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

Michael K. Wohlgenant

Department of Agricultural & Resource Economics, North Carolina State University, Raleigh, USA.

DOI: 10.4236/tel.[phone]                

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.

Keywords

Complementarity; Output Elasticity; Marginal Cost; Factor Price Change; Cost Pass-Through JEL Code: D2, D4, L4, L6

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	E. Silberberg, “Theory of the Firm in ‘Long-Run’ Equilibrium,” American Economic Review, Vol. 64, No. 4, 1974, pp. 734-741.
[2]	E. Silberberg, “The Structure of Economics: A Mathematical Analysis,” McGraw-Hill, Inc., New York, 1990.
[3]	R. Amir, “Supermodularity and Complementarity in Economics: An Elementary Survey,” Southern Economic Journal, Vol. 71, No. 3, 2005, pp. 636-660. doi:10.2307/20062066
[4]	D. Topkis, “Comparative Statics of the Firm,” Journal of Economic Theory, Vol. 67, 1995, pp. 370-401. doi:10.1006/jeth.1995.1078
[5]	H. Varian, “Microeconomic Analysis,” W.W. Norton & Co., New York, 1992.
[6]	J. Quirk, “Qualitative Comparative Statics,” Journal of Mathematical Economics, Vol. 28, 1997, pp. 127-154. doi:10.1016/S0304-4068(97)00800-8
[7]	G. Kosicki and K. Cahill, “Economics of Cost Pass through and Damages in Indirect Purchases Antitrust Cases,” Antitrust Bulletin, Vol. 51, No. 3, 2006, pp. 599- 630.
[8]	G. Hanoch, “Production and Demand Models with Direct or Indirect Implicit Additivity,” Econometrica, Vol. 43, No. 3, 1975, pp. 395-420. doi:10.2307/1914273
[9]	J. Bulow and P. Pfleiderer, “A note on the effect of cost changes on prices,” Journal of Political Economy, Vol. 91, No. 1, 1983, pp. 182-185. doi:10.1086/261135