Economies of Scale, Expansion Path, and Growth of Plants

Abstract

CASUAL observation reveals that plants of different sizes exist and have always existed with little tendency to become more concentrated in any particular size class. This can only mean that plants are not operating under conditions of long-run static equilibrium,' and that concept of scale cannot be used to explain actual size distribution or growth patterns of plants.2 Some writers have suggested idea of an distribution, presumably based on stochastic nature of human ability and human foresight.3 Mathematically, optimal distribution may be related to stationary distribution corresponding to some stochastic process describing growth of plants. This growth in turn is explained by such factors as economies of scale, economies of growth,4 profit margin variations,5 and other dynamic factors. appropriate frame of reference for optimal distribution is expansion path, or scale path. path may be regarded as representing basic manufacturing activity of an industry. Plants cluster around this path, and their sizes are given by their positions on path. size distribution of plants is therefore defined with respect to this path. Similarly, from one period to next, growth of plants is given by their movements along path.6 It is reasonable to assume that this path is characterized by fixed elasticities (rather than fixed proportions) among input and output variables, since plants become more capital intensive as they grow. present paper investigates ( 1 ) extent of economies of scale along expansion path for each of manufacturing industries, and (2) relationship between economies of scale and growth pattern of plants. Our principal hypothesis is that with a given expansion path or given returns to scale all plants tend to expand at same rate. In this case, a strict form of Gibrat's Law would apply and it is possible to speak of an equilibrium lognormal distribution of plants with constant dispersion. When a shift of expansion path takes place, there is also a change in returns to scale along path. Our hypothesis states that there should be a systematic relationship between changes in returns to scale and changes in dispersion of plants. changes in returns to scale result in a differential rate of growth for plants of different sizes, until a new equilibrium lognormal distribution is estab* I would like to thank Frank Child and John Harsanyi for their helpful comments, Joseph King for providing me with empirical materials, and National Science Foundation for financial support. 1 Hymer and Pashigian have argued convincingly that dispersion of firms cannot be attributed to constant returns to scale. Stephen Hymer and Peter Pashigian, Size and Rate of Growth, Journal of Political Economy, LXX (1962), 556-569. In this paper, we are concerned with behavior of plants. However, much of discussion pertaining to size of firm in literature is equally applicable to size of plant. 2Some realism is introduced if Gibrat's Law is made starting point. Gibrat, Hart, Prais and others have discovered that in a large number of industries size distribution of firms is approximately lognormal, and law of proportionate effect that average growth rate is approximately same for firms of different sizes -was generally adopted to explain distribution. Since this results in a continuing divergence of plant distribution over time, it was further proposed that a process of regression is at work, that is, that the firms in any given size class at time t would still be distributed lognormally at t + 1, but their mean size would be nearer to mean size of all firms. P. E. Hart and S. J. Prais, The Analysis of Business Concentration: A Statistical Approach, Journal of Royal Statistical Society, Series A, Part II (1956), 150-191. idea implies that there is some optimal firm size, and plants tend to move towards that optimum. However, it is difficult to argue that optimal size is mean size, because there is little reason for a firm to expand beyond an optimal size. 'See, for example, Milton Friedman's comment on Caleb Smith's paper in Business Concentration and Price Policy (Princeton University Press, 1955). 4 Edith Penrose, Theory of Growth of Firm (New York, 1959). ?Joseph Steindl, Small and Big Business (Oxford Institute of Statistics, Monograph No. 1, 1946). 6 If plant is not on path, its size is determined by position of its projection on path. Of course, technological change and substitution also take place from one period to another, resulting in a shift of expansion path. This is discussed in a later section in paper.