Many economic agents display monopolistic behavior. In particular, we will discuss two variants of monopolistic behavior as represented by a pure monopolist and by a perfectly dicriminating monopolist. We will assume that the monopolist will produce and sell a vector of outputs, as final commodities.

The essential characteristic of a monopolist is that he “owns” the set of demand functions that are related to his outputs. The meaning of “owning” the demand functions must be understood in the sense that a monopolist “develops” the markets for his products and, in this sense, he is aware of the demand functions for such products that can be satisfied only by his outputs.

Pure Monopolist

A pure monopolist is a monopolist who charges the same price for all the units of his products sold on the market. We assume that he faces inverse demand functions for his products defined as p = c - Dx, where D is a (n × n) symmetric positive semidefinite matrix representing the slopes of the demand functions, p is a (n × 1) vector of output prices, c is a (n × 1) vector of intercepts of the demand functions, and x is a (n × 1) vector of output quantities sold on the market by the pure monopolist.

A second assumption is that the monopolist uses a linear technology for producing his outputs. Such a technology is represented by the matrix A of dimensions (m × n), m < n.