Question

5. Bertrand model: Price competition in simultaneous move homogeneous product duopoly—explain in words. Consider the brick producers again. This time, each firm simultaneously and independently picks the price. Since the product is homogeneous, the consumer buys from the producer offering at a cheaper price. The market demand curve faced by the two firms is P=1 - 50000 (x+y), and costs are C1(x) = 0.02x and C (y) = 0.02y, where firm 1 produces x units and firm 2 produces y units of bricks. What price will each one of them charge in equilibrium? Why not any other price elaborate? How much will be the profit in equilibrium?

Answer 1

In the case of homogenous goods, the firms will charge the price equal to their marginal cost. As both firms have identical cost the prevailing price will be P=MC1=MC2. In this case, P=0.02.

The firm that charges the higher price will lose the market to its competitor as everyone will buy from its competitor. Then each firm will undercut each other prices until any one of them charges its average and marginal price. As both firms have the same technology both have the same costs and the marginal cost of the firms is equal to 0.02. Then at equilibrium, both firms will charge the lowest price possible without making loss is P=MC1=MC2=0.02.

At equilibrium as each firm charges its marginal or average cost, the profit of the firms is zero at equilibrium.