Question

Problem 4. Bertrand Competition with Different Costs Suppose two firms facing a demand D(p) compete by setting prices simultaneously (Bertrand Competition). Firm 1 has a constant marginal cost ci and Firm 2 has a marginal cost c2. Assume ci < C2, i.e., Firm 1 is more efficient. Show that (unlike the case with identical costs) p1 = C1 and P2 = c2 is not a Bertrand equilibrium.

Answer 1

It is given that cc This indicates that, firm 1 is more efficient than firm 2 pi Ci and p2 = c2 From this, Bertrand Nash equilibrium is not achieved Firm 1 is more efficient and incurs a cost of cj. Cost of firm 2 is c2. Therefore, firm 1 would increase price up to c2. As a result of this, profit eaned by firm 1 increases. At this price of c2, firm will not be able to sell any output or it cannot earn any positive economic profit. Fimm 2 will not incur any loss too. Therefore, under this situation, firm 1 would be made better off by increasing price. Therefore, charging a price p = c1 cannot be a Nash equilibrium Nash equilibrium could be obtained when pi c2- 1. p2= c2. Other than this, firm 1 could charge a price which is less than c2. Here, lower price is the minimum price and firm 2 can charge c2.