Answer to Question #318219 in Microeconomics for cartels

Question

A two-firm coal cartel that produces at a constant marginal cost of £22 faces a market inverse demand curve of P = 95 – 0.43Q. Initially, both firms agree to act like a monopolist, each producing 42.44 tonnes of coal. If one of the firms cheats on the agreement (assuming the other firm is compliant and continues to produce at 42.44 tonnes), how many tons of coal will the cheating firm produce?

Answer 1

A firm maximises its profits and quantity when

MR=MC

TR=P$\times$ Q

=(95-0.43Q)$\times$Q

TR=95Q-0.43Q$^2$

MR=$\frac{dTR}{dQ}$95Q-0.43Q$^2$

MR=95-0.86Q

MR=MC,where MC=22,therefore

95-0.86Q=22

0.86Q=73

Q=84.88 (optimal and max Q to be produced)

since each is to produce 42.44 which is half of the optimal Q when the one firm cheats it will opt to produce the maximum profitable quantity and therefore it will produce ,Q=84.88