Appendix A - Mathematical Model of Business Groups

Summary

The model of business groups described in Chapters 3 and 4 is formally developed in Feenstra, Huang, and Hamilton (2003), which is reproduced in part here, along with the mathematical Appendix from that paper.

The business groups model is a natural extension of the monopolistic competition framework used in industrial organization (Dixit and Stiglitz, 1977, Spence, 1976) and international trade (Helpman and Krugman, 1985). In this framework there are large numbers of firms, each producing a unique product. Although it is normally assumed that the firms operate independently, we shall allow groups of firms to jointly maximize profits, and such a group of firms is called a “business group.” Equivalently, we can think of a business group as a multi-product company, that chooses both the range of upstream and downstream goods to produce, and their optimal prices. Helpman and Krugman (1985, pp. 220–2) recognized that the monopolistic competition model had the potential to include economic organization in their discussion of “industrial complexes,” but this idea was not pursued further in the trade context; instead, the upstream and downstream linkages between firms became a building block of the new models in economic geography (Krugman, 1991, 1996). The equilibrium concept we use is closest in spirit to the work in industrial organization by Perry (1989, pp. 229–35), though also anticipated by the early work of Caves (1974).