Corporate takeovers, welfare, and the measurement of market concentration
So far in this chapter we have examined the effect of legal rules on merger incentives, issues that arise in the design of managerial compensation in the context of accident law, as well as issues around the influence that shareholders can have on managerial decisions within publicly held companies. Another key set of legal issues that arise in the context of mergers and corporate takeovers are those that involve competition and market concentration, and the link between concentration and economic welfare.
Can we use measures of market share to estimate aggregate welfare in oligopolistic markets? Suppose, for example, that there are four firms in an industry. We can compute the market share of each firm i as:
where Q=Zf=1qi is the aggregate market output. To make things concrete, suppose that we have:
We could then plot these on a graph, with market share rank on the horizontal axis, and cumulative market share on the vertical axis, as in Figure 10.6.1.
In Figure 10.6.1, we have also plotted market share curve for a market with a large number of firms, in which all firms have an equal share. The flatter the line, the more equal are the market shares. In a perfectly competitive market, there would be many firms, each with a small market share. Such a graph could be used to examine the 'competitiveness' or degree of 'concentration' of a particular industry.
Alternatively, in an industry with N > 2 firms, we could compute the Herfindahl-Hirschman index (HHI) which was encountered in Chapter 5:
Figure 10.6.1 Market shares
where, again, st = qt / Q. If a single firm in the industry is 'dominant' and has a very high market share, then the HHI is large (close to one). On the other hand, if no firm dominates, then each of the si are small, and so ? “1sf would be close to zero. In general, 0 < HHI < 1, with a lower value indicating a 'more competitive' market.