We study the problem of a monopolist who faces consumers with heterogeneous tastes a la Hotelling (1929). The monopolist first designs a product (positions herself) and then chooses the price. The standard monopoly model is nested as a special case with a fixed position. To determine the range...

We bring together the theories of duality and dynamic programming. We show that the dual of a separable dynamic optimization problem can be recursively decomposed. We provide a dual version of the principle of optimality and give conditions under which the dual Bellman operator is a contraction...