The Equivalence of Economies and Returns to Scale Revisited: Nonlinear Expansion Paths and the Definition of Scale

That increasing returns to scale is a sufficient condition for generating economies of scale is well understood. Many instructors and most textbooks, however, report that increasing returns is a necessary condition for scale economies. While the necessity of decreasing returns in generating diseconomies of scale can be proven locally for smooth technologies or generally for homothetic or non-variable returns technologies, no such requirement exists when considering discrete scale adjustments along more realistic expansion paths. We argue that the practice of equating economies and returns to scale is an inappropriate generalization that resulted from a historical preference for homothetic production functions.