Modeling Location and Production: An Application to U.S. Fully-Integrated Steel Plants

Abstract

I N Weber's (1929) theory of the location of industry, spatial firms produce under conditions of fixed-proportions and constant returns to scale, while their spatial consumers have priceinelastic demands. Weber's assumptions are relaxed separately in previous work. Moses (1958) and Alonso (1967) allow either for flexible technologies but inelastic demands or for pricesensitive demands but fixed-proportions technologies. This paper presents a behavioral and econometric model of spatial firms which simultaneously relaxes restrictive assumptions on both technology and demand. Assumptions of earlier models become testable hypotheses. The behavioral model is general to any spatial firm; the econometric model can be estimated for any industry. The paper reports an estimation of the model for a sample of fully-integrated steel plants in the United States. The steel industry is appropriate for illustrating the general model for two reasons. First, the important inputs in steel are localized, weight-losing materials, while transportation charges are a nontrivial part of the delivered prices of both these inputs and of steel products. Second, previous research lacks agreement about the principal determinants of steel plant locations. Disagreement also exists over the structure of production and the extent of scale economies in production, and the existence of substitution possibilities among inputs. Each of these disagreements is treated as a hypothesis within this paper. First, a model which includes the influences of both consumers and materials on location can distinguish the comparative influence of each. The literature lacks agreement on whether the steel industry is transport-oriented, in which case consumer demands are price-inelastic and an optimal location minimizes transport costs, or market-oriented, in which case, consumer demands are price-elastic and an optimal location reflects that sensitivity. Isard (1948) suggests the influences on location change over time, due to changes in technology and relative prices. Isard and Capron (1949) conclude the steel industry is transport-oriented. More recently, Hekman (1978) reports that the demand for steel is priceelastic. He concludes that locations in the steel industry are sensitive to consumer demands. The evidence in this paper portrays the steel industry as transport-oriented. Second, there are differing estimates of the extent of scale economies in steel production, ranging from constant returns to scale (Hekman, 1978), to a minimum efficient scale (m.e.s.) of twelve million tons (Cockerill, 1974). Scherer (1973) and Weiss (1976) estimate m.e.s. of four million tons, while Tarr (1977) gives the mid1970s m.e.s. at six million tons, an estimate reported in this paper as well. Third, the existence of substitution possibilities among inputs has implications for both location and production. If substitution possibilities are limited, Weber models of location may be applied to the steel industry. Previous research has characterized steelnmaking technology as fixed-proportions (Tsao and Day, 1971), Cobb-Douglas (Hekman, 1978) or having wide variation in substitution possibilities (Kopp and Smith, 1980; Moroney and Trapani, 1981). This paper presents estimated elasticities of substitution suggestive of great substitution possibilities among inputs. The behavioral model of location and production is presented and then transformed into an econometric model in section II. A brief discussion of regional markets for steel products and a description of the data appears in section III. Received for publication July 31, 1981. Revision accepted for publication July 7, 1982. * Wayne State University. This research is based on my Ph.D. dissertation at the University of Wisconsin-Madison. The advice of Frank M. Gollop, Eugene Smolensky and Charles A. Wilson is gratefully acknowledged. I have benefited from discussions with James Hamilton and Li Way Lee and comments by Jan Brueckner and several anonymous referees. Computing support has been provided by the Graduate Schools at the University of Wisconsin-Madison and Wayne State University. The responsibility for any remaining errors is mine. An earlier version of this paper was presented at the 1980 North American Meetings of the Econometric Society.