Spatial competition with heterogeneous …rms

I model horizontal and vertical dierentiation with heterogeneous …rms. The model nests the standard Hotelling model on the circumference of a circle. Firms play a three-stage game in which they enter and exit in the …rst stage, locate and choose quality in the second stage, and set their prices in the third stage. All relevant characteristics of …rms (quality, price, market share, and pro…t) are uniquely determined in strict subgame perfect Nash equilibria to the post-entry subgame. The distance between two neighbors is greater than average if and only if the average productivity of the two neighbors is greater than the average productivity in the market. A …rm's pro…t depends only on its own cost parameters and the "softness" of the market in which it sells. Market softness is a simple function of the number of …rms in the market and their average productivity. Because of a selection eect, denser markets are associated with more productive …rms and tougher competition.