Cournot Model

Question 1

Define Cournot Model

Answer 1

Simultaneous Quantity Setting

Question 2

How do players determine quantity?

Answer 2

Player one needs to maximise his payoff, given the strategy that player two might choose..

Player two must do the same,

Question 3

What is the reaction function for player 1, given what player 2 is doing?

Answer 3

Say player 2 chooses strategy a2 E A2, then player one must maximise pay off by basing their own strategy off a2.

a2 is fixed

Max          P1(a1, a2)
a1 E A1

Question 4

How do we solve the reaction functions?

Answer 4

Solve for a1 in terms of a2:

a1= R1(a2).

Solve for a2 in terms of a1:

a2= R2(a1).

If a1 and a2 are a solution to both reaction functions, then they’re a nash equilibrium.

Question 5

Define cournot equilbirum

Answer 5

Each firm is maximising its profits, given what it believes the other firm will set its output as.

Neither firm will find it profitable to change their output once it discovers the choice actually made by the other firm.

Question 6

How do we find price?

Answer 6

Rearrange the quantity function.

Question 7

How to find marginal revenue?

Answer 7

Derive the Total Revenue function.