Question: A pure monopolist operates in a market where he faces stochastic inverse demand functions, p˜ = c˜ - Dx, where D is an asymmetric positive semidefinite matrix and the random vector c˜ is distributed according to a normal density with mean E (c˜) and variance Var(c˜). This entrepreneur's preferences are expressed by the utility function u˜ = 1 - e - Φr^ , where φ > 0 is a constant risk aversion coefficient and r^ is stochastic revenue
(a) Set up and justify an appropriate model to represent the pure monopolist's behavior.
(b) Derive the dual specification and give a complete economic interpretation.
(c) Reformulate the problem as a linear complementarity problem.