Reaction Functions and ISO-Profit Curves

The concentration measures are used as a measure of the level of concentration in a product market. The Bain concentration ratio (CR) measures the market shares of the top three firms in the market. If the CR3 > 70% the market is defined as concentrated. But this measure also offers a window into possible divestiture options to bring the concentration levels back to a 70% or less standard threshold. However, the Bain CR measure is information deficient because any three random numbers for market share can add up to 70%.

So the 70% represents only a broad aggregate statistic telling a judge nothing about the underlying market shares and their distribution. Market entropy is about distribution and redistribution of market shares; it looks at the difference in shares between the top firm and (say) the fourth ranked firm. If the difference is minimal [40-35] then there is a greater chance of competition in that market than in a product market where the difference in [40-15].

The HHI index is used to compliment the Bain CR and it allows us to maximise the interpretation of the market share data. The HHI is the sum of the squares of the individual market shares. If the 1800 < HHI < 2200 the market is ranked in terms of moderate concentration (1800-2200) to high (above 2200) concentration levels. The accuracy of the data is very important because a significant inference can be drawn from the causation that a concentrated market is more likely to be collusive. In other words, that the firms in a concentrated market have a higher probability of price fixing.

The concentration-collusion debate is a serious debate within modern antitrust with implications for business, and the issue can arise when a market becomes more concentrated especially when the number of firms, n < 5. The number 5 is a crucial number in understanding firm behaviour. In markets where the number of firms is less than 5 there is a higher degree of interdependence amongst the firms and once the interdependence amongst the firms is recognised by the firms in a non cooperative game there is a greater degree of probability that one player will move to exploit the interdependence by exploiting the mutual interdependence and forming a cartel.

The advantage of joining a cartel is weighed in terms of a benefit-cost analysis: if the benefits of cartel profits > costs of litigation, if successfully prosecuted, there is a greater temptation to join the cartel. If all the firms realise that the benefits of being inside the cartel is greater than the benefits of being outside the cartel then all will join and a cartel is formed.

HHI Calculation

There are some recognised weaknesses in the computation of the CR3, the Bain concentration ratio: for example, it does not tell a judge anything about the underlying distribution or entropy across the market shares. It is possible to have a CR3 = 70% with different underlying market shares:

Each of the market structures do differ fundamentally in terms of the entropy or distribution of market shares. In Market I there is a dominant firm with 68% of the market and the nearest competitor has only 1%. Contrast this with Market II or III where no one firm has more than 40%. Market II and III could be deemed less anti-competitive than Market I, if the determination was solely and exclusively based on market shares criterion.

The divergence in market shares – a measure of entropy – can be presented as a mitigating set of circumstances in favour of a post-merger market share re-alignment. There is an old precedent in US antitrust in 1970s case of Lancaster Colony merger. In other words, if the post-merger market shares create a market where the divergence across market shares has been reduced, in particular if the divergence between the merged entity and the nearest competitor has been reduced, then there is hope for merger approval.

But there is another important consideration: not every large firm should be presumed guilty of alleged anti-competitive behaviour based on its market share profile. Dominant firm with 40-30% may fall into the category of monopoloid – that is, a large firm with high sustainable market shares, but does not act in an anti-competitive way, by increasing prices or keeping prices arbitrarily high over a long period of time. A monopoloid does not act in concert with rival firms – it acts in a unilateral way to sustain and defend market shares (Si).

In other to accommodate the inadequacies of the CR3, the HHI ratio, the Herfindahl-Hirschmann Index, captures the distribution of market shares and allows a finer computation of the level of concentration in an oligopoly market. The software will illustrate the HHI in action.

It is computed as the sum of market shares squared in order to capture the difference in shares across the firms in the product market under investigation.

In its sequence of steps to analyse a horizontal merger, for example, US Department of Justice antitrust official would begin by asking a simple question: does the merger involve a leading firm with share > 35% and twice the share of the second firm? If the answer is YES a challenge is likely; if NO a further calculation of the HHI within the 0.18 range, along with additional features to do with entry conditions, history of collusion in the market, product homogeneity and the degree of competition in the market, will determine collectively whether a challenge is more or less likely in the merger under investigation.

Illustration

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Key Points

To illustrate the meaning of concentration as used in modern antitrust.

To understand how the redistribution of market shares can contribute to increasing concentration in a market.