A homogenous product is produced by n rival firms. They have the same costs. The market demand is: P = 80 – Q where: Q = q1 + q2 + ... + qn %3D - The firms' total cost equations are: TC; = 50qi (I = 1, 2, .., n) a. In estimating its marginal revenue, each firm takes all its rivals' output as given and maximizes profit subject to that assumption. Write firm 1's total revenue and marginal revenue equations. TR1 = MR1 = b. Set MR1 = MC; to derive the equation of firm l's reaction curve, Q:*(Q2, Q3, write the reaction curve equation for firm 2. Qn). Also Qi*(q2, q3, 94, - qn) = ... q2*(qı, q3, q4, . qn) = %3D ... c. Solve for the profit-maximizing price and output per firm as functions of n. (Check your earlier result for the monopoly and duopoly cases: n = 1 and n = 2.) q* : %3D P* =

A homogenous product is produced by n rival firms. They have the same costs. The market demand is: P = 80 – Q where: Q = q1 + q2 + ... + qn %3D - The firms' total cost equations are: TC; = 50qi (I = 1, 2, .., n) a. In estimating its marginal revenue, each firm takes all its rivals' output as given and maximizes profit subject to that assumption. Write firm 1's total revenue and marginal revenue equations. TR1 = MR1 = b. Set MR1 = MC; to derive the equation of firm l's reaction curve, Q:(Q2, Q3, write the reaction curve equation for firm 2. Qn). Also Qi(q2, q3, 94, - qn) = ... q2(qı, q3, q4, . qn) = %3D ... c. Solve for the profit-maximizing price and output per firm as functions of n. (Check your earlier result for the monopoly and duopoly cases: n = 1 and n = 2.) q : %3D P* =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Finding a solution to this problem is hard because I’m not exactly sure how to generalize the cournot model. Could I have help please.

d. Calculate revenue, cost, and profit. Then find the combined output, revenue, cost, and (N =
Пі + П), profit:
Ri
%3D
C =
П
R =
C =

A homogenous product is produced by n rival firms. They have the same costs.
The market demand is:
P = 80 – Q
where: Q = qi + q2 + ... + qn
The firms' total cost equations are: TCj = 50qi
(I = 1, 2, ..., n)
a. In estimating its marginal revenue, each firm takes all its rivals' output as given and
maximizes profit subject to that assumption. Write firm 1's total revenue and marginal
revenue equations.
TR1 =
MR1 =
b. Set MR1 = MC; to derive the equation of firm 1's reaction curve, Q1*(Q2, Q3, ...,
write the reaction curve equation for firm 2.
Qn). Also
Q1*(q2, q3, q4,
...
("b
q2*(qı, q3, q4, ...
qn) =
c. Solve for the profit-maximizing price and output per firm as functions of n. (Check your
earlier result for the monopoly and duopoly cases: n = 1 andn = 2.)
q*
P* =

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