Oligopoly Models part 2?

Question

The inverse market demand in a homogeneous-product Cournot duopoly is P=100-2(Q1 + Q2) and costs are C1(Q1)=12Q1 and C2(Q2) = 20Q2.

1. Determine the reaction function for each firm.

2. Calculate each firm's equilibrium output.

3. Calculate the equilibrium market price.

4. Calculate the profit each firm earns in equilibrium.

Thank you in advance.

Answer 1

1. Reaction functions are:

Q1=22-Q2/2

Q2=20-Q1/2

2. Equilibrium output:

Q1=16

Q2=12

3. Equilibrium market price

P=44

4. Profits are:

π1= (44 - 12) * 16 = 512

π2= (44 - 20) * 12 = 288