Asymptotic relations in Cournot's game
In this note, I derive the asymptotic relation verified by oligopolists' iso-profit curves within Cournot's game. Thereafter, I provide an economic rationale for such a mathematical relation. The results of this exploration suggest that for each firm the asymptotes of the iso-profit curves convey the boundaries beyond which output competitors become net purchasers of the good supplied in the market.
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