# Non Collusive Cournot Duopoly model with two firms, zero costs and linear demand curve

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.

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

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.

• 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 Jan 9 at 14:01
• 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 Jan 9 at 14:02
• The word 'leftover' was my own addition it is not mentioned in book. I may be incorrect – DrStrangeLove Jan 9 at 14:08
• @DrStrangeLove So did I answer your question then? Firm A changes its production in period 3, it does not add additional production. – Giskard Jan 9 at 16:18