268 PART • Producers, Consumers, and Competitive Markets EX A M P L E COST FUNCTIONS FOR ELECTRIC POWER In 1955, consumers bought 369 billion kilowatt-hours (kwh) of electricity; in 1970 they bought 1083 billion Because there were fewer electric utilities in 1970, the output per firm had increased substantially Was this increase due to economies of scale or to other factors? If it was the result of economies of scale, it would be economically inefficient for regulators to “break up” electric utility monopolies An interesting study of scale economies was based on the years 1955 and 1970 for investor-owned utilities with more than $1 million in revenues.19 The cost of electric power was estimated by using a cost function that is somewhat more sophisticated than the quadratic and cubic functions discussed earlier.20 Table 7.4 shows the resulting estimates of the scale economies index The results are based on a classification of all utilities into five size categories, with the median output (measured in kilowatt-hours) in each category listed The positive values of SCI tell us that all sizes of firms had some economies of scale in 1955 However, the magnitude of the economies of scale diminishes as firm size increases The average cost curve associated with the 1955 study is drawn in Figure 7.17 and labeled 1955 The point of minimum average cost occurs at point A, at an output of approximately 20 billion kilowatts Because there were no firms of this size in 1955, no firm had exhausted the opportunity for returns to scale in production Note, however, that the average cost curve is relatively flat from an output of billion kilowatts and higher, a range in which of 124 firms produced When the same cost functions were estimated with 1970 data, the cost curve labeled 1970 in Figure 7.17 was the result The graph shows clearly that the average costs of production fell from 1955 to 1970 (The data are in real 1970 dollars.) But the flat part of the curve now begins at about 15 billion kwh By 1970, 24 of 80 firms were producing in this range Thus, many more firms were operating in the flat portion of the average cost curve in which economies of scale are not an important phenomenon More important, most of the firms were producing in a portion of the 1970 cost curve that was flatter than their point of operation on the 1955 curve (Five firms were at points of diseconomies of scale: Consolidated Edison [SCI = -0.003], TABLE 7.4 SCALE ECONOMIES IN THE ELECTRIC POWER INDUSTRY Output (million kwh) 43 338 1109 2226 5819 Value of SCI, 1955 41 26 16 10 04 19 This example is based on Laurits Christensen and William H Greene, “Economies of Scale in U.S Electric Power Generation,” Journal of Political Economy 84 (1976): 655–76 20 The translog cost function used in this study provides a more general functional relationship than any of those we have discussed