part J K L M ExerciseTwo firms compete for market shares producing similar goods under imperfect competition. The marketdemand curve is p = 24 – y, where y = y, + y2 is the summation of the firms' outputs. Total costsare TC, = 4y1 for the first company and TC2 = 2y2 for the second company. The second company istherefore more productive than the first. Now answer the following questions:(a) Compute the best response functions of each company. Then compute the Nash equilibrium inquantities. The Nash equilibrium in quantities is also called the Cournot equilibrium. Note that in thiscase the payoffs are given by the profit functions rather than by the levels of utility.(b) Plot the best response functions and the Nash equilibrium.(c) Show that the Nash equilibrium is stable.(d) Assume that the first company is a first mover (even though it is less productive) and chooses itsoutput level before the second company. Find the (Stackelberg) equilibrium in quantities.(e) Plot the Stackelberg equilibrium in the same plot from part (b).(f) Is the Stackelberg equilibrium stable or unstable?(g) Assume that an impartial spectator (which could be a cartel) maximizes joint profits. This isequivalent to an impartial spectator that maximizes a social welfare function that aggregates utilityfunctions, where the payoffs in this case are given by the profit functions. Find the equilibrium level ofjoint output, and also the equilibrium levels of output of each company. Is there a conflict of interestbetween the companies within the cartel?

The essential Cournot assumption is that each firm determines its own quantity while taking the…

(a) Compute the best response functions of each company. Then compute the Nash equilibrium in quantities. The Nash equilibrium in quantities is also called the Cournot equilibrium. Note that in this case the payoffs are given by the profit functions rather than by the levels of utility. (b) Plot the best response functions and the Nash equilibrium. (c) Show that the Nash equilibrium is stable.

(a) Compute the best response functions of each company. Then compute the Nash equilibrium in quantities. The Nash equilibrium in quantities is also called the Cournot equilibrium. Note that in this case the payoffs are given by the profit functions rather than by the levels of utility. (b) Plot the best response functions and the Nash equilibrium. (c) Show that the Nash equilibrium is stable.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter16: Bargaining

Section: Chapter Questions

Problem 16.1IP

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