Question

Please help me with this problem

6. Differentiated product Bertrand. Suppose that firm Y produces yellow marbles and that firm W produces white marbles. Further suppose that consumers' tastes are heterogeneous-some prefer yellow marbles while others prefer white ones. Firm-specific demands are given by: The subscripts y and w refer to yellow and white marbles, respectively (a) Suppose both firms have a marginal cost of $15/bag. What are the price and quantity sold (b) Now suppose that firm W has a marginal cost of only $10. What are the new prices and (c) If you are the owner of a firm that is at a comparative cost disadvantage and compete in a by both firms in the differentiated Nash-Bertrand equilibrium? quantities sold by both firms? Bertrand game, would you rather be in an industry with differentiated products or an industry with homogenous products? Why?

Answer 1

"Consider the given problem here there are two producer having their specific demand curves as follows- Q_y = 90 - 3 P_y + P_w & Q_w = 90 - 3 P_w + P_y The Profit fm of both the firm are given by pi_y = P_y Q_y - 15 Q_y, where ""15 Q_y"" be the cost fm pi_y = P_y (90 - 3 P_y + P_w) - 15 (90 - 3 P_y + P_w) = 90 P_y - 3 P^2_y + P_w P_y - 1350 + 45 P_y - 15 P_w = 135 P_y - 15 P_w - 1350 + P_w P_y - 3 P^2_y FOC require Partialdifferential pi_y/Partialdifferential P_y = 0 135 + P_w - 6 P_y = 0 = > 6 P_y = 135 P_w P_y = 22.5 + P_w/6 (1) be the Reaction fm of firm producing similarly the profit fm of a firm producing ""Yellow Marbles"" ""White Marble"" is given by- pi_w = P_w Q_w"

c).

In the “Bertrand Model” with the differentiated good a firm having cost disadvantaged will stray into the industry . Since, there are new customer will still purchase a particular good at the higher price compare the available substitute good. But in the case of the homogeneous good it’s not possible that the two firms will change different price. If a firm will have cost disadvantage will not able to service in to the industry.