Consider two firms (A and B) that produce the similar products, possibly with some degree of product differentiation. Because of brand loyalty, they face the following symmetric demand curves: QA = 12 - 2 PA + PB QB = 12 - 2 PB + PA In addition, MCA = MCB = 2.
(a) First, consider the scenario when there is no product differentiation. What would be the Bertrand equilibrium price in this market? Illustrate your answer using a well-labeled graph.
(b) Now, consider the scenario that there is product differentiation. Solve for Firm A's price reaction function PA = f(PB), and for Firm B's price reaction function PB = f(PA). What are the optimal prices in the market? Calculate output for each firm. Illustrate your answer using a well-labeled graph.
(c) Compare the results with no product differentiation in part (a) with those with product differentiation in part (b).