Question

An industry consists of two firms with identical demand function ? = 100 − ??, where ?? = ?1 + ?2. Both firms have identical cost ?? = 40??, where ? = 1,2. Both firms pay attention to the behaviour of their competitor in determining the output produced, and both firms make their decision simultaneously (no one moves first).

(a) If both firms decide to compete in determining their outputs, find the profit maximizing q and P and calculate the profit of each firm!

(b) If both firms collude and form a cartel and act as a monopolist, find the profit maximizing q and P and calculate the profit of each firm!

(c) In one graph, show and compare the above competitive and collusive solutions.

(d) In real life, which solution usually prevails? Compete or collude? Explain!

Answer 1

Answer:

(a) Given the identical demand function ? = 100 − ??, where ?? = ?1 + ?2.

Thus total revenue for firm-1, TR=P*q1=100q1-q1²-q1q2

and total revenue for firm-2, TR=P*q2=100q2-q2²-q1q2

Therefore MR for firm-1, MR1=100-2q1-q2 and MR for firm-2, MR2=100-2q2-q1

But the identical cost is given as Ci=40qi thus marginal cost, MC=40

The profit maximizing condition for firm-1: MR1=MC=>100-2q1-q2=40=>2q1+q2=60=>q1=(60-q2)/2

Here both the firms shall react to each other level of output and eventually they will produce where q1=q2

Thus, q1=q2=q and 2q1+q2=60=>3q=60=>q=60/3=20 and therefore QT=q1+q2=20+20=40

The profit maximizing price, P=100-QT=100-40=60

Thus, the maximum profit for firm-1=(P-MC)*q1=(60-40)*20=400 and

the maximum profit for firm-2=(P-MC)*q2=(60-40)*20=400.

(b) If they make cartel then the market inverse demand is P=100-Q

Thus, TR=100Q-Q² and MR=100-2Q

We know that the profit maximizing condition is given by MR=MC=>100-2Q=40=>Q=30

And profit maximizing price, P=100-Q=100-30=70

thus the maximum profit=(P-MC)*Q=(70-40)*30=900

(c) The following diagram shows that collusive (with cartel) is more profitable than the competitive solution.

(d) In real life, mostly collusion prevails because in the collusive market the producers usually charge more price earning more profit than the independent production.