A model of homogeneous input demand under price uncertainty

This paper examines the empirical validity of a model of homogeneous input demand under price uncertainty in which firms trade off expected input cost against its variability (risk) in selecting the optimal input supplier mix. Using recent work in time-series econometrics, this model is applied to the Japanese steam-coal import market, where five suppliers compete: China, the Soviet Union, South Africa, the United States, and Australia. (JEL L10, L72) The purpose of this paper is to derive and examine the empirical validity of a model of homogeneous input demand under price uncertainty. The motivation for this investigation is the common observation that firms simultaneously purchase a homogeneous factor of production from a variety of suppliers each charging a different price. Moreover, there are many instances when the price from one supplier is consistently above that of all other suppliers for an extended period of time yet firms continue to purchase from this supplier. This observation appears to violate the criterion of expected cost minimization for input choice.1 An attempt to explain these anomalies suggests that firms trade off the level of expected input cost against its variability in deciding how to allocate total input demand across available suppliers. By purchasing inputs from a variety of suppliers, the firm is diversifying away some of the price risk associated with satisfying demand from the single least-expected-cost supplier.2 Although the marginal rate of substitution (MRS) between risk and cost is not directly observable, we develop a methodology for empirically estimating this magnitude from a time-series of input purchases. This MRS is an estimate of the firm's risk preferences at the expected cost-risk pair selected. If we assume that this MRS between risk and cost is constant across all expected cost-risk pairs, then an input-price risk premium can be calculated. Subject to this assumption, the input-price risk premium is the percentage above the current * Department of Economics, Stanford University, Stanford, CA 94305, and Department of Economics and Institute for Environmental Studies, University of Illinois, Urbana, IL 61801, respectively. We thank seminar participants at Stanford University, the University of California-Berkeley, the University of Texas, the University of Washington, Purdue University, and the Norwegian School of Economics for comments on earlier drafts. Tom MaCurdy, Randy Mariger, Paul Newbold, Roger Noll, and Agnar Sandmo deserve special mention for their helpful comments. Vivian Hamilton expertly prepared the figures. We especially thank an anonymous referee for thoughtful comments and suggestions on the previous version of the paper. His many contributions are too numerous to mention individually. The final version of this paper was prepared while Wolak was a National Fellow of the Hoover Institution. IFor the sake of simplicity, assume that the price series are independent and identically distributed draws from a multivariate distribution. The null hypothesis of equal means for the prices becomes less likely the greater the number of observations that one price series remains above the others. Clearly, if firms are minimizing expected cost, they would purchase all of this input from the least-expected-price supplier. Hence, in this simple case, the nonzero market share of the consistently high-priced supplier is, with high probability, a violation of the expected-cost-minimization criterion of input choice. 51