Trustworthy Models for Antitrust Investigation

Suppose major cosmetics companies X and Y have proposed a merger. How do antitrust investigators at the U.S. Department of Justice determine beforehand whether the merger would result in a sharp rise in the price of cosmetics?

Using software developed by Vanderbilt University Professors Philip Crooke, Luke Froeb, and Steven Tschantz, and Justice Department Research Director Gregory Werden, antitrust enforcement agencies increasingly use Mathematica to simulate the effects of such horizontal mergers. The computational approach involves two steps: estimating a structural demand model and then computing or simulating the postmerger equilibrium to predict postmerger prices and quantities. Mathematica has been used to simulate mergers in products as diverse as breakfast cereal, bread, ski resorts, frozen fish, and tissue paper.

"Mathematica makes it easy to prototype and simulate models. I think that Mathematica has the potential to radically change the field of economics, much as calculus did 70 years ago." Luke Froeb, Vanderbilt University

The Vanderbilt professors have also put the simulations onto a Mathematica-driven website for use as a teaching tool for attorneys and M.B.A. students. "For example," says Dr. Froeb, "the cosmetics merger case turned on a low cross-elasticity of demand for the two companies' mascara products. Using the web, I can tell the story of the case and then show how this affected the predicted anticompetitive price rise."