Question: The textbook discussion of monopsonistic behavior begins with stating the system of inverse input supply functions,Ps = g + Gs, where G is a symmetric positive semidefinite matrix. Assuming that a pure monopsonist is a price taker on the market for final commodities, with commodity prices p = c, and that he operates a single plant using a linear technology A,
(a) Set up and justify the corresponding primal problem.
(b) Derive the dual problem and explain its meaning as a whole and of each component.
(c) In particular, show the entrepreneur's profit and give an appropriate economic explanation of the dual objective function.
(d) Cast the problem as a linear complementarity problem.