2. Consider a homogeneous product duopoly in which the (inverse) market demand i

Question

2. Consider a homogeneous product duopoly in which the (inverse) market demand is given by P = 20 – Q, where q1 + q2 = Q, and q1, q2 are the outputs produced by firms 1 and 2 respectively. Each firm has constant marginal and average cost equal to 2. (a) Find the Bertrand equilibrium prices, quantities and profits for firms 1 and 2. Explain briefly why this is a Nash equilibrium in which prices are the strategic variables. (7 marks) (b) Find the Cournot equilibrium prices, quantities and profits for firms 1 and 2. Is this a Nash equilibrium? (7 marks) (c) How does the outcome in (b) compare to that of the Stackelberg model, in which firm 1 is the leader and firm 2 is the follower. (Calculations are not required, but may be provided if desired.) (6 marks)

Explanation / Answer

a)

Bertran equilibrium is equal to the competitive market:

P =MC

20-Q = 2

Q = 18

P =2

Profit = 18*2 -18*2

       = 0

Both firms get economic profits only.

B)

Cournot output

= (2/3) *Competitive output

=(2/3) (18)

=12

P = 20 -12

= 6

Each firm produce 6 output

Profit of firm 1 = 6*6 - 6*2

                    =36 -12

                   =24

Similarly firm 2 also earns profit equal to 24

This is Nash equilibrium, both firms seek to maximize their profits provided strategy of other firm is given.

C)

In case of Stackelberg Model, one firm recognises that other firm will react to its decision. Thus, firm takes into account the reaction function of other firm.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.