The Armstrong-Vickers Research Partnership
The terrain between the Elysian field of perfect competition and the quagmire of unassailable monopoly is forbiddingly large and rather messy. There are two main clumps of terra firma.
One is monopolistic competition, where lots of firms all produce something just a little bit different, in location or non-spatial characteristics. A basic, stripped-down version of the Dixit and Stiglitz (1977) paper has been borrowed extensively to illuminate trade theory, growth, unemployment and public finance. Afforced by the algebraically brilliant but absurdly implausible device of Calvo pricing, it underpins all standard work on monetary policy transmission and the dynamics of inflation. It is easily adapted and relies greatly on symmetry. This is mostly a story of niches. The spatial aspect of monopolistic competition, which mostly begins with Hotelling (1929) and Salop (1979), deals with bigger entities. It is now a cornerstone in the grand edifice of the economic theory of politics.Monopolistic competition has a more complex and very powerful rival. This is oligopoly, competition among the few. Like monopolistic competition (where the substitution elasticity between varieties can range widely), oligopoly embraces perfect competition and monopoly as limiting cases. Unlike monopolistic competition, it takes interdependency very seriously. Competition may vary in intensity and character. It extends to the hypothetical warfare between an incumbent monopolist and a would-be entrant.
Vickers' first journal publications had, as we saw above, already been devoted to aspects of oligopoly. This was followed by others, extending Cournot's oligopoly model in various directions, for example, when players' costs differ. That leads to heterogeneity in their market shares, a phenomenon which is commonly observed but rarely explained systematically.
Oligopoly featured centre stage in two major sole-authored papers by Vickers in 1995 (one of which appeared in Oxford Economic Papers (Vickers 1995a), and the other in the Review of Economic Studies (Vickers 1995b), and also in an earlier one in 1989 (Vickers 1989).Oligopoly and monopoly, regulation and IO applications of principalagent problems have been among the main settings for Vickers' research with Mark Armstrong. Their collaboration has stretched over three decades. The first paper they published together was on price discrimination (Armstrong and Vickers 1991). So far, the duo have published no less than fifteen academic journal papers together. Most (Armstrong and Vickers 1991, 1993, 1998, 2000, 2001, 2010a, b, 2012, 2015, 2018a, b) have no other co-authors. But Simon Cowan (Oxford) and Ray Rees (Warwick) joined them for one each in 1995 (Armstrong et al. 1995a and Armstrong et al. 1995b respectively), and Jidong Zhou (now at Yale) for two (Armstrong et al. 2009a, b). There is also one new Armstrong and Vickers Oxford Discussion Paper (Armstrong and Vickers 2018b). Embryos of others nestle, no doubt, in the pipeline that will appear in due course.
One of the most celebrated Armstrong and Vickers papers (2010b) appeared in Econometrica. It is a valuable contribution to agency theory, which James Mirrlees (Armstrong’s DPhil supervisor and John Vickers' colleague) had helped to invent some 35 years before. But it starts with a key issue in regulation, the criterion for deciding whether a merger is good or bad for social welfare. One reason for the link is the fact that regulators often operate in the dark, for the firms they monitor may be able to conceal aspects of what they are doing. No ordinary mortal can spot everything that happens on the cricket field. A second umpire (like the square-leg umpire in a cricket match) can help. But even that will not ensure perfect vision.
In the very simplest Cournot oligopoly, for example, a horizontal merger is always bad for consumers.
Fewer firms entail a higher price and hence lower welfare for the people who buy the product. The two firms that merge will shrink, reducing their aggregate profits provided that there are still one or more other players left in the industry, but lifting the profits a little for those other players. If there were just two duopolists in the same industry, with entry restricted, they gain from a merger, and consumers typically suffer (but might just conceivably not, if that meant that there were now big costreducing synergies to exploit, for example). In more complex cases, where the merging firms operate in different industries or have vertical links, you could, for instance, see a merger reducing consumer surplus straight away but raising producer surplus by a larger amount. What is more, profits may get invested; that should raise consumers’ welfare in the future; and even if there were no extra investment, should profit recipients really be excluded from the notion of society’s welfare? What should be done in such cases? The question of how social welfare is defined becomes critical, therefore, for deciding whether the merger should proceed.This paper is rigorous and understandably quite abstract. It generalises the question. The utility of principal P depends upon one of a selection of actions, N, by an agent A. N is chosen by A from a longer list, L, but P cannot see what is in N. P needs to choose a list M of all the possible acts that he, P, permits A to do. The two lists, M and N, are subsets of L. Before acting, A tells P what he proposes to do. So, how does P choose M? It is not good enough for P to say, ‘Choose what you like from list M’: A might go for something that is not best from P’s standpoint. The authors prove various results about P’s optimal list M. The regulation analogy is this. Suppose P says, ‘Do what you like so long as the merger increases welfare defined as consumer surplus plus producers’ profit (which P would like maximised)’.
That is not good enough from P’s standpoint: a merger could increase welfare by that definition by greatly raising the merged firms’ profits, partly at the expense of consumers. So, the competition authority umpire should restrict list M to actions that raise consumer surplus on its own—P knows the firms will not do anything to damage their combined profits. There is an echo here of Vickers' demonstration in 1985 that the profit-seeking owner of a firm in a Cournot oligopoly can gain by getting a manager who seeks to maximise not profit, but total revenue. There is still more in Armstrong and Vickers (2010b), for example, on dynamics and the effects of the discounting of future payoffs at different rates.This Econometrica paper extends knowledge by providing solid analytical foundations for an important point. Like all the Armstrong and Vickers papers, it is rigorous and meticulous. While the inevitable technicalities make it challenging to digest, for example, for regulators and lawyers, there are other highly accessible publications that Armstrong and Vickers have recently written. Key points are made directly, and, whenever possible, in plain English. Three examples are their 2018 multiproduct pricing paper in the Journal of Political Economy (Armstrong and Vickers 2018a), their discussion of how contingent charges affect consumers' welfare in the Journal of Economic Literature (Armstrong and Vickers 2012), and a paper in the American Economic Review: Insights, on price discrimination in the presence of captive customers (Armstrong and Vickers 2019).
The first of these three compares Cournot oligopoly with both regulated and unregulated monopoly, when the firms produce more than a single product. This paper fills quite a big gap: there can be very few firms which are large enough to influence the prices of what they produce and yet make and sell only one single good. Among other results, Cournot equilibrium, they find, meets a famous test of efficiency (see Ramsey 1927).
Multiproduct pricing is the norm. Even more relevant, perhaps, to real-world concerns is the problem of contingent charges, like big penalties that most banks charge for unauthorised overdrafts. Here, Armstrong and Vickers show that such charges tend to redistribute from uninformed customers to informed ones, and go on to ask what welfare economics has to say about that.So many of Vickers' academic publications have been co-authored with Armstrong that it is easy to miss some of the fruit from other partnerships. There were many. Space precludes including most of them. But one such that clearly merits a mention is a paper which appeared in the American Economic Review on third-degree price discrimination by monopolists (see Aguirre et al. 2010). This appeared in the same year as the contingent charges paper. Many large firms sell different units to different people at different prices, and the IT revolution has often made this more common than it was. Is the practice harmful or beneficial for social welfare? Also, what does it mean for a firm's overall level of output? These are big policy questions. The Aguirre et al. paper is devoted to answering them. Like the work carried out by Armstrong, Yarrow and Harris, and all the papers that Vickers wrote alone or with others, it is addressed to a serious issue that matters, and on which economic analysis can throw a powerful light.
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