ABSTRACT
John Chipman (1965, 1970) pioneered the modelling of economies and diseconomies of scale that are external to the firm, which he called parametric external economies or diseconomies of scale. His formalization is based on the following idea: firm i uses labor Lt, and takes the output/labor ratio parametrically, i.e. it perceives a linear production function y i = kL;. In fact, the output-labor ratio depends on the aggregate level of activity, represented by the aggregate amount L of labor applied, or by the aggregate amount y of output obtained: we can formalize it as a function a(L, y) which is increasing in L or y (or both), i.e. y/L = k(a(L, y)). As an example, we have a one-input production function often used in economics, y = f (L), where k(–) can be equivalently written as f(L)/L or as ylf −1 (y). 1 There are parametric external diseconomies of scale if a is decreasing, or, in other words, if the aggregate technology displays decreasing output-labor ratios. Conversely, there are parametric external economies of scale if a is increasing.
