Cournot Competition with Two Firms

inverse demand function p(Q)b-aQ, Q

q

1

+

q

2

a ∈ [1, 5]

1.

b ∈ [1, 5]

5.

profit function for firm i∈{1,2}:

π

i

(

q

1

,

q

2

)=(p(Q)-

c

i

)

q

i

c

i

represents the marginal cost of firm i

c

1

∈[0,3]

1.

c

2

∈[0,3]

1.

plot 45° line

model

p(Q) = 5.-1.Q

π

1

(

q

1

,

q

2

) = (p(Q) - 1.)

q

1

π

2

(

q

1

,

q

2

) = (p(Q) - 1.)

q

2

Cournot equilibrium

*

(

q

1

)



b-2

c

1

+

c

2

3a

= 1.33333

*

(

q

2

)

=

b+

c

1

-2

c

2

3a

= 1.33333

equilibrium price: 2.33333

red line: best response of firm 1 for

q

2

green line: best response of firm 2 for

q

1

point: Cournot equilibrium

This Demonstration illustrates a simple Cournot competition in which there are only two firms, and the inverse function is

p(

q

1

,

q

2

)=b-a(

q

1

+

q

2

)

. The horizontal axis represents

q

1

and the vertical one represents

q

2

. A red line and a green line represent the best response of firms 1 and 2 for the production of another firm, respectively. Cournot equilibrium corresponds to the purple point at which two best response lines intersect.