In markets where sellers are able to price discriminate, individuals pay different prices that may be unobserved by the econometrician. This paper considers the structural estimation of a demand and supply model à la Berry et al. (1995, henceforth BLP) with such price discrimination and limited information on prices taking the form of, e.g., observing list prices from catalogues or average prices. Within this framework, identification is achieved not only with usual moment conditions on the demand side, but also through supply-side restrictions. The model can be estimated by GMM using a nested fixed point algorithm that extends BLP’s algorithm to our setting. We apply our methodology to estimate the demand and supply in the French new automobile market. Our results suggest that discounting arising from price discrimination is important. The average discount is estimated to be 9.6%, with large variation depending on buyers’ characteristics and cars’ specifications. Our results are consistent with other evidence on transaction prices in France.