Cournot model

Question 1

Assumptions

Answer 1

Two firms
Compete via choosing their quantities (simultaneously)
Face same inverse demand curve
Different cost functions

Question 2

How do firms pick their quantity

Answer 2

They form an expectation of the other’s quantity. They then react optimally to this.

Question 3

expectation of quantity 2 varies

Answer 3

As expectation varies, firm 1’s response will vary. This is captured by their reaction function f1(.).

Question 4

reaction functions

Answer 4

f1(q2e)
f2(q1e)

Question 5

Cournot equilibrium

Answer 5

q1c is firm 1’s best quantity when it expects firm 2 to pick q2e=q2c. And vice versa. Graphically where there two reaction curves meet

Question 6

How to get the reaction function

Answer 6

For firm 1:
Solve MC = MR. Then get q1 as the subject, this will be as a function of q2. This is the reaction function

Question 7

Requirements of cournot equilibrium

Answer 7

Each player is playing a best response to their beliefs.
The beliefs of the players about their opponents are correct.