Question

Suppose that the demand for marbles is given by Q= 80-5p, where Q is measured in bags of marbles. There are two firms that supply the market, and the firms produce identical marbles (i.e., they are homogenous products). Firm 1 has a constant

marginal cost of $10.00/bag, while firm 2 has a constant marginal cost of $5.00/bag.

5. Homogenous product Bertrand with 3 firms, Now suppose that there are three firms in the market, all producing identical marbles. Firms 1 and 2 are as in question 1 above, and firm 3 has a marginal cost of $5.00bag. Now what prices will the firms set in equilibrium, and how many bags of marbles will each firm sell?

Answer 1

In a Bertrand model, each firm competes against prices. If the firms are producing a homogeneous product, then the price war will last until the price is equal to the marginal cost of the high-cost firm. In this case, if three firms last the price war and each sell definite quantity at the equilibrium, then the market solution will be such that

$P=MC_1=10$

Therefore, the total market demand will be

$Q=80-5p=80-50=30$

Each firm will produce the same quantity of 10 units each at the equilibrium. In this case firm, 1 and two will earn a positive profit, and firm one will not earn zero profit.