Second best and monopoly: A cautionary tale

Abstract

The theory of second best, as originally conceived by Meade (1955) and popularized by Lipsey and Lancaster (1956), has been a much discussed topic for quite some time now. Second best rules have been devised for a number of situations, but very little has been done in terms of trying to get a feel for the magnitudes that may be involved. This paper intends to make a crude and tentative first step in this direction in the interest of making a similarly crude and tentative evaluation of the policy measures that the theory of second best might suggest. The second best problem that we will examine is the one analyzed by Rees (1968), Bergson (1972), and others where there is a government operated industry in an economy containing an untouchable monopoly. The one generally agreed upon implication of second best theory is that where there is an optimality condition that can't be achieved, then the desirability of achieving the remaining conditions is cast in doubt. Thus, in the case of an untouchable monopoly, the desirability of pricing at marginal cost in the government operated industry is cast in doubt and a second best pricing rule for this industry is desired. There are probably two reasons that the second best literature does not give much feel for magnitudes. The first is that most of the literature has been exclusively devoted to finding necessary conditions for second best optimality and necessary conditions in and of themselves indicate nothing about magnitudes. The second reason, as far as the well-informed layman and wellmotivated undergraduate are concerned, is that much of the literature is couched in ad hoc assumptions that don't readily lend themselves to intuitive interpretations. Accordingly, this paper is going to deal only with solutions rather than conditions, and to pose the problem in terms that would be intuitive to anyone interested in this type of question. Specifically, we will give a numerical example of second best pricing and discuss its implications. Although this approach is sadly lacking in generality, it may be useful in illustrating one possibility and will be accessible to any layman who is willing to skip the equations and trust the computational skills of the author.