120.4 137.3 165.5 129.0 140.6 128-1 144.8 123.0 147.4 88.2 115.7 122.9

q- 639.8/cap q- 3599.8/cap ÷ 9720.5/cap q- 1773.4/cap + 2597.2/cap q- 1069.0/cap + 2239.7/cap q- 845.4/cap + 931.8/cap q- 1154.8/cap -q- 392.5/cap -- 387.7/cap -- 137.5/cap

try

n

13.54 21.98 19.04 34.67 26.07 33.92 41.92 29.15 26.39 48.03 23.61 21.18 23"66

26 30 24 32 37 32 40 30 21 48 23 24 24

*All regression coefficients were significant at the 90 per cent level or higher. Also, try and R 2 are defined in the same way as in Table 7. w a s significant a t least t h e 90 p e r c e n t level in all b u t o n e o f t h e r e g r e s s i o n s as s h o w n in T a b l e s 7 a n d 8. T a b l e s 4 a n d 6 p r e s e n t U C C as e s t i m a t e d b y t h e r e g r e s s i o n e q u a t i o n s a n d i n d i c a t e t h a t m o s t o f t h e d e c l i n e in U C C d i s a p p e a r s as c e m e n t p l a n t s i n c r e a s e b e y o n d f o u r m i l l i o n b a r r e l s in a n n u a l c a p a c i t y a n d as c o a l fired g e n e r a t i n g p l a n t s i n c r e a s e b e y o n d 4 0 0 M W , b o t h o f w h i c h a r e o n l y a v e r a g e sized p l a n t s b y t o d a y ' s U . S . s t a n d a r d s . A final e x a m i n a t i o n o f T a b l e s 3 a n d 5 i n d i c a t e s a v e r y m i x e d p i c t u r e o f t h e t r e n d o f U C C t h r o u g h t i m e since it i n c r e a s e d c o n s i s t e n t l y in s o m e size g r o u p s , fell c o n s i s t e n t l y in o t h e r s , a n d r o s e a n d fell o r vice versa in others. T h e e s t i m a t e d U C C v a l u e s in T a b l e s 4 a n d 6 c l a r i f y this m i x e d p i c t u r e a n d i n d i c a t e t h a t t h e U C C c u r v e s d o n o t shift p a r a l l e l t o o n e a n o t h e r t h r o u g h time. F o r c e m e n t plants, UCC rose through time but the magnitude of the increase was largest 436

Omega, Vol. 1, No. 4 in the smallest plant size group. For generating plants, U C C rose consistently in the smallest plant size groups, rose and then returned to earlier levels in the larger size groups, and even fell ultimately in the largest generating plant size groups. In fact for the 1966--68 period, the U C C of coal fired generating plants in the largest size groups was $103/KW, lower than the $117/KW of the 192329 period. Since most of the generating capacity added in the 1966--68 period was in plants above 400MW in size, one can conclude that during this period electric utilities were able to add generating capacity at unit capacity costs below those of 50 years earlier. The last column of Table 5 shows that even the average U C C of 1968 was less than that of 1925. TABLE 9. HANDY WHITMAN CONSTRUCTION COST INDEX [31], TOTAL STEAM PRODUCTION PLANT--SOUTH CENTRAL DIVISION*

Index (1911 = I00)

Index (1911 = I00)

1925 1935 1943 1948 1950 1952 1954

1956 1958 1960 1962 1964 1967

210 227 283 427 456 516 566

656 753 758 727 742 805

*The index gives reproduction cost new for fossil steam power plants and covers labor, material and equipment. The index is based on costs by FPC account numbers. The South Central Division of the U.S. was selected because the index for this region increased the least between 1925 and 1967. Reference to Table 9, however, raises questions as to whether these construction cost changes are adequately measured by existing construction cost indexes. The H a n d y Whitman Construction Cost Index shown in Table 9 is specifically designed for fossil steam generating plants and is based on Federal Power Commission (hereafter FPC) cost accounts as is the electric power data of this study; yet the H a n d y Whitman Index indicates that if one were to reproduce new, in 1967, a plant built in 1925, it would cost nearly four times as much in 1967 as it did in 1925. While this may be true, several factors indicate that this index or similarly constructed indexes should not be used either to adjust past investment data or to plan future investment expenditures. Firstly, the finding that the U C C curves did not shift parallel to one another through time suggests that one construction cost index is inadequate--there is need for a different index for each plant size group. Furthermore, reference to Table 6 indicates that even in the smallest plant size group where U C C increased the most between 1925 and 1967, the increase was only about 200 per cent; yet the increase measured by the H a n d y Whitman Index was 400 per cent. The above factors suggest that the available construction cost indexes are poor measures of past 437

Huettner--Shifts of Long Run Average Cost Curves cost changes even when applied to the very production process for which they were specifically designed. More importantly, the above results suggest that present construction cost indexes are insensitive to changes in both plant size and technology. These indexes should be of little use for projecting UCC in the future or projecting investment requirements--even when a major process innovation is not expected. Finally, the use of these indexes to deflate past investment data is undesirable, not only because of their inaccuracy but also because of the implied assumption that the adjusted data may then be analyzed as if it were generated by a sample of plants lying on one LRAC curve or production function.

