We develop a nonparametric approach to identify and estimate consumer preferences and unobserved heterogeneity under nonlinear price schedules. Leveraging variation across multiple price schedules, we show that both the utility function and the distribution of preference types can be nonparametrically identified. The quantile function of unobserved types becomes solution of a functional equation, and we derive conditions ensuring identification. We propose an iterative approach for estimation, in which the regularization bias decays exponentially in the number of iterations while the variance grows only polynomially, yielding a near-parametric convergence rate. We propose a valid bootstrap procedure for finite-sample inference and extend the framework to accommodate potential endogeneity of prices and additional observed heterogeneity. Monte Carlo simulations and an empirical application to data from a European mail carrier demonstrate how we can recover the utility functions and preference distributions in finite samples.
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