Problem
For a given production possibility set Z, we say that z ∈ Z is efficient if there is no z' ∈ Z such that z' ≥ z and z' ≠z. Suppose that Z is convex and has the property that if z and z' are both in Z and a. ∈ (0, 1), then a.z+ (1-a.)z' is not efficient. Show that this implies that, for a competitive firm facing strictly positive prices p, the solution to FP(p) is unique. Construct a parallel definition for input requirement sets V(y) and give a parallel result concerning the uniqueness of solutions for FCMP( w, y ).
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.