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

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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.