SHIFTS IN LONG R U N AVERAGE VARIABLE COST CURVES THROUGH TIME Operating cost data are not available for any of the steel making or cement plants included in this study but, reportedly, unit operating costs decline as plant size increases for both types of plants. 23 The L shaped LRAVC curves suggested by these engineering studies in combination with the UCC curves of the preceding section would indicate that the corresponding LRAC curves are also L shaped. Furthermore, the non-parallel shifts in the UCC curves of cement plants suggest that the L R A C curves in cement making have not shifted parallel to one another through time. The available information on steel making plants is not sufficient to support any inference regarding shifts in their L R A C curves through time, however. In the case of electric power generation, inferences are unnecessary; operating cost data are available and the analysis that follows yields a clear pattern of non-parallel shifts in both the LRAVC curves and the LRAC curves through time. For convenience, the operating costs have been divided into fuel costs and non-fuel costs. Fuel costs are based on delivered fuel prices but no adjustment has been made for geographic differences in the fuel price. Non-fuel costs include both labor and supplies, do not include taxes, and are generally evenly divided between maintenance expenses and operating expenses. 24 The fuel consumption of the plants in B T U / K W H (i.e. British thermal units per kilowatt hour) has also been included in the analysis as a surrogate for fuel cost adjusted for geographic price differentials. Division of fuel cost per unit of output by fuel price per million BTU yields fuel consumption, therefore there is no need to resort to the use of a geographic price index. The analysis of unit operating costs and fuel consumption parallels the analysis of UCC. Stepwise regression analysis was used to identify the significant 23These reports are based on engineering estimates rather than on actual cost data. For open hearth plants see [6]. For cement plants see [1]. 24The data do not specify labor costs separately and so a more detailed breakdown of the data by FPC account would not add to the analysis. 438

Omega, Vol. 1, No. 4 variables and, as before, several f u n c t i o n a l forms were tested b u t the reciprocal f o r m yielded the best results in terms o f consistently high goodness o f fit (based o n R2), correctness of signs of the coefficients, a n d the theoretical expectation that u n i t operating costs are n o n - n e g a t i v e . 2s T a b u l a t i o n of the raw data by p l a n t size groups a n d listings o f the regressions equations have been excluded to shorten the exposition. The least squares estimates shown in Tables 10, 11 a n d 12 are similar to those for U C C in that adjustments have been m a d e for significant p l a n t characteristics such as fuel type, c o n s t r u c t i o n type, p l a n t factor, a n d supercritical or subcritical, z6 T h e tables also include ~ z a n d Cry,the s t a n d a r d error o f the estimate, to indicate the reliability o f the results. Confidence intervals m a y be o b t a i n e d by using the ~2cr rule a n d the value o f oy in these tables.

TABLE 10. ESTIMATED FUEL CONSUMPTION FOR SUBCRITICAL, COAL FIRED PLANTS BY PLANT SIZE GROUPS ( M W ) *

50 to 99

100 to 199

200 to 399

400 to 999

I000 to 1999

Rz

Year

0 to 49

1928-29 1930-39 1940-45 1946-49 1950 1951-52 1953-54 1955-56 1957-58 1959-60 1961-62 1963-65 1966-68

17,868 14,131 14,095 13,647 13,612 13,647 13,570 11,867 13,722 17,192 ----

17,001 13,649 12,270 12,840 12,167 11,600 11,933 10,658 11,235 11,713 10,158 11,607 --

16,784 13,528 11,814 12,638 11,806 11,089 11,524 10,356 10,613 10,343 9898 10,604 10,363

16,766 --12,537 -10,833 11,319 10,205 10,303 9659 9318 10,103 10,051

-----10,687 11,202 10,119 10,125 9268 9158 9817 9868

-------10,084 --9095 9702 9795

0.46 0.61 0.59 0.69 0.91 0.72 0.78 0.87 0.76 0.95 0.89 0.75 0.52

Cry 1976 2241 2160 1144 720 749 815 600 712 483 285 531 455

*Fuel consumption in BTU/KWH assuming a plant factor of 50 per cent. Also, trj, and ~2 are defined in the same way as in Table 7. For sample sizes, see Table 8.

