Returns to Scale

BIBLIOGRAPHY

Returns to scale are defined as the relation between an equi-proportionate change in all the inputs used in a commodity’s production and the resulting proportionate change in the output of that commodity. The three possibilities are labeled “decreasing,” “constant,” or “increasing returns,” depending on whether a given proportionate change in all inputs causes a less than proportionate, a proportionate, or a more than proportionate change in output. Although economists debate what generates these effects, all three types are used in microeconomic theory. The common assumption in neoclassical macroeconomics is that gross domestic product (GDP) behaves as if it were generated by an aggregate production function obeying constant returns to scale.

While commonly used in economics, the concept is also used in many of the social and physical sciences. For example, in 1986 Nathan Rosenberg and L. E. Birdzell noted that the invention of the three masted sailing ship allowed Europeans to build larger ships exploiting increasing returns to scale, such as carrying capacity increasing more than in proportion to the increase in materials for construction. In 1991 Leonard Dudley analyzed military returns to scale. Some technologies, such as stone-age weapons, entailed constant returns (a larger army could expect casualties equal to those of a smaller opponent), while others, such as bronze weapons, entailed increasing returns (a larger army could expect fewer casualties than a smaller opponent). Other applications of the concept include the analysis of networks, social organization, governance, and technological change.

Mainstream micro-economists typically argue that constant returns to scale, and hence horizontal long run average cost curves, are ubiquitous given complete divisibility of all inputs. The argument is in two parts. First, decreasing returns are ruled out because it is assumed that all production activities can be replicated, for example, by building a series of identical factories, identically run and managed. Second, increasing returns are ruled out by the proportionality postulate, which states that in the absence of indivisible inputs or hidden fixed factors, any activity can be subdivided so that an equi-proportionate reduction in all inputs yield the same percentage reduction in output. Thus, if there were increasing returns to scale, the larger scale of activities could be achieved and then subdivided, leaving inputs per unit of output unchanged.

The commonly assumed U-shaped long run average cost curve for a firm, with its single most efficient scale of output, is then explained in two parts. First, the falling part (increasing returns to scale) is due to such things as indivisibilities (or “lumpiness”) in some inputs so that too much must be used at small scales of output. The rising portion (decreasing returns) is usually explained rather weakly by such things as diseconomies of management in coordinating the activities of many separate production units.

An alternative view, implicit in the work of the nineteenth-century Austrian capital theorists such as Eugene von Böhm-Bawerk and Knut Wicksell, is that returns to scale are latent in the superior productive power of indirect or intermediate production processes that create capital goods. In the twentieth century, scholars B. Curtis Eaton and Richard G. Lipsey examined this theme, providing a proof by contradiction of the existence of latent returns to scale. Lipsey, Kenneth Carlaw, and Clifford Bekar develop this further in 2005. In their research, they maintained that the standard abstract argument for constant returns to scale based on replication and the proportionality postulate is scholastic in purporting to deduce empirical relations from a priori considerations. They argued that checking the hypothesis of the ubiquitous possibility of replication requires an appeal to empirical evidence. For example, replication may not be possible if more output is required at a point in space, such as building a larger bridge over a narrows or applying more pumping power at the pit head of a coal mine. They observed that “… if the list of possible missing inputs is defined as anything that might cause the neoclassical production function to display decreasing returns, such as climate, spatial conditions of production … and a host of other unspecified influences, the proposition becomes tautological and hence uninteresting empirically” (Lipsey et al., p. 399).

Lipsey and colleagues argued similarly with respect to the proportionality postulate. If, for example, one wishes to halve the horsepower of some automobile, a smaller engine is needed. But neither “subdividing” by halving the engine’s dimensions, nor by halving all the inputs that make it, will halve the engine’s power output. Physics shows that halving its dimensions alters its cost of production, the power delivered, and running costs in different proportions, while halving all the inputs is technically inefficient because of the different dimensionality of the various components. They further argued, “‘[h]istorical increasing returns’ [to scale] arise because the scale effects are permanently embedded in the geometry and physical nature of the world in which we live, but our ability to exploit them is dependent on the existing state of technology” (Lipsey et al., p. 397).

Increasing returns to scale also arise from complementarity among components of capital and the risk of breakdown, and decreasing returns from the time cost associated with waiting to extract the service flow from durable capital goods. In all of these cases, the relationship between indivisibilities and returns to scale is the reverse of the mainstream view. Indivisibilities—building capital goods with more capacity than the minimum possible— are the consequence of endogenous decisions to exploit naturally occurring scale effects, whereas in the mainstream view, exogenous indivisibilities are the cause of scale effects.

SEE ALSO Returns; Returns to a Fixed Factor; Returns to Scale, Asymmetric; Returns, Diminishing; Returns, Increasing

BIBLIOGRAPHY

Böhm-Bawerk. 1889. Positive Theory of Capital. Trans. W. Smart. New York: Scechert.

Carlaw, Kenneth I. 2004. Uncertainty and Complementarity Lead to Increasing Returns to Durability. Journal of Economic Behaviour and Organization 53 (2): 261–282.

Dudley, Leonard. 1991. The Word and the Sword: How Techniques of Information and Violence Have Shaped Our World. Cambridge, U.K.: Cambridge University Press.

Eaton, B. Curtis, and Richard G. Lipsey. 1997. Increasing Returns, Indivisibility and All That. In On the Foundations of Monopolistic Competition and Economic Geography: The Selected Essays of B. Curtis Eaton and Richard G. Lipsey. Cheltenham, U.K.: Edward Elgar Publishing.

Koopmans, Tjalling C. 1957. Three Essays on the State of Economic Science. New York: McGraw-Hill.

Lipsey, Richard G., Kenneth Carlaw, and Clifford Bekar. 2005. Economic Transformations: General Purpose Technologies and Long-Term Economic Growth. New York: Oxford University Press.

Rosenberg, Nathan, and L. E. Birdzell. 1986. How the West Grew Rich. New York: Basic Books.

Wicksell, Knut. [1893] 1954. Value, Capital and Rent. London: Allen and Unwin.

Kenneth I. Carlaw

Richard G. Lipsey