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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.

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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

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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.

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  • $\begingroup$ 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). $\endgroup$
    – DrStrangeLove
    Jan 9, 2019 at 14:01
  • $\begingroup$ 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. $\endgroup$
    – DrStrangeLove
    Jan 9, 2019 at 14:02
  • $\begingroup$ The word 'leftover' was my own addition it is not mentioned in book. I may be incorrect $\endgroup$
    – DrStrangeLove
    Jan 9, 2019 at 14:08
  • $\begingroup$ @DrStrangeLove So did I answer your question then? Firm A changes its production in period 3, it does not add additional production. $\endgroup$
    – Giskard
    Jan 9, 2019 at 16:18

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