Question

5. Let market demand be given by the demand curve Q(p) = 200 ? p . Each

firm’s cost function is TC(qi) = 20qi; i =1, 2.

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

(b) Graph each firm’s best-response function. Show the Cournot equilib- rium.

(c) Suppose that the duopolists collude. Find their joint profit maximizing price, output, and profit. Also find each firm’s output and profit.

(d) Does each firm have and incentive to increase output? What does this imply about the stability of the collusive agreement?

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

d)

There would not be incentive to increase output as these firms getting maximum profits with existing strategy. profits may rise if only one firm deviates, hence incentive remain over there for defecting.