The Edgeworth duopoly model, also known as Edgeworth solution, was developed by Francis Y. Edgeworth in his work “The Pure Theory of Monopoly”, 1897. It is a duopoly model similar to the duopoly model developed by Joseph Bertrand, in which two firms producing the same good compete in terms of prices. Edgeworth’s model presents a slight modification as it also includes constraints in the production capacity of the firms. In this market structure, firms have two potential options, to collude or not.
As shown in the adjacent figure, when firms choose to collude they will split and share the market and the production of the good. Firm1 will produce from O to F and firm2 from O to G, in this way the supply is limited and prices will be set at p. Revenues of each firm correspond to the rectangle above FO and OG, and each firm would enjoy an equal share. Note that d1 and d2 are parts of total demand, each part being supplied by one of the firms.
Collusion is not always possible as firms have incentives to break cooperation in their search for higher profits. Collusion is also considered an illegal business practice in many countries. Eventually one of the firms will decide to lower their prices and increase production in order to gain market share from the other competitor. Consequentially the other firms will do the same. This process will escalade up to the point in which the maximum production of both firms is achieved. When this point is reached (OD for firm1 and OE for firms2), price will not be reduced any further and will remain at p’, as the increase in demand that follows price reduction will not be satisfied with a larger amount of production. On the contrary, prices will start to rise little by little so firms will be able once again to increase their profits. Overtime this process will be repeated and prices will oscillate from p to p’.
The following figure shows how all this translates into market demand (D), and how quantities sold will oscillate from Q and Q’.
Overall the Edgeworth’s solution is a more realistic one than Bertrand’s and it answers Bertrand’s paradox. However, it does not give a definitive solution.