Pecuniary Effects, Second-Order Conditions, and the LRAC Curve

Abstract

It has long been known that if the production function is well behaved and input prices are constant, then a local (pointwise) equivalence exists between returns to and economies of for the cost-minimizing firm (e.g., Sandmo 1970). In particular, a point on the firm's long-run average cost (LRAC) curve that exhibits local economies (or diseconomies) of corresponds to an input vector at which the production function exhibits local increasing (or decreasing) returns to scale. However, as Sandmo observed, this pointwise equivalence not hold when the firm exercises some degree of monopsonistic power in factor markets, since there is then no direct connection between costs and the purely technological concept of returns to scale (p. 152). This observation has received considerable attention in this journal. Cohn (1992) argued that, when factor prices are endogenous, pecuniary effects associated with the firm's employment of factors might be sufficient to cause economies (or diseconomies) of even though the firm's technology exhibits decreasing (or increasing) returns to scale. Truett and Truett (1995) provided a numerical example using a Cobb-Douglas production function to illustrate the point that Cohn makes. More generally, Gelles and Mitchell (1996) formally derived a pointwise relationship between the slope of the firm's LRAC curve and the combined influences of technological returns to and monopsonistic pecuniary effects. The purpose of this article is two-fold. First, I explore the importance of second-order conditions in the cost-minimization problem confronting the monopsonistic employer of factor inputs. This is important because the presence of monopsonistic pecuniary effects can lead to several serious problems that these previous authors have ignored. Second, I describe an alternative approach to the presence of pecuniary effects that does not depend on the assumption that firms are monopsonistic in factor markets. This is important because there does not appear to be much evidence to support the claim that monopsony in factor markets is an actual cause of economies (or diseconomies) of scale, for example, an explanation for the empirically observed U-shaped LRAC curve.