We propose a model of price discrimination to account for the nonlinearity of unit prices of basic food items in developing countries. We allow consumers to differ in their marginal willingness and absolute ability to pay for a good, incorporate consumers' subsistence constraints, and model consumers' outside options from purchasing a good, such as self-production or access to other markets, which depend on consumers' preferences and income. We obtain a simple characterization of equilibrium non-linear pricing and show that nonlinear pricing leads to higher levels of consumption and lower marginal prices than those implied by the standard nonlinear pricing model. The model is nonparametrically and semiparametrically identified under common assumptions. We derive nonparametric and semiparametric estimators of the model's primitives, which can easily be implemented using individual-level data commonly available for beneficiaries of conditional cash transfer programs in developing countries. The model well accounts for our data on rural Mexican villages. Importantly, the standard nonlinear pricing model, a special case of our model, is almost always rejected. We find that sellers have large degrees of market power and exert it by price discriminating across consumers through distortionary quantity discounts. Contrary to the prediction of the standard model, consumption distortions are less pronounced for individuals purchasing small quantities, despite the steep decline of observed unit prices with quantity. Overall, most consumers tend to benefit from nonlinear pricing relative to linear pricing. A novel result is that when sellers have market power, policies such as cash transfers that affect households' ability to pay can effectively strengthen sellers' incentive to price discriminate and thereby give rise to asymmetric price changes for low and high quantities, which exacerbate the consumption distortions associated with nonlinear pricing. We find evidence of these patterns in response to transfers in our data. These results confirm the importance of our proposed extension of the standard nonlinear pricing model in evaluating the distributional effects of nonlinear pricing.