ZSThelinear and semilog functional forms were tested despite the "non-negative" criterion but both yielded lower R~ than the reciprocal form although the same variables were generally significant and of the proper sign. The double log form was also tested with satisfactory results exceeded only by the reciprocal form. See the Appendix of this study for a brief description of the stepwise regression analysis. Z6The number of boiler-turbine-generator units was also used in both the UCC and LRAVC curve analyses but in both cases it was not a significant factor (at the 90 per cent level). Note that supercritical plants have initial steam pressure greater than 3206 pounds per square inch relative to atmospheric pressure and therefore have metallurgical requirements different to traditional subcritical plants. Supercritical fossil fuel plants are theoretically more efficient than subcritical plants since the latent heat in the steam drops to zero for pressures above 3206 psi, and water turns directly to steam without boiling. 439

Huettner--Shifts of Long Run Average Cost Curves TABLE 11. ESTIMATED FUEL COST PER UNIT OF OUTPUT FOR SUBCRITICAL, COAL FIRED PLANTS BY PLANT SIZE GROUPS ( M W ) *

Year 1923-29 1930-39 1940-45 1946-49 1950 1951-52 195 3-5 4 1955-56 1957-58 1959-60 1961-62 1963-65 1966--68

0 to 49

50 to 99

100 to 199

200 to 399

NA NA 2.52 3.50 3.55 4.11 3"99 3"47 3"95 5"50 ----

NA NA 2"03 3.23 2.88 3.06 3"17 2"85 2"95 3"18 2"63 2"22 --

NA NA 1.91 3.16 2.72 2.80 2"97 2"64 2"70 2-60 2"45 2"22 2.13

NA . -3.13 -2.67 2.87 2.59 2"58 2'31 2'41 2.22 2"13

400 to 999

1000 to 1999

. .

. .

. . -----2'55 --2'37 2'22 2"13

---2.60 2-81 2"56 2.51 2"15 2"38 2.22 2'13

ae

. . 0.50 0.45 0.80 0.15 0"39 0"75 0"43 0"78 0"62 0"23 0"17

0.67 1"24 0.80 0-90 1"09 0' 66 0'58 0'48 0'28 0"71 0"44

* C o s t in m i l l s / K W H a s s u m i n g a p l a n t f a c t o r of 50 per cent. A l s o , try a n d ~ z a re defined i n the s a m e w a y as in T a b l e 7. F o r s a m p l e sizes, see T a b l e 8.

TABLE 12. ESTIMATED NON-FUEL COST PER UNIT OF OUTPUT FOR CONVENTIONAL, SUBCRITICAL, COAL FIRED PLANTS BY PLANT SIZE GROUPS ( M W ) *

Year 1923-29 1930-39 1940-45 1946-49 1950 1951-52 1953-54 19 55-5 6 1957-58 1959-60 196 1-6 2 1963-65 1966-68

0 to 49

50 to 99

100 to 199

200 to 399

NA NA 1"07 1.54 1-46 0"88 1.19 1-38 1.32 1"70 ----

NA NA 0'84 1 "35 0"85 0"87 0"91 0'98 0"86 0'85 0'90 0"77 --

NA NA 0"78 1-30 0"70 0"86 0"84 0"88 0.75 0"64 0"69 0"69 0"84

NA . -1-27 -0.86 0"81 0.83 0'69 0"54 0"58 0"65 0"66

400 to 999

1000 to 1999

. .

. .

----0'79 0"80 0.64 0.48 0'52 0'63 0.63

. . -----0-79 --0"49 0.62 0.51

~z

oy

. . 0"72 0"39 0-82 0'78 0' 84 0'95 0"30 0"93 0.78 0.42 0"46

0"33 0"70 0'45 0"19 0"21 0"18 0"71 0"09 0"17 0-20 0"18

* C o s t in m i l l s / K W H a s s u m i n g a p l a n t f a c t o r o f 50 p e r cent. N o n - f u e l c o s t s a re a l m o s t e n t i r e l y l a b o r costs. G e n e r a l l y t h e s e c o s t s are h a l f m a i n t e n a n c e a n d d i r e c t l a b o r , a n d h a l f s u p e r v i s i o n . A l s o , try a n d R z a r e defined in t h e s a m e w a y as i n T a b l e 7. F o r s a m p l e sizes, see T a b l e 8. 440

