Transcript Calibrated Economic Models

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
 Cournot
without Capacity Constraints
 Cournot
with Capacity Constraints
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

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

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
 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
 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

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
 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
A
merger simply destroys the highercost 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

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
 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%