The geometric analysis of Cournot-Nash (CN) equilibrium has been developed mainly by using reaction curves (see, e.g. Tirole (1988), Cabral (2000)). Since they are defined in the quantity space, the use of such graphical approach yields a discontinuity with respect to the perfectly competitive, the competitive monopolistic and the monopolistic cases, whose graphical representation is carried out in the price-quantity space. Recently, Fulton (1997), using the graphical version of the first order condition, shows how reactions curves are obtained from the price-quantity space. More recently, Sarkar, Gupta and Pal (1998) and Dufwenberg (2001) have provided graphical analyses of CN equilibrium using directly diagrams in the price-quantity space. While the former work's geometrical approach is obtained from mathematical elaboration of the first-order condition for profit maximization, the latter bases the geometrical conditions of equilibrium exploiting an interesting property of a family of rectangles. In either cases, however, the geometric method employed lacks of immediate economic interpretation. The aim of this paper is to develop a simple geometrical analysis of CN equilibrium only in the price-quantity space by exploiting the economic content of the first-order condition. Apart its conceptual simplicity, the advantage of our approach is threefold: first, the first-order condition is used only in terms of its economic content, rather than for its mathematical properties; this ensures that our graphical approach maintains a strong economic interpretation. Moreover, as we shall point out later, our approach yields, as particular case, Dufwenberg's rectangle method; thus, it enriches the latter method with economic content and with a geometric approach. Second, our approach makes it crystal-clear the economic nature of the externality existing among oligopolists. Two immediate implications of this fact are: (i) that our approach provides an economically grounded explanation of the origin of cartel instability; (ii) it allows us also to immediately extend oligopoly within the more general commons and anti-commons framework, as recently considered by Buchanan and Yoon (2000). Third, the approach here proposed seems to be particularly suitable for generalizations, further applications and very fine-grained analysis
