A Generalized Herfindahl-Hirschmann Index

Economics was a subject I first discovered in high school a class that all students were required to take which inexplicitly became my favorite class of the year. I was enthralled by the idea of using mathematics to model the behavior of individuals and firms across the country. Until I met my mentor Professor Cheng-Zhong Qin, that is how I saw economics: a collection of simple and elegant theories that described all of economic activity. In truth, however, the complexities of the modern economy far outpace the mainstream theories economists use to describe it, most of which were developed before the mid-20th century. The great struggle of the next generation of economic researchers is not to develop new theories, but to adapt existing theory to the 21st century. Only this process can reconcile the original goal of economicsto be a model of the global economy�with the realities of our world … Cross-holdings exist when one business holds a non-voting stake in a direct competitor. Because these stakes are non-voting, they are allowed under current antitrust regulations; since sales are unaffected, they also fail to affect the HHI. However, recent economic literature has established that cross-holdings have a substantial impact on competition. In fact, in extreme scenarios it is possible for a multi-firm industry with cross-holdings to operate indistinguishably from a pure monopoly … Our project has two parts: first, we use conditions of Cournot Equilibrium (a special case of oligopoly) to derive a generalized form of the HHI, which we call the Generalized Herfindahl-Hirschman Index (GHHI) …

• Economics