Using Mathematicato Enforce the Antitrust Laws

A decision by the Federal Trade Commission (FTC) or Department of Justice (DOJ) to challenge a merger under the antitrust laws can affect stock prices and thousands of jobs. Increasingly, both the FTC and DOJ are turning to Mathematica to help them determine which mergers are anticompetitive.

Using software developed by Vanderbilt Professors Philip Crooke, Luke Froeb, and Steven Tschantz (pictured above) and Justice Department Research Director Gregory Werden, the antitrust enforcement agencies are using Mathematica to simulate the effects of mergers. Mergers found to significantly raise price are likely to face a court challenge.

The use of Mathematica has added structure to the decision making process at the agencies, and has raised the importance of economics in the merger evaluation process. The software has been used to evaluate mergers in products as diverse as breakfast cereals, cosmetics, tissue paper, ski resorts, and bread.

The use of the software in several high profile cases, like L'Oreal-Maybelline and General Mills-Chex, has convinced even attorneys of its merits. Writing in the Spring 97 issue of Antitrust, a publication of the American Bar Association, one attorney called it "one of the most interesting and potentially useful recent developments in antitrust merger analysis."

To help antitrust attorneys and practitioners learn the methodology, the Vanderbilt Professors have created some interactive web games, at http://www.antitrust.org/simulation.html, based on actual cases, that illustrate how the methodology is used. The Unilateral Effects game illustrates the models used in the L'Oreal-Maybelline merger, and the second game, Spatial Merger Simulation, is based on a case of Froeb's at the Department of Justice. This case involved predicting the loss of competition that resulted from mergers between timber mills in National Forests.

The graph above depicts the loss of competition in a forest when the mills, denoted by red dots, merge. The darker shaded areas indicate bigger price effects. Professor Froeb also uses these games in his classes at the Owen Graduate School of Management.

The merger simulation software is written up in "Simulating Mergers among Noncooperative Oligopolists," in Computational Economics and Finance: Modeling and Analysis with Mathematica, edited by Hal Varian (TELOS, Springer-Verlag) 1996. Currently the Vanderbilt Professors are updating the software and hope to have a beta version out soon.

Key features of Mathematica used:
Numeric--FindRoot
Symbolic--Solve
Graphic--ListContourPlot
Programming
Notebook

Froeb's favorite Mathematica feature: "Mathematica is a high-level language that makes it easy to prototype and simulate models. You can do both numerical, and symbolic operations without switching back and forth between platforms. I predict that Mathematica will become a very important tool in economics."