Omega, Vol. 1, No. 4 Table 10 presents the estimated fuel consumption for subcritical, coal fired plants. As expected, for plants built during any given time period, the fuel consumption improves as plant size increases, but the magnitude of the improvement diminishes rapidly. Note that plant factor (defined as the ratio of output to practical capacity) has been held constant at 50 per cent across all plant sizes. Plant factor for the first full year of production was negatively correlated with plant size between 1923 and 1939 (r ----- -- 0.24), positively correlated between 1940 and 1962 (1" -----0.25), and uncorrelated between 1963 and 1968 (r = 0.005). Throughout the 45 years covered, a 10 point increase in the plant factor of a new plant would yield on the average a 2 per cent improvement in fuel efficiency. Historically, plant factor for the entire U.S. electric power industry has increased from 30 per cent to 55 per cent over the past 45 years, while average industry fuel efficiency has improved from about 19,000 B T U / K W H to 11,000 BTU/ KWH. The above suggests that only a minor part of the improved industry fuel consumption should be attributed to the much higher industry plant factor; most of the improvement is the result of the technological change embodied in each new plant, z7 A final review of Table 10 indicates that, although fuel consumption improved in all size groups through time, the magnitude of the improvement was greater the larger the size group. Table 11 is not as useful as Table 10 for cross-sectional analysis since no adjustment has been made for geographic variations in fuel prices. Three interesting results are apparent, however. The first is that plant factor was not a significant explanatory variable. 2s The second result concerns the time trend of fuel costs per unit of output. Fuel prices have increased substantially during the period 1940-1968, but this trend has been offset by the improved fuel consumption shown in Table 10 to yield generally rising unit costs up to the 1950s and generally falling unit costs after the 1950s. The only exception is for the new plants in the smallest plant size group where unit costs have more than doubled. Assuming that the cost patterns of the newest plants form the lower bound for the costs of all generating plants, one can conclude that unit fuel costs have more than doubled for any generating plant under 50MW in size but have not increased as rapidly for any generating plant over 50MW in size. The third point to note about Table 11 is the appearance that little has changed in the 28 years covered. The powerful effects of technological change evidenced ZTIncreased plant size is assumed to be a form of technological change. This view will be discussed more thoroughly in the final section of the paper. zsSince plant factor was significant but of only minor importance in the fuel consumption regressions, it is not surprising that it was not significant in the fuel cost regressions. Furthermore, American generating plants have multiple sets of tubes and valves connecting the boiler and the turbine .When the load on the generator decreases, the boiler fires are reduced to conserve fuel and the valves connecting the boiler and turbine are adjusted to reduce the volume of steam passing through the turbine, while maintaining both boiler pressure and temperature. Note that unit operating costs are expressed in mills/KWH. A mill is one-tenth of a cent in U.S. currency. 441

D

Huettner--Shifts of Long Run Average Cost Curves i n the physical measures of T a b l e 10 do n o t appear as sharply i n the u n i t cost measure o f T a b l e 11. This indicates that a n y analysis o f technological change m u s t dig below even the u n i t cost level if the effects are to be seen. z9 T h e estimated n o n - f u e l costs per u n i t of o u t p u t shown in T a b l e 12 are based o n a p l a n t factor of 50 per cent in all size groups. U n i t n o n - f u e l costs are highly d e p e n d e n t o n p l a n t factor a n d o n the average a 10 p o i n t increase in p l a n t factor will result in a 15 per cent decrease in u n i t n o n - f u e l costs. Table 12 has n o t b e e n adjusted for a n y geographic differences in wages b u t the u n a d j u s t e d cross-sectional figures indicate that u n i t n o n - f u e l costs generally declined for plants above 2 0 0 M W a n d r e m a i n e d fairly stable for plants between 50 a n d 2 0 0 M W i n size. F o r the smallest p l a n t size group, the t r e n d over the entire period was generally upward. Despite the rapid increase i n wages between 1940 a n d 1968, u n i t n o n - f u e l costs for the large new p l a n t s built in the 1966-68 period are lower t h a n for new plants built in the 1940--45 period. I f one again assumes that the u n i t costs of the new plants constitute a lower b o u n d for the u n i t costs of all generating plants t h r o u g h time, one can conclude t h a t u n i t non-fuel costs have increased m o s t rapidly for plants u n d e r 5 0 M W i n size a n d least rapidly for the largest p l a n t sizes. Table 13 presents estimates o f the total variable costs per u n i t of output. A review o f these estimates indicates clearly that the L R A V C curves have n o t TABLE 13.

Year 1923-29 1930-39 1940--45 1946-49 1950 1951-52 1953-54 1955-56

1957-58 1959-60 1961-62 1963-65 1966-68

ESTIMATED TOTAL VARIABLE COST PER UNIT OF OUTPUT FOR CONVENTIONAL SUBCRITICAL, COAL FIRED PLANTS BY PLANT SIZE GROUPS ( i W ) *

0 to 49

50 to 99

100 to 199

200 to 399

400 to 999

1000 to 1999

NA NA 3.59 5.04 5.01 4.99 5.18 4.85 5.27 7.20 ----

NA NA 2.87 4.58 3.73 3.93 4.08 3.83 3.81 4.03 3.53 2.99 --

NA NA 2.69 4.46 3.42 3.66 3.81 3.52 3.45 3.24 3.14 2.91 2.97

NA --4"40 -3.53 3.68 3.42 3'27 2"85 2.99 2"87 2.79

-----3.46 3.60 3.36 3'15 2.63 2.90 2.85 2.76

-------3'34 --2.86 2.84 2.64

*Cost in mills/KWH assuming a plant factor of 50 per cent. Estimates for this table were computed by adding the cost figures in Tables 11 and 12. 29Many studies of productivity at the national level conclude that only a small percentage of productivity increase should be attributed to technological change. Perhaps the aggregation of plants of all ages, sizes, cost structures and types of processes is a major problem. Also, many of these studies actually fail to dig beneath cost levels, especially in regard to capital inputs, since aggregate average costs are generally deflated by a price or cost index to yield a pseudo-physical measure of inputs and outputs. See [14] for further discussion. 442

