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The Sources of Varying Returns To, and Economies Of, Scale by Richard G

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The Sources of Varying Returns To, and Economies Of, Scale by Richard G A RECONSIDERATION OF THE THEORY OF NON-LINEAR SCALE EFFECTS: The Sources of Varying Returns to, and Economies of, Scale by Richard G. Lipsey Emeritus Professor of Economics Simon Fraser University [email protected] http://www.sfu.ca/~rlipsey August 2017 Forthcoming in Evolutionary Economics Jason Potts and John Foster editors One of the Cambridge Elements series Cambridge University Press 1 ABSTRACT The main thrust of this paper is a critical assessment of the theory and evidence concerning the sources of scale effects. It is argued that the analysis of static scale effects is important because scale effects are embedding in our world and new technologies associated with an evolving economy often allow their exploitation when they cannot be exploited in less technically advanced and smaller economies. So, although static equilibrium theory is not a good vehicle for studying economic growth, showing how scale effects operate when output varies with given technology helps us to understand the scale effects that occur when output rises as a result of economic growth, even though that is typically driven by technological change. The set of production functions that are consistent with Viner’s treatment of long run cost curves are distinguished from 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 operations are such that it is an imperfect tool for analysing the scale effects that firms actually face. The relation between scale effects and the size of the firm are discussed. It is shown that under certain commonly occurring circumstances the ability to replicate production facilities is consistent with short ranges of diseconomies of scale and an indefinite range of increasing returns. Next comes a detailed analysis of the sources of positive scale effects and a critical assessment of the treatment of these in a large sample of the existing literature. 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. 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 only one of these types of indivisibility can be a source of scale effects. 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. Unless ruled out by definition, diseconomies of scale are found to be a real possibility in many circumstances. When these occur in some parts of complex capital goods or plants, they limit the extent to which economies in other parts can be exploited by increasing the scale of the whole operation. Finally, brief consideration is given to the literature concerning the factors that limit the exploitation of the scale effects that are ubiquitous in the real world and to the consequences of their exploitation. JELL Classification: D 240 Key Words: economies of scale, production function, returns to scale, indivisibilities, replication, long run cost curves. 2 I. BACKGROUND CONCEPTUAL ISSUES ........................................................................ 6 THE USE OF STATIC ANALYSIS ............................................................................................................................ 6 ISSUES OF DEFINITION ...................................................................................................................................... 6 APPROACHES TO STUDYING SCALE EFFECTS .......................................................................................................... 7 DISPLAYING SCALE EFFECTS ............................................................................................................................... 8 Through Cost Curves .............................................................................................................................. 8 Through a production function .............................................................................................................. 9 Through Growth ..................................................................................................................................... 9 Replication and Reconfiguration .......................................................................................................... 11 Two types of Production Functions ...................................................................................................... 12 Two PF Definitions .......................................................................................................................................... 12 Variables in the PF ........................................................................................................................................... 13 Returns and Efficiency Effect’s in the PF ......................................................................................................... 15 Further Problems with the PF ......................................................................................................................... 16 EFFICIENCIES OF DESIGN ................................................................................................................................. 17 SCALE EFFECTS AND FIRM SIZE ......................................................................................................................... 17 Implications of MES Relative to Market Size ........................................................................................ 18 Replication with Increasing Unit Costs ................................................................................................. 19 Replication with Non-Plant-Specific Fixed Costs .................................................................................. 19 II. THE SOURCES OF POSITIVE SCALE EFFECTS ............................................................ 20 SCALE EFFECTS IN TWO-STAGE PRODUCTION ...................................................................................................... 20 PERVASIVENESS OF SCALE EFFECTS .................................................................................................................... 21 SCALE EFFECTS DUE TO INDIVISIBILITIES ............................................................................................................. 22 Ex post divisibility and indivisibility ...................................................................................................... 23 Ex ante divisibility and indivisibility ...................................................................................................... 23 An indivisible plant .......................................................................................................................................... 23 An indivisible capital good............................................................................................................................... 25 Which variable: a stock or a flow? ....................................................................................................... 25 Indivisibilities as sources ...................................................................................................................... 26 Ex post indivisibilities ...................................................................................................................................... 26 Ex ante indivisibility of a plant ......................................................................................................................... 26 Ex ante indivisibility of an individual capital good ........................................................................................... 27 Interesting exceptions .......................................................................................................................... 28 Summary: indivisibilities as valid sources of scale effects. ................................................................... 28 Indivisibilities in the literature .............................................................................................................. 28 Ex post divisibility and indivisibility ................................................................................................................. 29 Discreteness ...................................................................................................................................................
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