A RECONSIDERATION OF THE THEORY OF NON-LINEAR SCALE EFFECTS: Causes and Consequences of Varying Returns to, and Economies of, Scale

This paper reconsiders the explanations of why a firm’s costs vary when its scale of operations varies over the long run, as expressed by its long run average cost curve and described as economies and diseconomies of scale. The first half of the paper deals with considerations of theory. It is argued that the nature of our world, with its 3-dimensions, its physical laws and the many random elements in its behaviour, is such that when the scale of anything changes, we should always expect to encounter non-linear scale effects. Static effects concerning the nature of the cost and production functions at a moment in time, which are the concern of this paper, are distinguished from dynamic effects over time, the concern of Allyn Young and his followers. It is argued that both treatments are valid but deal with distinctly different issues. A treatment of the sources of scale effects, particularly in the reconfiguration of capital goods, leads to a distinction between the set of production functions that are consistent with Viner’s treatment of long run cost curves and the single production function that is found in virtually all modern microeconomic textbooks. It is argued that the inconsistencies and ambiguities relating to the use of such a single production function to cover all possible scales of a firm’s production are such that it is an imperfect tool for analysing the scale effects that firms actually face. The second half of the paper critically assesses the treatment of scale issues in a large sample of the existing literature. Most authors list a series of examples of sources that are assumed to give rise to scale effects but seldom attempt to show in any detail how these are supposed to work. When we do this, some alleged sources are found not to give rise to scale effects at all, while others have effects that differ from what has been assumed. Furthermore, there is seldom agreement among authors whether a particular source is a cause of varying returns to scale or economies of scale. Most authors argue that indivisibilities are an important source of scale effects, although these are seldom well defined, nor are the precise ways in which these are supposed to work typically analysed. When we do this, we identify two basic types of indivisibilities, ex post and ex ante, plus several variations of each of these main types. We then argue that the discussion of indivisibilities has been confused by use of different implicit definitions of the term and also that their importance as a source of scale effects has been greatly over stated. The ability to replicate production facilities is found to be consistent with ranges of rising followed by ranges of falling unit costs and, in some important circumstances, to be consistent with falling unit costs over an indefinite range of output. Constant returns production functions are found to be inconsistent with much that is known about actual production techniques, even when firms expand by duplicating identical plants. Although several authors argue that the US market is large enough for scale effects to be exhausted, this may be true of some industries, but is clearly not true for the many industries in which non-plant specific costs are significant enough to confer an economy of scale on the firm as it increases the number of its ‘plants’ indefinitely. Unless ruled out by definition, decreasing returns are found to be a real possibility in many circumstances.