Nonlinear Pricing to Produce Information

We investigate the firm's dynamic nonlinear pricing problem when facing consumers whose tastes vary according to a scalar index. We relax the standard assumption that the firm knows the distribution of this index. In general the firm should determine its marginal price schedule as if it were myopic, and produce information by lowering the price schedule; “bunching” consumers at positive purchase levels should be avoided. As a special case we also consider a market characterized by homogeneous consumers with a static, but unknown, demand curve. We show that when there are repeat purchases the forward-looking firm should tend towards penetration pricing; otherwise its strategy should tend towards skimming. We extend our insights to more general settings and discuss implications for pricing product lines.