# Cournot Oligopoly

Two companies make decisions about their planned output simultaneously and the decisions are made independent of what the competition will do. One company makes a decision about their output and this decision will have no impact on the decision of the competition’s planned output. With a cournot duopoly output is greater than in a monopoly but less than perfect competition. Meaning
price is lower with cournot duopoly than monopoly but still higher than perfect competition.

Cournot is a type of olibopoly that is best defied using these four charateristics.
1. There are few firms in the market serving many consumers.
2. The firms produce either differentiated or homogeneous products.
3. Each firm believes rivals will hold their output constant if it changes its output.
4. Barriers to entry exist.

## Best-Response (Reaction Function) for Cournot Duopoly

This is a function that defines the profit-maximizing level of output for a firm for given output levels of another firm. This equations relates the profit-maximization levelt of output of firm 1 (Q1) to the output of firm 2 (Q2)

Q1 = r2(Q2)
Q2 = r2(Q1)

Linear (inverse) Demand Function
P = a - b(Q1+Q2)

Cost Function
C1 (Q1) = c1 Q1
C2 ( Q2) = c2 Q2

Reaction Functions
Q1 = r1(Q2) (a-c1) / 2b - Q2 / 2
Q2 = r2(Q1) (a-c2) / 2b - Q1 / 2

## Question

Suppose the inverse demand function for 2 Cournot duopolists is given by :

P = 5 – (Q1 + Q2)

1. What is each firm’s marginal revenue?
2. What are the reaction functions for the two firms?
3. What are the Cournot equilibrium outputs?
4. What is the equilibrium price?

1. MR1(Q1,Q2) 5 – Q2 – Q1
MR2(Q1,Q2) 5 – Q2 – Q1

2. Q1 = r(Q2)5/2 - Q2/2
Q2= r(Q1) = 5/2 - Q1 / 2

3. Solve for the unknowns from above

Q1= 5/2 - ( 5/2-Q1/2) / 2
Q1 = 5/3
Q2 = 5/2 - (5/3) /2
Q2 = 5/3

4. Q = Q1 + Q2 5/3+ 5/310/3
P = 5 - (10/3)
P = 5/3