Question

Suppose that the incumbent firm faces an inverse demand function P = 110 − Q, and has a constant marginal cost equal to 10. The potential entrant has a constant marginal cost equal to 10 and a fixed cost of 100. The incumbent firm first determines its quantity and commit to this amount. The potential entrant then determines whether it would enter and the quantity.

1. Given that the entrant enters and the incumbent's quantity q1, the entrant's optimal strategy?
2. What is the minimum level of the incumbent's quantity that the entrant decides to stay out of the market?
3. Should the incumbent use the limit pricing strategy to deter the potential entrant to enter?

Answer 1

a)

Let the output of incumbent firm be Q1

and then output of entrant be Q2

P=110-Q

P=110-Q1-Q2

Total Revenue in case of entrant=TR2=P*Q2=110Q2-Q1Q2-Q2^2

Marginal Revenue=MR2=dTR2/dQ2=110-Q1-2Q2

Set MR2=MC2

110-Q1-2Q2=10

2Q2=100-Q1

Q2=50-0.5Q1 (Entrant's optimal response)

b)

Total Cost of entrant=10Q2+100

Profit of entrant is given by

Profit fot entrant=P*Q2-(10*Q2+100)=(P-10)*Q2-100

We know that P=110-Q1-Q2

Profit fot entrant=(110-Q1-Q2-10)*Q2-100

Set Q2=50-0.5Q1 (entrant's response output)

Profit fot entrant=[110-Q1-(50-0.5Q1)-10]*(50-0.5Q1)-100

Profit fot entrant=(50-0.5Q1)^2-100

Entrant will stay out of market if 0

(50-0.5Q1)^2-100=0

50-0.5Q1=10

0.5Q1=40

Q1=80

If incumbant sets a outut of 80 units, entrant will stay out of market.

iii)

If incumbant produces 80 units, then output of entrant is zero,

P=110-Q1-Q2=110-80-0=$30

It is above marginal cost of incumbant. So, incumbant can still make a positive profit.

So, incumbant can go for limit pricing.