N3

5. Suppose Ontario's healthcare system is subject to a physician cooperative (i.e., cartel) whose objective is to maximize physician salary by limiting physician supply. Letting denote the number of physicians employed by the healthcare system, the physician salary curve is () = 200,000 + 20 0.001 2 while the competitive physician inverse supply curve is () = 200,000 + 5. The first function represents the salary arising for a given level of employment while the latter represents the minimum salary required to induce a given level of employment to be supplied.

(c) Let denote the number of physicians at which physician salary is maximized and let denote the efficient number of physicians that would arise under a competitive equilibrium. Derive the values of and and illustrate them in an appropriate diagram depicting () and ().

(d) Let () be the inverse physician supply curve arising from the cooperative's efforts to limit physician supply. Redraw your diagram of Part (c) and modify it to illustrate the cooperative equilibrium. Derive the expression for ().