Question

Consider an oligopolistic market with demand represented by P=250-5Q. Assume that the MC for each firm is MC=50.

a)       If the firms each have the same MC and the market is characterized by price competition (like Bertrand competition), what will be the equilibrium price? Quantity? Industry profits?

b)      If the few firms are, instead able to perfectly collude, what will be the equilibrium price? Quantity? Industry profits?

c)       If the market is characterized by quantity competition (Cournot) and there are TWO firms, what will be the equilibrium price? Quantity? Industry profits?

d)      If the market is characterized by quantity competition (Cournot) and there are FIVE firms, what will be the equilibrium price? Quantity? Industry profits?

Answer 1

a)

In the case of price competition, each firm sets its output level such that P=MC

So,

Market price=MC=50

We are given

P=250-5Q

Put P=50

50=250-5Q

Q=40

Total industry cost=Q*MC=40*50=2000

Total industry revenue=P*Q=50*40=2000

Profit=Total Cost-Total Revenue=2000-2000=0

b)

Industry will behave like monopolist.

P=250-5Q

Total Revenue=TR=(250-5Q)*Q=250Q-5Q^2

Marginal Revenue=MR=dTR/dQ=250-10Q

Set MR=MC for profit maximization

250-10Q=50

10Q=200

Q=20

P=250-5Q=250-5*20=150

Total Cost=TC=MC*Q=50*20=1000

Total Revenue=TR=P*Q=150*20=3000

Total Profit=TR-TC=3000-1000=2000

c)

Since firms have similar and constant marginal cost, We can apply Counot theorem

If market demand is given by

p=a-bQ

and each of the N firms has constant marginal cost c, then equilibrium price is given by

Here N=2, a=250, c=50, b=50

P=250-5Q

350/3=250-5Q

400/3=5Q

Q=80/3

So, output of each firm=(80/3)/2=40/3

Total Cost=TC=MC*Q=50*80/3=4000/3=1333.33

Total Revenue=TR=P*Q=(350/3)*80/3=3111.11

Total Industry Profit=TR-TC=3111.11-1333.33=1777.78

d)

Here N=3, a=250, c=50, b=50

P=250-5Q

100=250-5Q

150=5Q

Q=30

Output of each firm=Q/3=30/3=10

Total Cost=TC=MC*Q=50*30=1500

Total Revenue=TR=P*Q=100*30=3000

Total Industry Profit=TR-TC=3000-1500=1500

ii)

Here N=5, a=250, c=50, b=50

P=250-5Q

250/3=250-5Q

500/3=5Q

Q=100/3

Output of each firm=Q/5=20/3

Total Cost=TC=MC*Q=50*100/3=1666.67

Total Revenue=TR=P*Q=(250/3)*(100/3)=2777.78

Total Industry Profit=TR-TC=2777.78-1666.67=1111.11