Question

Given the industry demand QD = 60 - 10.0P and supply function QS = 20.0P. Assuming the industry is organized into a cartel, what is the industry price/output combination that will maximize profits for cartel members? Hint: as a cartel, industry MR = 6 - 0.2Q and, since the industry supply curve represents the horizontal sum of the marginal cost curves for individual producers, MC is the inverse supply curve.

Answer 1

Rewriting the Supply and Demand functions in Q

P=6-QD/10= 6-0.1QD

P=QS/20= 0.05QS

Industry MR= 6-0.2Q

Industry MC= Inverse Supply curve= 0.05Q

Now for profit maximizing condition. MR=MC (Industry will keep producing if MR>MC and stop when MR becomes equal to MC)

6-0.2Q=0.05Q

0.15Q=6

Q=40

Therefore the profit maximizing quantity in the industry=Q=40

Price= 6-0.1Q= 6-4=2$

Therefore the profit maximizing price=2$

Hope it helps. Do ask for any clarifications if required.