Suppose an industry has a duopoly structure. Where the duopoly engage in Bertrand competition (competition in prices).

Suppose both agents have the same cost of production given by

ci(Qi) = 6QiforQi 0,and i {1,2 }

Agentigets a residual demand given by

502p if pi < pj

Q(pi) =1/2(502pi) if pi = pj

0 ifpi> pj

(a) Find the best response function for each duopolist. (Hint: find the optimal price for each agent

while taking the price of the other agent as given.)

(b) Find the price and quantities in the Bertrand-Nash equilibrium.

(c) What can you say about the consumer surplus in the Bertrand equilibrium?