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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. Potentially Useful Models. Dominant Firm

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merger simulation with homogeneous goods

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

potentially useful models
Potentially Useful Models
  • Dominant Firm
  • Cournot without Capacity Constraints
  • Cournot with Capacity Constraints
the dominant firm model
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
assumptions facilitating calibration of the dominant firm model
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
alternative calibration of the dominant firm model
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
example dominant firm merger simulation
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%

the cournot model
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
assumptions facilitating calibration of the cournot model
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
example cournot merger simulation
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%

issues with constant marginal cost and no capacity constraints
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
a calibrated cournot model with capacity constraints
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
example cournot merger simulation with capacity constraints
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%