Omega, Vol. 1, No. 4 shifted parallel to one another through time. The unit operating costs of new plants under 50MW in size have increased rapidly through time while those of the largest plants have decreased slightly. While Table 13 indicates that economic plant life should be directly related to plant size, it does not explain why the unit operating costs of an existing small plant should increase more rapidly through time than those of an existing large plant. One answer to this question is suggested by the percentages in Table 14. The estimates in Table 14 indicate TABLE 14. NON-FUEL COST AS A PERCENTAGE OF TOTAL OPERATING COSTS FOR CONVENTIONAL, SUBCRITICAL, COAL FIRED PLANTS BY PLANT SIZE GROUP ( M W ) * 0 to Year 1923-29 1930-39 1940-45 1946-49 1950 1951-52 1953-54 1955-56 1957-58 1959-60 1961-62 1963-65 1966-68

49 . . 41-4 30'6 29"2 17"6 25"4 29"5 25-0 23 '6 ----

50 to 99 . .

. . 29'3 29"4 22'8 22" 1 25"6 28"4 24.4 21" 1 25.5 25'8 --

100 to

200 to

199

399 . . -28"9 -24"4 25.4 28" 1 21.1 19"0 19"4 22-6 23"7

. . 29"0 29"2 20"5 23"5 25'6 28"4 21 "8 19"8 22"0 23"7 28'3

400 to

1000 to

999

1999

. . ---24"8 25"4 27.9 20.3 18.2 17.9 22"1 22.8

-----27"8 --17.1 21 "8 19"3

*All calculations are based on a plant factor of 50 per cent. Estimates for this table were computed from cost figures in Tables 12 and 13. that, at any point in time, the unit labor costs of a new plant decline more rapidly than unit fuel costs as plant size increases. Unit labor costs are a smaller percentage of total unit operating costs for larger plants but historically the price of labor has risen faster than the price of fuel? ° Since factor proportions are fixed in existing plants, the rapidly rising labor prices will have a smaller impact on operating costs in those plants where labor costs are the smallest percentage of total operating costs. 3°~ Small plants lose their cost competitiveness more quickly through time than do large plants, hence large plants should have a longer economic life even though the physical lives of large and small plants may not differ. 3°This historical relationship between labor prices and fuel prices is valid for the U.S See [17]. a°aThis finding suggests that it may be sensible for electric utilities to over-capitalize once dynamic factors are considered. For example, an electric utility anticipating input price increases over the life of a generating plant could substitute present capital for future labor and fuel and reduce operating costs over the life of the plant. The plant would be overcapitalized relative to current input prices (the Averch Johnson effect) but not with respect to future input prices over the economic life of the plant. In fact, the economic life of the plant should be enhanced. 443

Huettner--Shifts of Long Run Average Cost Curves One additional point to be raised concerning generating plants is the minimum efficient plant size. Minimum efficient plant size will be defined as the minimum plant size needed to achieve total unit costs not more than 10 per cent higher than those achieved by the largest plants built at the same point in time. A review of the cost figures in Tables 6 and 13 indicates that the minimum plant size is slightly over 300MW and that this has been true for every time period between 1951 and 1968. This conclusion is rather surprising in view of the fact that this is a rather moderate plant size by present day U.S. standards and in view of the sizeable economies of scale generally attributed to electric power generation (see the studies in Table 1). In fact, the economies of scale are generally regarded to be so substantial that electric power generation is classified as a natural monopoly by American economists. The failure of previous studies to note this rather moderate minimum efficient plant size may be due to part to their failure to include sufficient numbers of plants larger than 400MW in their samples. The final point to be raised concerns the computation of depreciation charges. In an industry as increasingly capital-intensive as electric power, capital charges (including depreciation) are a large portion of total costs hence plant life should be a very significant factor. 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. When the average total cost of constructing and operating a new unit falls below the operating costs (without capital charges) of the old, the older unit is uneconomic and should be superseded. 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. The accounting practice of assigning the same life expectancy to all units would seem to result in unrealistically high capital charges to efficient units and low charges to inefficient units. Because of the correlation between unit size and efficiency (both in fuel and in labor costs), there is a good possibility that capital charges based on accounting data have a scale-opposed bias. For similar reasons, the studies of scale economies reviewed in Table 1 have all probably underestimated the true economies of scale for the range of plant sizes encompassed by their samples.

