Oligopolists?

Question

1. Two oligopolists are facing the following market demand curve:

Q=2600 – 400P

With MC=ATC=2.

a) Find Reaction Curves and graph them

b) Find Cournot solution. Does either firm have a reason to change its quantity of output? Why or why not?

c) Using a price-quantity diagram, compare Cournot, Monopoly (Cartel) and competitive solutions. Calculate total profits in the market for each scenario.

Answer 1

a)

Q=2600-400P

400P=2600-Q

P=6.5-Q/400

Q=A+B

P=6.5-(A+B)/400

MC=2

MR=MC

MR=(TR)'

TR(A)=P*A=6.5A-A²/400-BA/400

MR(A)=6.5-A/200-B/400

Since costs are symmetrical MR(A)=MR(B) ; TR(A)=TR(B), so

MR(B)=6.5-B/200-A/400

(A)

MR=MC

6.5-A/200-B/400=2

4.5-B/400=A/200

A=900-B/2 <<Reaction function for A

(B)

B=900-A/2 <<Reaction function for B

b)

B=900-A/2= 900 - 450 + B/4

3B/4=450

B=600

A=600

Q=A+B=1200

P=6.5-Q/400

P=6.5-3=3

c)

Perfect competition (for two firms!!!) Profit=0 so TR=TC

6.5Q-Q²/400=2Q

4.5Q-Q²/400=0

Q(4.5-Q/400)=0

4.5=Q/400

Q=1800 or 900 each

P=6.5-4.5=2

Profits=0

Cartel(Monopoly) for two firms A=B so

Q=2A; MC=2; P=6.5-A/200 ; TR=6.5A-A²/200; MR=6.5-A/100

MR=MC

6.5-A/100=2

A=4.5*100=450=B

Q=900

P=6.5-2.25=4.25

Profits=(4.25-2)*900 = 2.25*900 = 2025 all or 1012.5 each

Cournout profits=TR-TC= (3 - 2)*600 = 600 each or 1200 total profits.