Knowledge that Transforms

Technical has become a controversial social issue, but the nature of technical progress is badly understood. Economists may best contribute to the discussion by analyzing technical change as an instance of choice subject to a constraint of limited technological opportunity. The innovation possibility frontier (Charles Kennedy) is one hypothetical constraint on technological opportunity. Models based on the innovation possibility frontier customarily assume steady growth (E. M. Drandrakis and Edmund S. Phelps, William Fellner and McCain) and are rather well understood. They have been incisively criticized by Nordhaus, who proposed, as a general alternative, the hypothesis of an isotech map. An exploration of the characteristics of optimum inventions, in terms of the isotech hypothesis seems of some interest. A single isotech, the C-isotech, is the set of all techniques attainable at a given cost, C. Thus in the standard neoclassical model, the production function is the zero-isotech. The isotech map will depend on the history of technical development as a whole and so cannot be stable over time.' The generality of the isotech hypothesis makes it possible to raise some questions of considerable interest, which are beyond the range of the innovation possibility frontier hypothesis. Because scale is a major determinant of the social impact of technology, (E. Schumaker) we shall as an example explore John K. Galbraith's imperatives of large scale.2 We first explore some characteristics of optimum inventions. We suppose that an invention is characterized by capital intensity, k, and labor intensity, n, as usual; and also by the minimum capital scale [, and the durability of the capital good, m. The capital good is supposed to be a one-hoss shay. The isotech map is represented by a cost function

Harvey Averch and Leland Johnson in their pioneering paper on regulatory modeling found that a firm regulated by a maximum allowed rate of return on capital would generally find it advantageous to substitute capital for other inputs to produce its output in an overly capital intensive manner. However, they and others have suggested that this misallocation of inputs would not exist if the firm's production function was of the fixed proportion type so that the firm could not substitute inputs.' This paper examines the behavior-of the regulated firm with a fixed proportion production function. It concludes that the firm produces efficiently only if demand is sufficiently elastic so that marginal revenue exceeds marginal noncapital cost. Lowering the allowed return on capital in an attempt to increase output beyond the point where marginal revenue equals marginal noncapital cost will prompt the firm to acquire idle capital and will not bring forth any increase in output. The L-shaped isoquant associated with fixed proportion production functions may be particularly relevant to public utilities. The complex technology utilized involves both limited substitutability of other inputs for existing plant and equipment, and long lifetimes for this capital.2 Even if the Lshaped isoquant is not applicable to new capital investment, it may be applicable for existing capital plant and equipment. Thus a significant part of the firm's capacity can be considered to have minimal input substitution possibilities over a substantial period of time. The firm without factor substitutability can react to regulation by being overly capital intensive only by padding its rate base with idle capital. To develop the condition under which the firm with a fixed proportion production function would produce inefficiently, the following notation will be employed: r = profit q = output R(q) = revenue function K = physical units of capital L = physical units of labor3 q = q (min (K/a, L/b) = the fixed proportion production function with a > O and b > 0 r = cost of obtaining funds, the unit cost of capital4 *Assistant professor of economics, Kansas State University. I am grateful to C. F. Christ, P. J. Gormeley, B. L. Jaffee, and F. T. Sparrow for their comments on an .earlier draft of this paper. I also acknowledge the very useful suggestions made by the anonymous referee. I They write: If it [the production function] involves fixed proportions, . . . the regulated firm is constrained to the efficient expansion path (p. 1057). Gordon Corey echoed their result in a recent article in which he states, If there were fixed proportions in production, the expansion paths of the regulated and unregulated firm would be identical (p. 364). Frederick Scherer also agrees, the limiting case of zero substitution elasticity (associated with L-shaped isoquants) there will be no departure from the socially optimal capital/labor ratio (p. 532). While David McNicol (p. 432, fn. 10) questions the Averch-Johnson result that no misallocation would occur with a fixed proportion production function, he provides no conditions for its occurrence or nonoccurrence. 2For example, the Federal Power Commission (pp. 1-29) reports steam electric plant equipment life is estimated to about thirty to thirty-five years. Also, depreciation rates for regulated industry, while admittedly conservative, suggest long lifetimes for physical capital. Alfred E. Kahn (p. 118) gives depreciation rates for regulated industries in the 2 to 5.4 percent range which implies physical capital lives in excess of fifteen years. 3The term labor is used here by convention, but can be thought of more generally as including all noncapital inputs. 4The cost of capital is equal to its acquisition cost multiplied by the cost of obtaining funds. In the following, capital units will be measured so that the acquisition cost of a unit of capital is equal to unity.