Good representations and solvable groups

We give a characterization of connected solvable groups in terms of the existence of representations with certain geometric properties. The existence of such representations for the group of upper triangular matrices played an important role in the proof of the authors' equivariant Riemann-Roch theorem.Comment: To appear Michigan Math. Journal; dedicated to William Fulton on his 60th birthda

Multi-product Bertrand Oligopoly with exogenous and endogenous consumer heterogeneity

We develop a spatial model in which consumers receive firm-specific location shocks and firms endogenously determine both franchise/product locations and prices. Remarkably, firms fail to profit from endogenous product-specific heterogeneity alone: while ex-post consumer heterogeneity ensures positive gross profits, competition for market share results in socially excessive product lines and zero net profits. With added exogenous taste heterogeneity, endogenous spatial heterogeneity drives profits below their levels with only taste heterogeneity. Finally, we introduce multiple product lines and show that when product costs differ across lines, firms earn positive profits as long as consumer preferences over lines are imperfectly correlated