CoasianBargaining Problem

Consider two businesspeople who own adjacent stores in a small shopping center. Bridget owns a Ritual Salon and knows that her clients and staff enjoy listening to music during their appointments. Genevieve owns Breath and Body Yoga and Meditation Studioand knows that music is distracting to her clients as they practice.

Bridget benefits from turning up the volume according to the function MB = 12 - 0.3*V, where V is the volume level on her speaker.Genevieve loses from each increase in music volume according to the function MC = 0.5*V. Using these functions, answer the following questions about Coasian bargaining.

(a) First, find the socially optimal level of volume. Next, find Bridget's optimal volume level if she set the volume without regard to Genevieve. What volume level would Genevieve choose, ignoring Bridget?

(b) Now suppose that Bridget and Genevieve can costlessly bargain over the volume level. Consider the volume levels V = 5, 10, 15, 20, 25. If Bridget owned the rights to set the volume, at which of these levels would she be willing to accept the bribe that Genevieve would be willing to pay for reducing the volume level? What about the case where Genevieve owned the rights?

(c) Show that regardless of who holds the rights to set volume levels, the two women will reach a bargaining agreement at the socially optimal level found in part a. In your own words, explain why the results of Coasian bargaining and socially optimizing are the same. (Hint: you might look at the optimality condition for each situation.)

(d) Describe in your own words or graph the effect on the outcome if Genevieve were to claim that her marginal cost of increasing volume was higher than it actually is?