THEORETICAL

AND

MANAGERIAL

IMPLICATIONS

One of the more important conclusions of this study is that economic plant life is directly related to plant size. This finding should be of greater concern as the capital intensiveness of production processes under study increases. At the very least this finding suggests that there is a scale bias in existing studies of economies of scale and current methods of computing depreciation charges. 444

Omega, Vol. 1, No. 4 Certainly decision makers and corporate planners should recognize that these biases exist. More important, however, is the need to recognize the causes of unequal economic plant lives. Recognition of the fact that LRAVC curves do not shift parallel to one another through time should lead to improved corporate planning, cost forecasting and plant size decisions. For economists this recognition would be a first step toward the development of theories that fill the void between the static theory of LRAC curves and theories of increasing, decreasing and constant cost industries. This point merits further discussion. The future costs of an industry should depend on both the movement of the LRAC curves through time and future plant size decisions. The likelihood that a given cost pattern would occur for an industry should be a function of the scale economies of the industry, since these economies should generate cost pressures to increase plant size as long as geographic markets are sufficiently large to absorb the output. Because of these cost pressures, an industry with substantial economies of scale beyond current plant sizes could achieve declining unit costs in the future even if the LRAC curves shifted upward slightly through time. 31 An industry in which there were no economies of scale beyond current plant sizes would most likely experience increasing unit costs in the future unless technological change could offset input price increases enough to cause the LRAC curves to shift downward through time. Table 15 presents one possible set of ordinal rankings TABLE 15. SCALEECONOMICSAND INDUSTRYCOSTPATTERNS Likelihood that the stated industry cost pattern will occur Scale economies beyond present, typical, industry plant size None Modest Substantial

Decreasing cost industry

Constant cost industry

Increasing cost industry

Very low Low Very high

Low Moderate High

Very high High Very low

of the likelihood of each industry cost pattern occurring. This table is, of course, based on the assumption that all other things are equal. Incidentally, since this study found that there are at best only moderate economies of scale in electric power generation beyond current plant sizes, one could hypothesize that the generating sector of the industry will probably not experience decreasing unit costs in the future--in fact, the opposite is more likely. The findings of this study indicate the complex set of forces at work to bedevil any projection of future investment requirements. Many important factors such as rates of diffusion of new technologies have not even been considered; alUse of larger plants could also reduce pressures on input prices by using these inputs more efficiently. Furthermore, the costs of large plants tend to increase less rapidly through time than those of small plants.

445

Huettner--Shifts of Long Run Average Cost Curves yet past experience indicates that few simple answers exist for this complex problem. Construction cost indexes or price indexes are certainly of questionable value in such an undertaking. There is some likelihood, however, that cost pressures will force continued increases in plant size, due to the fact that UCC has undergone less change through time in the large plant size groups. This indicates that projections of future UCC and investment requirements would be greatly improved if estimated by plant size group. On the other hand, the range of variation in UCC seems to be much narrower than anticipated and this suggests that major sources of uncertainty in investment projections lie elsewhere. As noted earlier, the major purpose of this study was the extension of the traditional, static LRAC curve framework to a dynamic framework. This effort should be useful for two reasons. Firstly, many questions, such as optimal plant or firm size, should be answered in a dynamic framework if appropriate managerial or anti-trust issues are to be considered. Secondly, the use of a dynamic LRAC curve framework shifts the emphasis of studies of scale economies back to costs. Production function studies of scale economies have not emphasized costs, but have instead been preoccupied with classification of changes into various categories. While this may be useful for some purposes, it is not. useful for others. Furthermore, the production function approach requires the use of several assumptions that have been questioned in this study. 32 Perhaps the major criticism of the traditional static LRAC curve model is that it offers economists few insights into understanding technological change or scale economies. For example, changes in plant size are assumed to be accomplished with fixed technology, but questions should be raised concerning the way in which large plants differ from small plants and whether a switch from an existing production process to another would be desirable. The limited information available for the various steel making processes suggests that the various processes may have widely different cost structures and that each production process is limited to different (but perhaps overlapping) size ranges. Large variations in plant size would seem to require a switch from one steel making process to another and the resultant change in cost structures would probably yield a LRAC curve unlike the smooth U shaped curve generally drawn. Once a dynamic LRAC curve framework is adopted, the questioning process becomes even more fruitful. Why should UCC or unit operating costs decline as plant size increases ? How should economists evaluate alternative technological improvements for possible effects on UCC or unit operating costs ? Complete answers to these problems are not available but some insights may be gained by tracing a series of technological developments in generating plants. 32In addition the production function approach generally requires the use of variables for which adequate measures are frequently unavailable. For example, physical measures of labor and capital inputs are required but adequate physical measures are generally not available. As shown above, use of the LRAC curve framework does not require physical measures of the inputs--it merely requires an adequate measure of both capacity and output. 446

