In choosing the level of quality to purchase, the buyer of a differentiated product also chooses a point on the marginal price schedule for that product. Hence, in general, the demand functions for product characteristics cannot be consistently estimated by ordinary least squares. Market equilibrium results in a matching of characteristics of demanders and suppliers. This matching restricts the use of buyer and seller characteristics as instruments when estimating demand and supply functions for product characteristics. The paper develops these issues. A stochastic structure for hedonic equilibrium models is then proposed, identification results are presented, and estimation procedures are outlined.