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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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.

Extraits

[...] Cournot equilibrium, neither firm will find it profitable to change its output once it discovers the choice actually made by the other firm.”[5] (See diagram II.1) Back to our example: a bQ2 Q1 = and 2b If we substitute Q1 for Q we obtain the following equilibrium quantities: a a Q1 = , and symmetrically Q2 = . 3b 3b 2a a Therefore, Qi = and p = . 3b 3 In Stackelberg, the equilibrium is at the point where the leader's isoprofit line yielding the highest profit possible (i.e. the lowest curve) touches the reaction curve for the follower. That is, the leader produces where he gets the highest profits given how the follower will react. [...]

[...] 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 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. [...]

[...] Black, Oxford dictionary of Economics Pass, C Lowes B. & Davies, L., Collins Dictionary, Economics, 3rd edition, Collins “Friedman, D. Chapter 11, Hard Problems: “Game Theory, Strategic Behaviour, and Oligopoly” at http://www.daviddfriedman.com/Academic/Price_Theory/PThy_Chapter_11/PThy_C hapter_11.html Explain ‘conjectural variation' in Cournot duopoly, evaluate its impacts and discuss the policy implication” at http://www.nedprod.com/NeoCapitalism/EC3201%20Essay.pdf Le duopole et la concurrence en quantité at http://yildizoglu.u- bordeaux4.fr/micro2web/node33.html E. Kalai and W. Stanford, “Conjectural variations strategies in dynamic Cournot games with fast reactions”, September 1983, available at http://www.kellogg.northwestern.edu/research/math/papers/575.pdf . K. [...]

[...] The new Leader gains in profits, the consumers gain in price decrease and therefore in consumer surplus. The level of Welfare in Stackelberg equilibrium is higher than that in Cournot equilibrium . Stackelberg equilibrium Q2* Q2 Q1 Cournot Equilibrium Reaction function of Firm 1 Reaction function of Firm 2 Q1* Cournot Equilibrium Each firm is producing a profit-maximising level of output given the expected output choice of the other firm. The assumptions on the other firm's production are confirmed in equilibrium. [...]

[...] Firm 1 believes that if it increases its output by 1 unit, total sales will increase by 1 unit, and subsequently Firm 2's output will stay exactly the same. Firm 2 follows the same reasoning. In a Stackelberg industry, the reasoning is twofold: the follower chooses after the leader, therefore it makes its decisions according to its own reaction function derived from its profit-maximising conditions and from QL* the quantity the leader produces is a situation similar to Cournot; the leader on the contrary, knows that his choice will affect its competitor's strategy. [...]