Antonio Martner, Banco Central de Chile

Paper: Aggregate Outcomes of Nonlinear Prices in Supply Chains

Abstract: We study the welfare implications of nonlinear pricing in supply chains. Using population-level firm-to-firm transactions from Chile, we find indicative evidence that sellers engage in quantity-dependent and buyer-specific pricing strategies. We develop a general equilibrium model where firms pay and charge nonlinear prices. Under standard assumptions, we show that the optimal pricing scheme takes the form of a two-part tariff—comprising a flat fee and a marginal price—consistent with the price schedules observed in the data. Nonlinear pricing increases output per firm but distorts firm entry because flat fees redistribute profits unevenly across firms. Quantifying the model, we find that welfare under nonlinear prices reaches about 75% of the efficient benchmark. In a counterfactual policy that bans all price discrimination—constraining firms to uniform pricing, a single, quantity-invariant price for all buyers—welfare falls to about 49% of the efficient benchmark. Firms constrained to uniform pricing raise marginal prices that compound along supply chains, amplifying deadweight losses through markup accumulation. When interpreting the same data as uniform pricing, rather than nonlinear pricing, measured welfare is about 57% of the efficient benchmark. These results indicate that prohibiting price discrimination can be welfare-reducing and that the measured aggregate welfare impact of market power in supply chains depends meaningfully on the extent to which firms use nonlinear pricing.