1. Homepage
  2. Exam
  3. [2021] Economics 482 Game Theory and Economics - Midterm Exam - Q2 Cournot Competition

[2021] Economics 482 Game Theory and Economics - Midterm Exam - Q2 Cournot Competition

This question has been solved
Engage in a Conversation

2. The following is a version of the Cournot competition game with four firms, in which the firms simultaneously choose nonnegative quantities of a good to produce. When the firms’ choices are the profile (q1, q2, q3, q4), the price at which the firms sell their output is α q1 q2 q3 q4 if q1 +q2 +q3 +q4 < α; otherwise, the price of the good they sell is zero. Each firm i has a cost of producing qi units of output of ci ×qi, where ci 0; different firms can have different cost functions. A firm’s payoff is its profit, the revenue it gets from selling its output qi minus its cost. CourseNana.COM

1.     (a)  Write down the expression for the payoff firm 1, as function of all of the firms’ choices of quantities, as well as of α and any of the marginal costs ci, for the case in which q1+q2+q3+q4 < α. [Note: other firms’ payoffs will look similar.] (4 points) CourseNana.COM

2.     (b)  Find firm 1’s best response function for this game, for values of (q2, q3, q4) such that q2 + q3 + q4 + c1 < α. [Note: other firms’ best-response functions will look similar.] (6 points) CourseNana.COM

3.     (c)  Suppose that firm 1 has a cost function such that c1 = 0; and that firms 2, 3 and 4 have the same cost function: c2 = c3 = c4 = c. Find a Nash equilibrium of this game in which firms 2, 3, and 4 choose the same quantity as each other (but not, in general, the same quantity as firm 1), with all quantities expressed as functions of α and c. You may assume that each firm chooses a positive quantity in the equilibrium (and, as such, determines its best response as in part (b)), which will be true as long as α is sufficiently greater than c. Remember that since firms 2, 3, and 4 are assumed to choose the same output as each other, you are really only solving for two outputs. (10 points) CourseNana.COM

4.     (d)  Suppose that firms 2, 3 and 4’s cost per unit c increases, while firm 1’s remains at 0. Say whether this makes firm 1’s equilibrium quantity greater or smaller; whether it makes firm 2, 3 and 4’s equilibrium quantities greater or smaller; whether it makes the total quantity produced by all firms greater or smaller; and whether it increases or decreases the price of the good that consumers pay in the equilibrium. (7 points) CourseNana.COM


Get the Solution to This Question

WeChat WeChat
Whatsapp WhatsApp
Economics 482代写,Game Theory and Economics代写,Midterm Exam代写,Nash equilibrium代写,Dominant Action代写,Rutgers代写,The State University of New Jersey代写,Payoff Matrix代写,Economics 482代编,Game Theory and Economics代编,Midterm Exam代编,Nash equilibrium代编,Dominant Action代编,Rutgers代编,The State University of New Jersey代编,Payoff Matrix代编,Economics 482代考,Game Theory and Economics代考,Midterm Exam代考,Nash equilibrium代考,Dominant Action代考,Rutgers代考,The State University of New Jersey代考,Payoff Matrix代考,Economics 482help,Game Theory and Economicshelp,Midterm Examhelp,Nash equilibriumhelp,Dominant Actionhelp,Rutgershelp,The State University of New Jerseyhelp,Payoff Matrixhelp,Economics 482作业代写,Game Theory and Economics作业代写,Midterm Exam作业代写,Nash equilibrium作业代写,Dominant Action作业代写,Rutgers作业代写,The State University of New Jersey作业代写,Payoff Matrix作业代写,Economics 482编程代写,Game Theory and Economics编程代写,Midterm Exam编程代写,Nash equilibrium编程代写,Dominant Action编程代写,Rutgers编程代写,The State University of New Jersey编程代写,Payoff Matrix编程代写,Economics 482programming help,Game Theory and Economicsprogramming help,Midterm Examprogramming help,Nash equilibriumprogramming help,Dominant Actionprogramming help,Rutgersprogramming help,The State University of New Jerseyprogramming help,Payoff Matrixprogramming help,Economics 482assignment help,Game Theory and Economicsassignment help,Midterm Examassignment help,Nash equilibriumassignment help,Dominant Actionassignment help,Rutgersassignment help,The State University of New Jerseyassignment help,Payoff Matrixassignment help,Economics 482solution,Game Theory and Economicssolution,Midterm Examsolution,Nash equilibriumsolution,Dominant Actionsolution,Rutgerssolution,The State University of New Jerseysolution,Payoff Matrixsolution,