Question: differentiated bertrand competition versus price leadership the demand for two...
Differentiated Bertrand competition versus price leadership. The demand for two brands of laundry detergent, Wave (W) and Rah (R), are given by the following demands:
Qw =80–2pW +pR QR =80–2pR +pWThe firms have identical cost functions, with a constant marginal cost of 10. The firms compete in prices.
(a) What is the best response function for each firm? (that is, what is firm W's optimal price as a function of firm R’s price, and vice-versa?) What is the equilibrium to the one-shot pricing game? What are the profits of each firm?
(b) Suppose the manufacturer of Wave could commit to setting pw before the manufacturer of Rah could set pR. How would this change the equilibrium? What are the profits of each firm in this case? Should Wave take advantage of this commitment possibility? Why or why not?
(c) Is there a first or second-mover advantage in this game? First-mover advantage is like the conventional Stackelberg quantity-leadership story, while second-mover advantage is reversed. Explain the intuition for your answer, and compare / contrast with the Stackelberg quantity-setting story.