Question

Two firms are considering producing a new product, tempered glass for the auto market. They will make the same product and face the same demand curve, given by p = 100 − 4Q, where p is in dollars per pound of glass produced and Q is thousands of pounds produced per month. Firm 1 has marginal cost MC₁ = $5 per pound, while firm 2 has MC₂ = $10 per pound.

If the firms engage in Bertrand price competition,

(a) What will be the resulting price in the market?

(b) How much output will be produced by each firm?

(c) What is each firm's producer's surplus?

Answer 1

This is Bertrand model, and each firm tries to cut down price until it becomes equal to the marginal cost of production (MC).

a)

Since marginal cost of firm 2 is larger than the marginal cost of firm 1. Thus, firm 2 would be producing zero output.

P = MC

is condition for equilibrium price in Bertrand model.

Price shall be $ 5

b)

Firm 2 will produce zero output.

output of firm 1, P = MC

100 - 4Q = 5

95 = 4Q

Q = 95/4

= 19

c)

Since price is equal to MC, and MC is constant. Thus, Firm does not earn producer surplus.