Efficiency and Pricing in the Coal Industry - Henderson, James M. (The Review of Economics and Statistics, 1956)
A SHORT-RUN model for the coal industry was formulated and solved in an article in the last issue of this REVIEW.2 The model is composed of two interrelated linear programming problems. Its data are spatially distributed demands for coal, capacities of spatially distributed coal deposits, and the unit costs of all possible deliveries from the deposits to the demand locations. The first programming problem, the delivery system, is to select a set of deliveries which minimizes the cost of meeting the given demands subject to the capacity restrictions; and the second, the price system, is to select a set of delivered prices for the demand locations and unit royalties for the deposits which maximizes total revenue net of royalty payments subject to the condition that every possible delivery must yield a nonpositive profit. The optimum solutions for these two problems were shown to provide a complete description of a perfectly competitive equilibrium. The model is normative in the sense that its solutions are those which would prevail if the assumptions of perfect competition were realized. The prices and royalties determined in the price system are only consistent with perfect competition, but the minimum-cost solution of the delivery system is consistent with monopoly as well as perfect competition. The solution of the delivery system furnishes a numerical description of efficiency in the sense that total cost cannot be reduced by any possible rearrangement of delivery levels, and the solution of the price system furnishes a numerical description of perfectly competitive pricing. The model was implemented with historical figures for the demands, capacities, and unit costs; and numerical solutions were computed for the delivery and price systems for I947, 1949, and I95I.3 The numerical values of the variables given in the normative solutions are in the present paper compared with the corresponding actual values. Actual outputs for the deposits recognized in the applications of the model are compared with efficient outputs derived from the solutions of the delivery system, in order to indicate how closely the coal industry approaches the efficient norm established by the model. The decline in output between I947 and I949 and the conformity of the actual outputs for surface deposits are specifically considered. Actual f.o.b. mine prices are compared with corresponding competitive prices derived from the solutions of the price system, to indicate the extent to which the prices prevailing in the coal industry approximate those established by the model. No industry meets all of the assumptions of perfect competition, and the question to be answered by our analysis is not whether the coal industry meets these assumptions, but rather how closely it meets them. The extent of competition in individual industries has been the subject of a large number of studies. A common procedure in such a study is to examine various factors, for example the number of sellers and buyers, the method of price determination, and the existence of selling costs, and then to judge the competitive structure of the industry on the basis of these f actors.4 These analyses are valuable in describing the niature of competition within an industry, but the extent to which an industry deviates from a perfectly competitive solution may not be directly related to the number of non-competitive practices which can be listed. The effects of one