The sensitivity of profits to changes in location decision variables: the use of aggregated data in the empirical analysis of a resource recovery firm

Abstract

The purpose of theoretical and empirical production-location models is to determine the conditions under which locational stability is maintained in terms of transportation costs. The presence of variables in the theory for which there are no empirical analogs has constrained researchers to use mathematical programming models with micro-level data. In this study the linear-location model developed by Sakashita and Emerson is modified to accommodate an aggregated data base and a one input/one output site configuration. The presence of aggregated data further limits the partial equilibrium model by the removal of all elasticities from the second-order equations. Thus, given these differences, the first objective is to determine if the empirical model is applicable in terms of testing the theoretical model. The second objective is to determine the sensitivity of profits to changes in the location decision variables at optimal and suboptimal locations. Aggregated time-series data covering a four-year period was provided by a midwestern U.S. resource recovery firm. One regression on the data determined the homogeneity of the production function, a condition necessary for stability. A second regression determined the relationship between output and average costs at simulated locations. Tests on the sensitivity of profits with respect to changes in distance and transportation rates clearly show that the firm is not maximizing profits at its current location and that optimal production will occur at the input site. In addition, an analysis using the space-cost curve developed by D. M. Smith shows that costs will be minimized at the input site. Finally, there is a discussion on the relationship between the flatness of the average cost curve and the type of technology employed by the firm in terms of "its ability to rationally continue operating at a suboptimal location.