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Oligopoly I: Edgeworth duopoly model

Summary

The bigger a firm is, the more efficient. Therefore, bigger and fewer firms in the market should mean lower prices and more goods produced. However, as we can see everyday, this is not really the case. In this LP we see what oligopolies are, and how their behaviour affects the economy. We also see what different types of duopolies there are, and which ones are best suited to analyse this kind of market structure.

Basic definitions:

Types of duopolies:

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.

In this Learning Path we’ve learned about oligopolies. We started by learning how oligopolies are few firms with great negotiating powers. Then, we studied a few different duopoly models. Cournot’s model deals with quantity competition as a simultaneous game, while Stackelberg’s considers a sequential game. Then, we saw how Bertrand’s model deals with price competition, but creating what is known as the Bertrand paradox. It was solved by Francis Y. Edgeworth.

Oligopoly I: Bertrand duopoly