Nonlinear Pricing of Food in Village Economies

We consider a nonlinear pricing model, in which consumers' marginal willingness to pay and absolute ability to pay are noncontractible, to explain the nonlinearity of unit prices of basic food items (bulk discounting) in developing countries. We allow consumers to face binding budget-constraints due to subsistence concerns and allow their outside options to trading with a seller to depend on their characteristics. We show that, under certain conditions, the nonlinear pricing problem with budget-constrained consumers is equivalent to the nonlinear pricing problem with so-called countervailing incentives, in which consumers are not budget-constrained but their outside utilities depend on their types. Hence, by applying standard techniques, we obtain a simple characterization of optimal nonlinear pricing for our general case. Based on this characterization we show that, contrary to the prediction of standard models, nonlinear pricing can positively affect the level of consumption and the surplus enjoyed by the purchasers of the smallest quantities, typically the poorest consumers, compared to linear pricing. In particular, due to their effect on offered prices and quantities, budget constraints may lead to higher levels of consumption and surplus among the poor that those attained in the absence of these constraints. Lastly, we prove that our model is nonparametrically identified, we provide a simple test of the standard nonlinear pricing model vis-a-vis our model, and we derive nonparametric estimators of the model primitives. These estimators can be easily implemented using individual-level data commonly available for beneficiaries of conditional cash transfer programs in developing countries. Our estimates imply that nonlinear prices have a beneficial impact on the poor in most of the villages we analyze. These results confirm the importance of incorporating our proposed extensions of the standard nonlinear pricing model to evaluate the distributional effects of nonlinear pricing.