Question

A two-firm industry is characterized by Cournot competition. The two firms face a market demand given by P = 200 - 2(QA + QB), where QA is firm A's output and QB is firm B's output. Each firm produces the product at a constant marginal cost of $40 (i.e. MC = 40)

a.) What is firm 1's reaction function?

b.) How many units of output does firm A produce?

c.) what is the market price of each firm?

d.) if the cartel acts like a monopoly, what is the market price?

Answer 1

(a) The reaction function of a firm is the quantity it will produce to maximise profits,but this value is a function of the quantity produced by the other firm, that is, it depends on the quantity produced by the other firm.

The profit function of Firm A is given as:

The profit maximising condition is:

This relation above, where the output of Firm A is expressed as a function of the output of Firm 2, is called the reaction function of Firm A.

(b) Similarly, we find the reaction function for Firm B as follows

The profit maximising condition is:

This is the reaction function of firm B.

Substituting the reaction function of firm B in the reaction function of firm A, we get:

Since both firms have the same MD=C and similar reaction functions, we have Q_B = 26.67

(c) Both firms sell at the same market price given by the demand function faced by them.

(d) Now if both firms form a cartel and act like a monopoly, we have the following price and profit functions:

(Since they act as monopoly, there is only one output, that is, Q)

Profit maximisation condition implies MR = MC, that is, the first derivative of profit function equals zero.

Using this value of output, we find the market price as follows

Therefore, we see that in the earlier case, higher quantity was produced by both firms (53.34 units) and supplied at a lower price (93.32). A cartel functioning as a monopoly leads to higher prices (140) and lesser quantity produced and sold (30).