Non linear pricing in village economies

Abstract

We consider a nonlinear pricing model in which marginal willingness to pay and absolute ability to pay differ across consumers in order to explain the nonlinearity of unit prices of basic food items in developing countries. We model consumers’ subsistence constraints and allow outside options from purchasing a good to depend on consumers' ’preference for the good. We obtain a simple characterization of optimal nonlinear pricing. Based on this characterization, we show that nonlinear pricing leads to higher consumption, lower marginal prices, and higher consumer surplus than implied by the standard nonlinear pricing model. We derive a number of comparative statics results that differentiate our model from the standard one and develop a test that formally allows to distinguish between the two models. We prove that our model is nonparametrically identified under usual assumptions and derive nonparametric estimators of the model primitives. These estimators, as well as the test we propose, can be easily implemented using individual-level data commonly available for beneficiaries of conditional cash transfer programs in developing countries. We rely on these estimators to assess the welfare impact of nonlinear pricing. We …find that the model well accounts for the data and that at the estimated primitives, nonlinear pricing especially benefits consumers who purchase small and intermediate quantities compared to linear pricing. We further show that failure to account for the endogeneity of prices, especially in the presence of heterogeneous preferences and constraints among consumers, can lead to an incorrect assessment of the impact of common food subsidization policies, which boost consumption but may give rise to significant price increases. Overall these results confirm the importance of incorporating our proposed extensions of the standard nonlinear pricing model to evaluate the distributional effects of nonlinear pricing. The paper is co-authored with Elena Pastorino.