Omega, Vol. 1, No. 4

A wide range of technological developments enhanced the performance of generating stations during the period studied [17], yet there is no effective means of isolating the individual benefits resulting from each improvement. Nor in many cases is there any means of separating the effects of technological change and of increased equipment, unit or plant size. For these reasons no attempts have been made in this study to separate substitution effects, scale effects and technological changes when only their combined impacts could be measured. Within the wide range of possible technological changes affecting unit costs, this study has considered only three categories: those involving shifts from one basic production process to another (e.g. Bessemer, open hearth and basic oxygen steel making); those involving changes through time within given production processes; and those involving differences among plants of various sizes constructed at the same point in time and ostensibly using the same technology, but actually reflecting significant though less obvious differences in embodied technological details. As for the first of the above categories of technological change, there is ample evidence that unit costs may either increase or decrease and that future innovations and their impacts are difficult to foresee. The last of the above categories is, of course, the subject of traditional LRAC curve analysis and the empirical and theoretical expectations are well known. The second of the above categories of technological change deserves more emphasis than it has received in the past for two reasons. Firstly, as noted earlier, some studies of technology have concluded that most technological change is gradual, even evolutionary, rather than revolutionary. Secondly, the analysis of the second and third sections suggests that the evolutionary type of technological change has benefited large plants more than small plants. For example, the unit costs of large plants decreased more (or increased less) than those of small plants through time. This suggests that evolutionary technological changes have offset rising input prices more for large plants than for small ones. The major point, however, is that if there is any hope of discerning predictable, consistent patterns in the cost effects of technological changes through time, this category should be the most fruitful place to begin the search. ACKNOWLEDGEMENTS This research was, in part, supported by an AmericanIron and Steel Institute Dissertation Fellowship. I would also like to thank Professor Bela Gold and Dr. John Landon for their instructive comments. REFERENCES 1. BAINJS (1959) Industrial Organization. Wiley,New York. 2. BALASSAB (1969) The Theory of Economic Integration. Irwin, Homewood,I11. 3. BARZELY (1963) Productivity in the electric power industry, 1929-1955. Rev. Econ. Statist., 45, Nov., 395--408. 447

H u e t t n e r - - S h i f t s o f Long Run Average Cost Curves 4. BARZELY (1964) The production function and technical change in the steam power industry..Jr, polit. Econ., 72, 133-150. 5. BAUMOLWJ (1965) Economic Theory and Operations Analysis. Prentice-Hall, Englewood Cliffs, N.J. 6. BRUNIL (1964) Internal economies of scale with a given technique. J. ind. Econ., 12, (3), 175-190. 7. CHASE JD (1970) Plant cost vs capacity: new way to use exponents. Chem. Engng, 6 April, 1t3-122 8. CHn'TON CH (1950) 0"6 factor applied to complete plant costs Chem. Engr, April, 112-114. 9. COHENKJ and CYERTRM Theory o f the Firm. Prentice-Hall, Englewood Cliffs, N.J. 10. DrIRYMES PJ and KURZ M (1964) Technology and scale in electricity generation. Econometrica, 32, 287-315. 11. GALATINM (1968) Economies of Scale and Technological Change in Thermal Power Generation. North Holland, Amsterdam. 12. GOLD B (1955) Foundations o f Productivity Analysis. University of Pittsburgh Press. 13. GOLD B (1971) Explorations in Managerial Economics. Basic Books, New York. 14. GOLD B (1973) Technology, productivity and economic analysis. Omega, 1, 5-24. 15. GUTnRIE KM (1970) Capital and operating costs for 54 chemical processes. Chem. Engng, 15 June, 140-156. 16. HOLLANDER S (1965) The Sources of Increased Efficiency--A Study of DuPont Rayon Plants. M.I.T., Cambridge, Mass. 17. HUETTNERDA (1972) The Effect o f Plant Size and Technological Change on Investment Requirements for New Capital Facilities. PhD Dissertation, Case Western Reserve University, Cleveland, Ohio. 18. JOHNSTONJ (1960) Statistical Cost Functions. McGraw-Hill, New York. 19. KIRCHMAYERLK, MELLORAG, O'MARAJF and STEVENSONJR (1955) An investigation of the economic size of steam electric generating units. AIEE Trans., 74, (3), August, 600-609. 20. KOMIYAR (1962) Technological progress and production function in the United States steam power industry. Rev. Econ. Statist., 44, May, 156-166. 21. LIN6 S (1964) Economies o f Scale in the Steam-Electric Power Generating Industry. North Holland, Amsterdam. 22. LOMAXKS (1952) Cost curves for electricity generation. Economica, 19, 193-197. 23. MANSFIELDE (1970) Microeconomics. Norton, New York. 24. McNuLTY J (1956) Administrative costs and scale of operation in the U.S. electric power industry. J. ind. Econ, 5, 30-43. 25. NERLOVE M (1968) Returns to scale in electricity supply. In Readings in Economic Statistics and Econometrics (Ed. ZELLNERA et al.). Little, Brown & Co., Boston. 26. OLSEN CE (1970) Cost Considerations for Efficient Electricity Supply. Michigan State University Public Utilities Studies, East Lansing, MI. 27. SALTERWEG (1960)Productivity and Technical Change. Cambridge University Press, England. 28. SCHWARTZNL and KAMIEN MI (1972) Some economic consequences of anticipating technical advance, West. Econ. J., 10, June, 123-138. 29. SHEPHARDRW (1970) Theory of Cost and Production Functions. Princeton University Press, Princeton. 30. UZAWAH (1964) Duality principles in the theory of cost and production. Int. Econ. Rev., 6, May, 74-92. 31. WHITMAN (1968) The Handy Whitman Index of Public Utility Construction Costs. Whitman, Requardt and Associates, Baltimore, MD.

