Industry Performance Gradient Indexes
Abstract
This paper presents a theory of indexes which measure the rate of potential improvement in the welfare performance of an industry. These indexes indicate the magnitude of gross social gains achievable from appropriate governmental intervention (for example, antitrust, regulatory and deregulatory actions, or threats thereof). The indexes are local measures which can be calculated from data pertaining to the current industry structure (i.e., market shares and demand elasticities). Surprisingly, the indexes reduce to simple transformations of standard indexes of market concentration' and monopoly power (namely the m-firm concentration ratio, the Herfindahl index, and the Lerner index) given familiar sets of assumptions on firm behavior (respectively: collusive price-leadership, quantity Cournot, and pure monopoly). Since different modes of firms' conduct lead to different indexes, the choice among concentration index formulae should be based on an assessment of the behavior of the industry's firms. We find that the potential improvement in welfare performance is as sensitive to mode of conduct and other industry data as it is to the observed market shares. Consequently, our analysis provides a quantification of the idea that concentration per se does not necessarily warrant governmental intervention. Our theory at once provides a general index concept, new rigorously based practical indexes, a conceptual framework for the interpretation of standard indexes, and insights into appropriate criteria for governmental intervention. A rational appraisal of the desirability of a governmental action towards an industry can be phrased as a comparison of the benefits and the costs of the intervention. Each of the many possible governmental actions can conceptually be associated with the vectors qo and q of the outputs of the firms in the industry, before and after the intervention, respectively. The gross benefits of each action may be expressed as W(q) W(q?), where W(.) is the sum of consumers' and producers' surpluses. While received theory does guide the specification of the social objective function, little can be said at this level of generality about the social cost of governmental action which moves industry outputs from qo to q. Even so, it is useful to examine the benefit side of the rational calculus of intervention. It appears that the government regards an industry with high values of the standard concentration indexes as a prime candidate for intervention.2 Thus, using the cost-benefit vocabulary, the prevailing view seems to be that the concentration indexes are strongly positively correlated with W(q) W(q?), where q is the result of appropriate corrective action. In this paper we synthesize the rigorous cost-benefit and the practical index number approaches to the identification of industries where the government's intervention efforts will be well placed. Our aim is to develop tools capable of assessing W(q) W(q?). Yet, to ensure that the tools are practical ones, we accept constraints implicit in the index number methodology and confine ourselves to the use of information on only the current situation of the industry. Consequently, we focus on the rate of change of W( ) at qo; that is, on the current sensitivity of social welfare *American Telephone and Telegraph Company and Princeton University, respectively. This paper was written while we were employed by Bell Laboratories and is partly based on Dansby's doctoral dissertation. We are grateful to W. J. Baumol, A. Weiss, and S. Winter for extremely helDful comments and discussions. 'The measurement of industrial concentration is discussed by Morris Adelman, John Blair, and Russell Parker. The data used in these measurements typically come from Bureau of the Census or Federal Trade Commission sources. See J. E. Morton. 2Although economists debate the relative merits of various concentration indexes (see Eugene Singer or James Delaney), the government unabashedly uses these indexes to guide intervention activities (see F. M. Scherer).
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