Question

Consider the Bertrand competition where Firm A's profit function is XA(PA, PB)= (pA)(QA(PA,PB))-(C(QA(PA,PB))) where QA(PA,PB) is the demand for firm A's product given the posted prices. Firm A's and B's products are identical, so consumers will go to the lowest price. QA(PA,PB)= Q(PA) if PA<PB, (1/2)(Q(PA)) if PA=PB, and 0 if PA>PB. where Q(P)=15.5-0.5P. However, make the change that firm B’s cost function is CB (Q) = 2Q. Firm A’s cost function remains the same at CA (Q) = Q. Furthermore, constrain prices to be divisible only into cents. So, there is a discreteness imposed on the strategy choice.
a) Determine firm A’s best response function P*A (PB). Argue your answer.
b) Determine firm B’s best response function P*B (PA). Argue your answer.
c) What is the price at which output goods are sold in the Bertrand Nash equilibrium? Carefully argue your answer.
d) How much demand is firm A facing in the Bertrand Nash equilibrium?

Answer 1