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Omega, Vol. 1, No. 4 APPENDIX

Data sources All of the construction and operating cost data in this study are based on experience in new American production plants operating within the continental United States. The cost figures are in current dollars, i.e. none of the cost data have been adjusted by use of a cost or price index. The plants included in this study were all new plants and the construction cost data are for the year the plant commenced operations. Operating cost data were taken from the second full year of plant operations in order to exclude distortions caused by startup problems. Furthermore, the new plants in this study were all at new locations and plants with units commencing operations more than one year after the first unit were excluded from the sample. These restrictions were placed on the sample to exclude plants embodying two or more technological vintages and plants with construction costs encompassing several time periods. None of the studies reviewed in Table 1 has taken these precautions with respect to their samples. The data sources were: (a) Electric Power: Federal Power Commission--Steam Electric Plant Construction Cost and Annual Production Expense--U.S. Government Printing Office, Washington, D.C., 1948 and annual supplements 1949-1968. (b) Cement: "Review and Forecast" published in January issues of Pit and Quarry, 19231969. About 10 per cent of the data were obtained directly from American cement companies. (c) Steel: Data were obtained directly from five major American steel producers. Although the sample sizes were quite large (390 generating plants, 120 cement plants and 36 steel making plants) stepwise regression was used because of the number of plant characteristics in the analysis. In order to avoid the well-known hazards that can occur with unbridled use of stepwise regression analysis, several precautions were taken. Firstly, the explanatory variables were allowed to both enter and exit in the stepwise program used. This program also recomputed the coefficients of all of the variables at each step of the regression. Secondly, several large sub-samples of plants having common characteristics were used to verify the basic model before the use of stepwise regression. The use of these sub-samples substantially reduced the number of plant characteristics so that standard linear regression could be used. This pre-testing eliminated the potential hazards that may accompany the use of stepwise regression analysis.

Nameplate capacity ratings In 1937 the development of hydrogen cooled generators allowed redesign of generators for higher temperatures with reduced size, weight and cost. Hydrogen cooling replaced air cooling and lowered generator operating temperatures by reducing windage losses. This development was quickly incorporated in all new equipment and by 1940 was a standard specification for all new generators over 25MW. The fact that the capacity of a generating plant will increase approximately 1 per cent for each one pound increase in the hydrogen cooling pressure of the generator created many difficulties with "nameplate" capacity ratings prior to 1960. Since a generator is designed to operate within a range of hydrogen cooling pressures, the capacity will depend on the hydrogen pressure selected as the standard for rating capacity. Generator manufacturers give each new generator a nameplate rating but this rating (prior to 1960) was generally based on a low hydrogen cooling pressure since it was a performance guarantee. The Federal Power Commission (hereafter FPC) used this "nameplate" rating in its published data even though plants were always run at the maximum hydrogen pressure. The FPC data understated the actual capacity of the majority of plants built between 1940 and 1960. In the late 1950s, the FPC started to uprate the capacity of these plants and finally in 1960 it adopted the practice of rating all plants at the maximum hydrogen cooling pressure for which they were designed. Since the upratings done in the late 1950s generally increased the recorded capacity of a plant by 20 per cent (and in many cases 30 per cent), substantial errors result if the nameplate ratings are used for plants constructed between 1940 and 1960. None of the four studies in Table 1 than used nameplate capacity has included these upratings in their data (as they should have) and, in fact, none of them even mentions that such a problem exists. Furthermore, since the FPC used the nameplate capacity ratings to 449

Huettner--Shifts of Long Run Average Cost Curves compute both plant factor and cost per kilowatt of installed capacity (UCC), these two items of data must also be recomputed to include the capacity upratings of the late 1950s. None of these four studies has made either of these two additional adjustments to the FPC data. Another problem related to capacity ratings is the treatment of house service units. All power plants have station auxiliaries such as equipment for coal handling and preparation, ash removal, boiler feed and water circulation, station lighting, and miscellaneous purposes. In coal fired plants, these station auxiliaries generally use about 6-7 per cent of the gross plant capacity, in oil fired plants about 5 per cent and in gas fired plants about 4 per cent. Some plants use house service units to generate the power to run the station auxiliaries while other plants consume part of the gross plant output to run these auxiliaries. Prior to 1956 the nameplate capacity rating at maximum hydrogen cooling pressure did not generally include known house service units nor did it exclude that unknown part of the capacity consumed by station auxiliaries in plants lacking house service units. Clearly for the years prior to 1956 the only possible adjustment is to add the capacity of house service units, where they are used, to the maximum nameplate capacity rating of the plant to yield gross plant capacity. This adjustment was applied to all of the FPC capacity ratings in this study in order to ensure comparability among plants. Note that this adjustment was rarely required for the years after 1956. The raw unit capacity cost and plant utilization data published by the FPC were also recomputed to reflect this change. Again, none of the four studies in Table 1 that used nameplate capacity has made any of these adjustments to the raw FPC data.

450