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Explain the role of conjectural variations within the context of quantity settings duopoly. Use this idea to explain the difference between Cournot and Stackelberg models of duopoly

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  1. Introduction.
  2. Conjectural variations.
    1. The underlying idea of duopoly and more generally of oligopoly.
    2. The Cournot model of duopoly.
  3. Stackelberg v. Cournot.
    1. Cournot.
    2. Stackelberg.
  4. Conclusion.
  5. Bibliography.

In the context of oligopoly, firms do not have to worry about strategic behaviour as do monopolies, as far as consumers are concerned. Nonetheless, as they face competition from a few other firms, strategies in terms of price-setting and quantity-setting are of prime importance. What we want to look at in this essay is the range of the different strategies a duopolistic firm (i.e. an oligopoly that faces only one competitor) might choose, in a non-cooperative quantity-setting context. We want to introduce the concept of conjectural variations in that analysis, as it helps understanding the divergence between the two main models of duopolistic quantity-setting, Cournot and Stackelberg. By doing so, we will be able to compare these two approaches to duopolistic profit-maximizing firms and to determine why firms should adopt one strategy or the other.

[...] Therefore, reaction functions in Cournot and Stackelberg models have different meanings: while they reflect expectations of both firms about their respective competitor's output in Cournot, they picture the actual follower's reactions to be anticipated by the leader in Stackelberg. Looking at conjectural variations allows us to quantify these conjectures. These divergences about firm's beliefs are anything but futile, as they result in different outcomes for the firms while completely shaping their strategies. Conjectural variations are assumptions made by the firms: how to decide which ones to make? [...]


[...] So there is no stable equilibrium and several options emerge: either one of the firm is influent enough to win this fight, and the industry ends up in a Stackelberg equilibrium that benefits this powerful firm; or none of them is dominant enough and the industry tends toward a Cournot equilibrium where both firms produce on their own reaction functions and thus maximise their profits to the extent they can afford given what the other produces which they cannot affect; finally they could collude and maximise their joint profits[6]. [...]


[...] a - bQL TS= + QL (from Stackelberg leader's point of view in our 2b example) QF Slope = ( ?QF/?QL= - The leader knows his choice will affect his competitor's and that if increases its output by 1 unit, its competitor will decrease his by unit that is total sales will only increase by TS= Q2* + Q1 (from Cournot firm 1's point of view) = Q1* + Q2 (from Cournot firm 2's point of view) = QL* + QF (from Stackelberg Follower point of view) Slope = 1 ( ?Qcompetitor/?Qfirm = 0 Firms having that kind of conjectural variations believe their choice is the only one that will affect Total Sales at the time they choose. [...]

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