Simulation Methods
Cournot Oligopoly
Farrell and Shapiro (1990) highlighted issues of the Department of Justice’s Merger Guidelines (1984), with its use of Herfindahl-Hirschman indices. The main issues they raised were the base assumptions that: # Outputs remain unchanged in the merger process (both companies retained their initial outputs); # There is a reliable and inverse relationship between market concentration) and market performance. They sought to instead to model mergers by Cournot oligopoly theory, establishing a series of propositions in both mergers effect on price and welfare. To establish their propositions a series of assumptions and conditions were made: # Each firm’s reaction curves slope downwards, such that an increase in a rivals’ output lowers the firm’s marginal revenue. This assumption is made as if marginal revenues were unaffected by the others output, the equilibrium would not be a function of quantity. Which is necessary for application of Cournot theory. # Each firm’s residual demand curve intersects above its marginal cost curve. This assumption is made as if marginal cost decreased with quantity, as it can in some cases withPrice-based Propositions
# A merger raises its price if and only if the merged company markup is less than the sum of the pre-merger constituent markups, and the post-merger aggregate quantity is unchanged. # If a merger generates no synergies, then in the long run it causes market price to rise. # If a merger generates no synergies, then in the short run it will raise price if: ## Capital is immobile across facilities; ## All merging firms are equally efficient, and their long-run production has constant returns to scale.Welfare-based Propositions
# If sub-sect of colluding firms within a Cournot oligopolistic market change their behaviour, then their net effect on the other firms and customer is a function of the equilibrium change (XI) of the colluder’s output. A small reduction in XI has a net positive effect on outsiders and customers if the total outsider market share and response function are larger than the colluder’s market share. # If there is a merger between colluding firms such that it their initial market share is not greater than the outsiders, the price and marginal cost functions are non-negative in the 2nd and 3rd order for all the outsider firms, then if the merger is profitable and would raise the price, then it would also raise welfare. # The sign of the net effect on welfare from a small outwards shift in an individual firm’s reaction curves function is given by the difference between that firm’s market share and the sum total of each of the other firms reaction functions multiplied by their individual market shares. In a market with large rival firms, a sufficiently small entrant will have a net negative effect on welfare, as the market share taken from other firms is at a higher marginal cost than the increase in customer welfare. Therefore, overall welfare decreases. # Reducing imports by a quota will raise domestic welfare if and only if the share of imports are less than the reaction-weighted sum of domestic producers shares. This means for a sufficiently small import sector, excluding all imports will raise welfare. This is due to the lower marginal cost of domestic producers generating a larger welfare gain than the customer welfare loss due to domestic price increases.References