Question

25.) Duopolists face a market demand curve given by P = 90 - Q where Q is total market demand. Each firm can produce output at a constant marginal cost of 30 per unit. There are no fixed costs. If the duopolists behave, according to the Bertrand model, determine the (1) equilibrium price, (2) quantity, and (3) economic profits for the total market and (4) the consumer surplus, and (5) dead weight loss.

Answer 1

Bertrand developed two firms called duopoly model in 1883. it differ from famous Cournot’s duopoly model in which firms choose their optimal quantity produced instead of prices. contrary to this Bertrand assumed that each firm expects that the rival will keep its price constant, irrespective of its own decision about pricing.

Thus each firm is faced the same market demand, and aims to own profit maximization on the assumption that the price of the competitor will remain constant. So there is perfect competition between both firms and both charges price equal to marginal cost. Note that Bertrand’s model does not lead to the joint profit maximization due to the fact that firms behave naively, by always assuming that their rival will keep its price fixed. hence they never learn from past experience where rival did not keep its price constant. The industry profit could be maximised if they recognized their dependence and past mistakes, and abandoned the Bertrand pattern of behaviour.

In Bertrand model, two firms set price equal to marginal cost.  

(1) equilibrium price will be 30

(2) quantity= 60 since (90-Q=30)

(3) economic profits for the total market = 0

(4) the consumer surplus = Q*(price-price at Q=0)/2= 60*(90-30)/2=1800

(5) dead weight loss=0 since it works as perfect competition.