<p>The temporal constraints (i.e. what happens in a period) are not very clear in this question. It is likely that the good sold is not a durable good and hence there is no "leftover demand" between periods, demand is simply 'reset'.</p>

<p>In period 2 leftover demand appears because firm B assumes firm A will not change its production from period 1.</p>

<p>Then in period 3 firm A will best respond to the unchanging production of firm B from period 2.</p>

CC BY-SA 4.0
2019-01-09T14:01:53.653Z
This example of commodity used in the book is same what cournot himself used to illustrate his model. The commodity is mineral water extracted from a ever-flowing mineral water fountain ie zero costs ( I'm not sure about durability).
DrStrangeLove
CC BY-SA 4.0
2019-01-09T14:02:42.887Z
As far as my understanding goes the game is not inter-temporal here. Firm A starts first produces its profit maximizing commodity. Firm B follows and produces its own profit-maximizing commodity. Again Firm A follows. No time dimension here.
DrStrangeLove
CC BY-SA 4.0
2019-01-09T14:08:16.967Z
The word 'leftover' was my own addition it is not mentioned in book.  I may be incorrect
DrStrangeLove
CC BY-SA 4.0
2019-01-09T16:18:57.330Z
@DrStrangeLove So did I answer your question then? Firm A changes its production in period 3, it does not add additional production.
Giskard
CC BY-SA 4.0
2019-01-09T08:23:03.777Z
2019-01-09T08:23:03.777Z
Giskard
<p>I am reading Modern Microeconomics by Koutsoyiannis. In a Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve. </p>

<p>Firm A produces half the total market demand to maximise revenue.</p>

<p><a href="https://i.sstatic.net/29zSq.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/29zSq.jpg" alt="Diagram"></a></p>

<p>Further, Firm B takes A's output as given and operates on the left over demand curve eD' and produces 1/4th of output (AB).</p>

<p>Now Firm A in period 3 should respond by taking the leftover demand curve e'D' and produce <span class="math-container">$\frac{1}{2}$</span> of the leftover market that is <span class="math-container">$ (1 - \frac{1}{2} - \frac{1}{4})\frac{1}{2} = \frac{1}{8}th $</span> of total market output. </p>

<p>But it is mentioned
<a href="https://i.sstatic.net/C9wu8.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/C9wu8.jpg" alt="enter image description here"></a></p>

<microeconomics><mathematical-economics><oligopoly>
Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve
DrStrangeLove
# Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve

(Asked by: username_0 on 2019-01-09)

I am reading Modern Microeconomics by Koutsoyiannis. In a Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve.

Firm A produces half the total market demand to maximise revenue.

[![Diagram](https://i.sstatic.net/29zSq.jpg)](https://i.sstatic.net/29zSq.jpg)

Further, Firm B takes A's output as given and operates on the left over demand curve eD' and produces 1/4th of output (AB).

Now Firm A in period 3 should respond by taking the leftover demand curve e'D' and produce $\frac{1}{2}$ of the leftover market that is $ (1 - \frac{1}{2} - \frac{1}{4})\frac{1}{2} = \frac{1}{8}th $ of total market output.

But it is mentioned
[![enter image description here](https://i.sstatic.net/C9wu8.jpg)](https://i.sstatic.net/C9wu8.jpg)

**Tags:** microeconomics, mathematical-economics, oligopoly


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## 1 answers

### Answer by username_1 on 2019-01-09. Score: 1

The temporal constraints (i.e. what happens in a period) are not very clear in this question. It is likely that the good sold is not a durable good and hence there is no "leftover demand" between periods, demand is simply 'reset'.

In period 2 leftover demand appears because firm B assumes firm A will not change its production from period 1.

Then in period 3 firm A will best respond to the unchanging production of firm B from period 2.

> **Comments:**
> **username_0**: This example of commodity used in the book is same what cournot himself used to illustrate his model. The commodity is mineral water extracted from a ever-flowing mineral water fountain ie zero costs ( I'm not sure about durability).  
> **username_0**: As far as my understanding goes the game is not inter-temporal here. Firm A starts first produces its profit maximizing commodity. Firm B follows and produces its own profit-maximizing commodity. Again Firm A follows. No time dimension here.  
> **username_0**: The word 'leftover' was my own addition it is not mentioned in book.  I may be incorrect  
> **username_1**: @username_0 So did I answer your question then? Firm A changes its production in period 3, it does not add additional production.  

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