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Homework answers / question archive / The (inverse) demand for a homogeneous product is P = 10-00259, where is total output
The (inverse) demand for a homogeneous product is P = 10-00259, where is total output. Oligopolistic interactions among firms that produce the product are Bertrand. If two or more firms charge the same price, then sales are divided equally among the firms. Firms / and 2 have marginal costs of $5.50 and firm 3's marginal cost is $6.00. In the Bertrand equilibrium, what is each firm's output? 92 93
Given that the product is identical, consumers will purchase the product from the lowest price seller. This will first reduce the price down to the first marginal cost which is $6. But the marginal cost of other two firms is less than $6 so firm 3 will be out of market as the price is reduced below 6 dollars. Finally the price will settle at the marginal cost of 5.50 dollars because it is the marginal cost for both the firms
At this price the market quantity is (10-5.5)/0.0025 = 1800 units which will be divided between the two firms. Therefore
q1 = 900
q2 = 900
q3 = 0
