Input Complementarity Implies Output Elasticities Larger than One: Implications for Cost Pass-Through

Michael K Wohlgenant

doi:10.4236/tel.2012.21009

Abstract

When inputs in the firm’s production function are pair-wise complements, I show that all variable factors of the firm are output elastic. Via Silberberg’s analysis, this implies that for given output of a competitive firm that marginal cost will rise more than average cost for a factor price increase. Accounting for changes in output through profit maximization and industry equilibrium change in output price, I show that cost pass-through can be larger than one in a competitive industry when inputs are complementary. Because input complementarity seems likely with commodity aggregates like materials, labor, energy, and capital, this could provide an alternative explanation for over cost shifting in commodity-oriented industries like the oil industry and food industries. This approach also allows researchers to abandon the highly restrictive assumption of constant elasticity of demand function facing the firm that is required under imperfect competition with constant marginal costs.

Highlights

Where c y, w1, w2, wn 1, xn is the firm’s cost function and subscripts denote partial derivatives
In the general case of input complementarity in production, I have shown that output elasticities of all variable
A direct implication of this finding is that with input complementarity, marginal cost will increase more than average cost for an increase in factor price

Summary

Introduction

Where c y, w1, w2 , , wn 1, xn is the firm’s cost function and subscripts denote partial derivatives. Where marginal mcco,wsit cy wi with respect wi to cy is the a change in elasticity of the i-th factor tphreicei-,th fxai yct or , axind ys i xi is the wi xi cy y output elasticity of is the share of total cost of the i-th factor in output valued at marginal cost. Equation (2) shows there is a one-to-one relationship between the elasticity of marginal cost with respect to factor price and its output elasticity. The elasticity of marginal cost with respect to wi will be larger (smaller) than si according as general, we cannot say xiwy itihs larger (smaller) than 1. WOHLGENANT rity is a reasonable assumption when dealing with aggregate inputs like labor, materials, energy, and capital. This assumption plays a crucial role in supermodularity and monotone comparative statics [3]1

The Basic Result

Implications for Cost Pass-Through

Findings

Conclusions