Question

Let market demand be given by Q(P) = 200 ? P. Each firm’s cost function is C(qi ) = 20qi , where i = 1, 2.

(a) Using the Cournot model, find each firm’s output, profit, and price.

(b) Graph each firm’s reaction function. Show the Cournot equilibrium.

(c) Suppose that the duopolists collude. Find their joint profit-maximizing price, output, and

profit; find each firm’s output and profit.

(d) Does each firm have an incentive to increase output? What is the optimal defection for each

firm? What does this imply about the stability of their collusive agreement?

(e) Suppose that the cost function is now C (qi ) = 20qi + 400. What is the free-entry number of

firms?

Answer 1

a)

P = 200 - Q

TC = 20Q

MC = 20

Competitive Equilibrium

P = MC

200 -Q = 20

Q = 180

P = 20

Cournot Equilibrium:

= (2/3)* 180

= 120

Each firm produces 60 units.

Price = 200 -Q

= 200 - 120

= $80

Profit = TR - TC

= 120*80 - 120*20

= 9600 - 2400

= $ 7200

Each firm profit is $ 3600

b)

C)

If they collude, it implies that they are now monopoly:

P = 200 - Q

TR = 200Q - Q^2

MR = 200 - 2Q

MC = 20

Equilibrium; MR =MC

200 - 2Q = 20

2Q = 180

Q =90

P = 200 - 90

= 110

Profit = TR - TC

=110*90 - 20*90

= 9900 - 1800

= 8100

= 4050 is each firm profit