This blog post revisits the economic historian J. H. Clapham’s1922 classic paper ‘Of Empty Economic Boxes‘ published in The Economic Journal, and raises some critical questions about the continued use of constant returns to scale (CRS hereafter) assumption in marginalist (or neoclassical) microeconomics and macroeconomics. In 1926, Piero Sraffa took Clapham’s 1922 paper as a starting point to mount a more devastating logical critique of Marshallian notions of increasing returns and the representative firm; this was published as part of a symposium in the Economic Journal.
What is returns to scale’ According to marginalist economics, the technique of producing a commodity may be represented by a functional relationship between inputs (say, k’and l) and output (say, y): y’= f(k,l). If all the inputs are multiplied by a positive scalar m, and the resultant output is expressed as mr’y, then r’represents the magnitude of the returns to scale. If r = 1, the technique exhibits CRS, if r < 1, it exhibits diminishing returns to scale (DRS), and if r’> 1, it exhibits increasing returns to scale (IRS).
Despite the ‘advances’ in mainstream economics research, the marginalist theory of value and distribution still requires the CRS assumption (and the diminishing returns to a factor assumption) to make several key claims. The aggregate production function employed in the Solow growth model is assumed to exhibit CRS. And the Solow growth model forms the core of supply-sidegrowth accounting exercises which are used to make policy prescriptions (for a critique of one such exercise for the Indian economy, see Joshi & Thomas 2013).
The central argument in Clapham’s article is that the categories of diminishing returns, constant returns, and increasing returns industries are ’empty economic boxes’. In other words, from the standpoint of actual economies, these categories lack empirical and historical content. Consequently, industries cannot be classified into one or the other box a priori.
Clapham asks: what does AC Pigou (in his Economics of Welfare) mean when he writes ‘when conditions of diminishing returns prevail’ (p. 305)’ According to Clapham ‘constant returns…must always remain a mathematical point, their box an empty one’ (p. 310). He acknowledges that different kinds of returns have a ‘logical’ and ‘pedagogic value’ which ‘goes so prettily into graphs and equations’ (p. 312). How can we then use this framework to draw policy conclusions given the inability to classify industries a priori into constant, diminishing, and increasing returns’
The following observation by Clapham is insightful and worth thinking about further. He writes that diminishing returns must be balanced with increasing returns to arrive at constant returns (p. 309). Surely, this makes no conceptual sense and neither does it have any basis in empirical reality. As Clapham puts it, with CRS ‘the conception of the balance of forces, man’s organization versusNature’s reluctance, was worked out’ (p. 309). In other words, is CRS an expression of the balancing of the symmetrical forces of IRS (‘man’s organization’) and DRS (‘Nature’s reluctance’)’ For a visual representation, see the images below. If so, it would add to the symmetrical concepts found in the marginalist toolbox, most notably that of supply and demand. However, beyond the ease of exposition symmetry provides us, is it really how the actual world works’
CRS, DRS, and IRS posit an a priori functional relationship between labour (L) and capital (K), the ‘factors of production’ and output (Y) for an individual firm and for an economy: Y=f(L,K). While the idea underlying the production function, whether industry-level or aggregate-level, that outputs are produced by inputs is commonsensical and intuitive, its expression as a mathematical function isn’t as benign. Since marginalist economics requires continuous functions (often, of a monotonic nature) to ensure the existence of equilibrium, the ‘f’ is able to map infinitesimal combinations of Land Kto a unique Y. This ‘one-way street’, to use Sraffa’s phrase in his 1960 classic Production of Commodities by Means of Commodities(see my blog post Sraffa), between ‘factors of production’ and output is conceptually unsatisfactory because it misses a fundamental aspect about modern economies: the structural interdependence between inputs and outputs. In addition, it assumes that capital goods (K) are infinitely divisible, a very difficult assumption to uphold.
John Eatwell (2008; first published in 1987), in his entry on ‘returns to scale’ published in The New Palgrave Dictionary of Economics, also notes the apparent symmetry between IRS and DRS but points out its spuriousness. While there is no evidence of functional relationships in Adam Smith and David Ricardo, Smith’s discussion of division of labour, capital accumulation, and economic growth indicates that he recognised scale-enabled technological progress and Ricardo recognised diminishing returns to land, a non-reproducible input in production. Subsequently, Alfred Marshall, in his Principles of Economics, ‘attempted to formulate a unified, symmetric, analysis of returns to scale which would provide the rationale for the construction of the supply curve of a competitive industry, derived in turn from the equilibria of the firms within the industry’ (Eatwell 2008, p. 140). This point was initially noted by Sraffa 1926, and later much more thoroughly investigated also by Krishna Bharadwaj (1978).
It is well understood that the question of returns to scale is important in the construction of the supply curves which are integral for the marginalist price theory. Therefore, a thorough critical study of mainstream price theory and a renewal in the interest in rival price theories (found in Ricardo, Marx, Sraffa, and Kalecki, among others) are warranted. This is crucial because it is value or price theory which provides us with the economic possibilities a competitive economy generates. If it generates unemployment and worsens inequality, we know that intervention of a particular kind is necessary. However, if it generates full employment and reduces inequality, then it supports the idea of making markets more competitive and reducing government intervention.
Clapham, J. H. (1922), “Of Empty Economic Boxes.”‘The Economic Journal,’vol. 32, no. 127, pp. 305-14.
Eatwell, John (2008), ‘Returns to Scale’. In: Durlauf S.N., Blume L.E. (eds.) The New Palgrave Dictionary of Economics. London: Palgrave Macmillan.
Sraffa, Piero (1926), “The Laws of Returns under Competitive Conditions.”‘The Economic Journal,’vol. 36, no. 144, pp. 535-50.
I thank Mohib Ali for his helpful comments.