Prices for superstars can flatten out

We reconsider Rosen’s economics of superstars model establishing, in the case of single-type consumers, a constant price-to-quality ratio. Rosen also conjectured that, in the case of multiple-type consumers, the normal course of consumer behavior forces the price-to-quality relationship to be convex and prevents it from being concave. We show that this conjecture is false and explain why there is no a priori reason to rule out concavity in the price-to-quality relationship. In this model, the market matches consumers to artists on the basis of quality: consumers of each type select only one level of quality, supplied by artists endowed with a specific level of talent. The concavity or convexity of the price-to-quality relationship is non-trivially related to the way both populations are matched. Consumers with poor knowledge have greater fixed costs above and beyond the price they have to pay on the market. They are therefore less reluctant when prices rise sharply and they specialize in levels of quality that entail a high marginal appreciation of quality: this can mean either a high or a low level of quality, depending on price curvature. With convexity, as Rosen pointed out, they turn toward superstars. Symmetrically, convexity encourages connoisseurs to turn toward low quality. But concavity too is fully possible: consumer–artist matching, for the same reasons, simply has the reverse effect. Connoisseurs go for great talents, whose price of quality flattens out. The global shape of the price-to-quality relationship (concave or convex) is determined by market clearing conditions and, more crucially, by the distribution of agents on both sides. Copyright Springer Science+Business Media New York 2014