Question

Suppose that companies A and B have constant average costs and marginal costs, so we have the following: MC = 12 and MC = 10, The demand for the production of the companies is

QD = 1000-40P

a) If the companies practice Bertrand competition, what will be the market price of a Nash equilibrium?
b) What will be the benefits of each company?
c) Will this balance be efficient in the Pareto sense?

Answer 1

A)In Bertrand competiton with homogeneous good, the firm with lower price gets entire market.

Firm B has lower cost Equal to 10, so it can capture whole by charging any price lower than 12.

Equilibrium price=11

Q=1000-40*11=560

B) Benefit of firm A=0

Benefit to firm B=(11-10)*560=560

C) pareto efficent is a situation,from which no one can better off without worsening off atleast one.

No, This is not Pareto efficent,as if

P=20, q=1000-40*20=200

Qa=100,Qb=100

Profit A=(20-12)*100=800, Profit B=(20-10)*100=1000

So both firm gets benefit from changing the price ,so p=11 ,is not Pareto efficent.