Question

Exercise: Consider a market in which two firms i = 1, 2 produce a homogeneous product at constant marginal cost c = 4, facing total demand described by the linear inverse demand curve P = 16 − Q. First assume that the firms compete by simultaneously choosing prices a la Bertrand.

1. Suppose that F1 expects F2 to set some price p2 above the marginal cost c but below the monopoly price p m. What is F1’s best response BR1(p2) to this price p2?

2. What is the Nash equilibrium price, and why? What are firm profits at this price?

3. Suppose that F2’s marginal cost increases to 5, holding F1’s marginal cost constant at 4 as above. Applying the “undercutting” logic discussed in lecture, what will be the new equilibrium price? Will either firm earn positive profit?

Answer 1

1)

Under the Bertrand model, each firm tries to undercut other ones. Thus, temporarily whole output gets transferred to one to another.

F1 would set price would be less than the price of F2, Hence, the price of F1 would be less than Price P2 of F2.

Price of F1 = c or MC < P1 <P2.

2)

Nash equilibrium will be set up where P = MC.

Each will try to undercut others and eventually reaches where each charge price equal to the Marginal cost of production.

16-Q = 4

Q = 12

Each produces 6 units.

Nash equilibrium: ( 6,6)

Both earn only zero economic profit.

3)

F2 cost is larger than F1 cost, Thus, under competition firm, F2 would be out of the market.

F1 would charge price which be less than cost of F2. Hence, There will be positive profit for firm F1 only if it continue to charge price more than its Marginal cost and less than marginal cost of F2.