Merger Simulation with Homogeneous Goods

1. Merger Simulation with Homogeneous Goods Gregory J. Werden Senior Economic Counsel Antitrust Division U.S. Department of Justice The views expressed herein are not purported to reflect those of the U.S. Department of Justice

2. Potentially Useful Models • Dominant Firm • Cournot without Capacity Constraints • Cournot with Capacity Constraints

3. The Dominant Firm Model • Competitive Fringe Fringe firms act competitively, maximizing profit by equating marginal cost to the market price • Dominant Firm The one dominant firm acts as a monopolist with respect to its residual demand curve, which is that part of industry demand not supplied by the fringe • Invented by Karl Forchheimer in 1908

4. Assumptions Facilitating Calibrationof the Dominant Firm Model • Assume linear or isoelastic demand and marginal cost proportional to output and inversely proportional to capital stock • Calibration requires just market shares of the merging firms and the pre-merger equilibrium (price, quantity, and elasticity of demand) • Percentage price increases are invariant to the pre-merger price and quantity

5. Alternative Calibrationof the Dominant Firm Model • Other demand assumptions require additional demand information • Less restrictive cost assumptions require more information about the merging firm’s costs and the elasticity of fringe supply • The more that is known, the less that must be assumed to fill gaps in what is known

6. Example Dominant FirmMerger Simulation • Pre-merger equilibrium Demand elasticity: 1.2 Merging firm’s shares: 50, 10 • Price-increase predictions Linear demand: 2.9% Isoelastic demand: 3.5%

7. The Cournot Model • Firms and Strategies Firms are characterized by their cost functions, and they choose quantities to maximize profits • Equilibrium An equilibrium is a set of quantities such that each firm is happy with its quantity, given those of rivals • Invented by A.A. Cournot in 1838

8. Assumptions Facilitating Calibrationof the Cournot Model • Assume linear or isoelastic demand, and marginal costs that are either constant or depend on output and capital as before • Calibration requires the market shares of all firms and the pre-merger equilibrium (price, quantity, and elasticity of demand) • Percentage price increases are invariant to the pre-merger price and quantity

9. Example Cournot Merger Simulation • Pre-merger equilibrium Demand elasticity: 1.2 Market shares: 40, 20, 20, 10, 10 • Price increases: constant marginal cost Linear demand: 1.7% Isoelastic demand: 2.6% • Price increases: capital-based costs Linear demand: 2.5% Isoelastic demand: 3.5%

10. Issues with Constant Marginal Costand No Capacity Constraints • A merger simply destroys the higher-cost merging firm • Real-world mergers almost never just destroy a firm • Some valuable asset (e.g., capacity or goodwill) normally is acquired

11. A Calibrated Cournot Modelwith Capacity Constraints • Marginal cost is constant until the capacity constraint is reached • Capacity-constrained firms are calibrated by an aggregate pre-merger market share • Other firms act as Cournot competitors and are calibrated by shares and excess capacities

12. Example Cournot Merger Simulationwith Capacity Constraints • Pre-merger equilibrium (just as before) Demand elasticity: 1.2 Shares: 40, 20, 20, 10, 10 Excess capacities: all 10% • Price increase predictions Linear demand: 2.1% Isoelastic demand: 3.5%