ECON 132 Lecture Notes - Lecture 11: Marginal Revenue, Demand Curve, Marginal Cost

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Published on 26 Mar 2019
School
Department
Course
Cournot Duopoly Model 1 of 4
Prepared by Genevieve Peters UCSD Economics 132
Background
The basic Cournot duopoly model is based on the following assumptions:
Firms produce a homogenous product.
Firms know their market demand curve.
Firms choose output to maximize profits.
Firms choose their output levels simultaneously.
Each firm takes the output of its competitor as given.
Variables
1
Q= firm 1’s output )( 11 QTC = firm 1’s total cost function
2
Q= firm 2’s output )( 22 QTC = firm 2’s total cost function
21 QQQ = total market output ),( 21 QQP = market inverse demand curve
Objective Functions
Firm 1’s objective function is: )(),(),( 11121211 QTCQQQPQQ
Firm 2’s objective function is: )(),(),( 22221212 QTCQQQPQQ
First order Conditions
Each firm seeks to find the maximum of it’s own profit function:
Firm 1’s FOC is: 0
)(
),(
),(),(
1
11
211
1
21
1
211
Q
QTC
QQPQ
Q
QQP
Q
QQ
Firm 2’s FOC is: 0
)(
),(
),(),(
2
22
212
2
21
2
212
Q
QTC
QQPQ
Q
QQP
Q
QQ
The first order conditions for each firm tells the firm to choose their own output
so that their own marginal revenue equals their own marginal cost.
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