FACTOR INTENSITY AND SITE GEOLOGY AS DETERMINANTS OF RETURNS TO SCALE IN COAL MINING Gale A. Boyd* Abstract--Increasing returns to scale (RTS) is frequently pos- tulated as affecting productivity in surface coal mining. How- ever, it is not clear whether increased capital intensity or increased output is the relevant phenomenon. A ray-homo- thetic production function that incorporates the capital-labor mix and fixed site geology into the scale elasticity is presented and estimated with a micro (mine level) dataset. The results indicate that higher capital intensity contributes to higher RTS for some types of capital equipment, but not all. On the average increasing RTS was found, with few mines approach- ing optimal scale. I. Introduction T HE literature of coal mining productivity contains many references to returns to scale as a factor in strip mining productivity.' However, different analysts use different definitions of "scale,"' and consequently their results are mixed. Some analysts associate returns to scale with larger pieces of capital equipment; 2 others use the more traditional economic notion of output volume and the scale elasticity;3 others simply relate output volume to labor productivity.4 It may be true that developments in large pieces of earth-moving equipment have been implemented at surface mines with large output volume, but this does not necessarily imply increasing returns to this par- ticular capital input. This confusion in the mining literature in the use of the term "scale," coupled with the more general observation that large firms (not just large mines) rarely have the same capital-labor mix as their smaller counterparts, leads to a hypothesis that a different capital-labor mix yields different economies of scale. The application of ray-homothetic production functions leads to an easily testable hypothesis on the impact of input mix to economies of scale. Additionally, these functions are more general than their homothetic namesakes. Fare (1975) has shown that they do not generate linear expansion paths. convex isoquants, or exhibit strong dispos- ability of inputs. The properties of convexity and strong disposability are necessary for a dual, cost function analysis of the production structure. If the true underlying production function is ray- homothetic, the dual approach is inappropriate, therefore these functions are a desirable tool for productivity analysis in general and in particular when input mix is believed to be an important determinant of economies of scale.5 Newcombe (1978) illustrates that geological conditions are a key determinant of strip mine productivity. The decision to open a mine and the scale of that mine critically depend on the site geology.6 By appropriate choice of homothetic transformation, it is possible to model another significant phenomenon in strip mining, capacity constraints that arise from the mine site geology.7 The mine site geology is, by nature, permanently fixed to the firm. Key geological descriptors like the coal seam thickness or reserves determine the Received for publication November 13, 1985. Revision accepted for publication June 18, 1986. *Argonne National Laboratory. This paper follows substantially the results of my Ph.D. thesis. I would like to thank my wife, Emily Boyd; my mother, Norma Parrish; my chairman, Rolf Fare; and my conmmittee for their patience and assistance during my graduate work. The errpiricai work contained herein would not have been possible without the support of the Coal Technology Laboratory at Southern Illinois University-Carbondale, who provided the data. Work on this paper was partially supported by the U.S. Departmient of Energy, Office of Fossil Energy, under Contract W-31-109-Eng-38. I would also like to acknowledge the helpful comments of Ken Rose and two anonymous referees in the preparation of this paper. Any errors remaining are the sole responsibility of the author. l For a complete discussion, see Boyd (1984). 2 See Hill (1980), Lakhani (1980), Murray (1980), and Zimmerman (1981). 3See Fare and Yoon (1983), Kruvant, Moody, and Valentine (1982), Maddala (1965), and Myers and Fire (1982). 4See Baker (1979) and Malhotra (1975). 5 One significant drawback with a production function ap- proach, however, is that endogeneity of the input variables will result in inconsistent estimates. Since the cost function is the principal way around this problem, we are faced with a meth- odological tradeoff between an undesirable statistical proce- dure and an undesirable theoretical procedure. The choice in this case is made in favor of the more satisfying theoretical method. 6 For a discussion of mine site engineering and site geology, see Skelly and Loy (1975). 7 Capacity bounds are often referred to but rarely explicitly modeled. The approach used here is applicable to any firm with fixed inputs that imply an upper bound on output. [ 18 ] Copyright ?) 1987