Perfect price discrimination with costless arbitrage

The ability of a monopoly seller to prevent resale is often presented as a necessary condition for first degree price discrimination. In this paper, we explore this claim and show that, even with costless arbitrage markets, price discrimination may continue to be both feasible and profit maximizing despite potential resale. With finite numbers of consumers, arbitrage markets may be 'thin', in the sense that there can be too few low-valuation consumers to supply high-valuation consumers. We examine both ex ante and ex post arbitrage markets and show how a monopoly can exploit potential 'thinness' to profitably price discriminate. In each case, we present sufficient conditions for equilibrium price discrimination. We note that the form of such discrimination depends on the nature of the arbitrage market and consider business strategies that a monopoly might adopt to exacerbate market thinness. Our results show how market depth and the effectiveness of arbitrage can be the key elements for price discrimination, rather than the per se prevention of reselling.