Question

Market demand is given by
P (Q) = (
100 − Q if Q < 100
0 otherwise
Suppose that two firms both have average variable cost c = $50. Assuming that firms compete
in prices, then:
1. Define the reaction functions of the firms;
2. Find the Bertrand equilibrium;
3. Would your answer change if there were three firms? Why

Answer 1

A) Reaction functions

BR1( P2) : P1 = { 50, P2 <=50

{ P2 -e, if P2>50, where e tends to zero

BR2(P1) : P2 = { 50, P1<= 50,

{ P1-e, if P1> 50

b.) Since Bertrand duopoly , with symmetry, homogeneous products, so at equilibrium, since AC is fixed , so MC = 50

P1 = P2 = MC = 50, ans.)

C) no answer won't change

Bcoz if any firm deviates from price = 50, then it will be non profitable deviation.

No firm will charge price below 50, as it will incur loss.

If it charge price higher than 50, then it will loose it's market share to zero , since consumers will buy from lowest cost firm.