Screenshot 2023-11-28 213735

A monopolist’s Inverse demand function Is estimated as P=150 — 3Q. The company produces output at two facllities; the marginal cost of producing at facility 11s MCy(@Qy) = 6@, and the marginal cost of producing at facllity 2 Is MC3(Q)) = 2Q5. a. Provide the equation for the monopolist’'s marginal revenue function. (Hint:Recall that 1+ Q> = Q) wRa=[ 150]@-[_6jl@a-[ 6o b. Determine the profit-maximizing level of output for each facility. Output for facility : [ 5] @ Output for facility 2: [ 15| @ c. Determine the profit-maximizing price. s[ %o Explanation a. Since the Inverse demand Is P=150 - 3Q;- 3@ marginal revenue Is MR(@Q) =150 - 6Q;- 6Q 2. b. Solving these two equations simultaneously ylelds Q;=5and Q>=15. 150 -6Qy-6Q2>=6Qy 150 -6Qy-6Q2=2Q7 c. Glven @Qy=5and Q>=15, P=150 - 15 - 45 = $90.