Microeconomics Course E John Hey

Welcome! Professoressa Maria Covadonga de la Iglesia Villasol, Departamento de Fundamentos del Análisis Económico I, Universidad Complutense de Madrid. Is here through Erasmus to share ideas on teaching.

This week The final week of the course. Today, Tuesday: Duopoly. Tomorrow, Wednesday: Example 1 of the exams. Thursday: Example 2 of the exams. Before tomorrow, try Example 1 and before Thursday, try Example 2. It is a waste of your time coming to the lectures if you have not done so.

Game Theory In Chapter 29 we talked about games, in which two players have to choose simultaneously the value of some decision variables, the values of which affect both players. We introduced the idea of a Nash Equilibrium in which each is optimising given the decision of the other. Today we will apply that in Duopoly.

Chapter 31 Duopoly A market in which there are two sellers – two firms – Firm 1 and Firm 2, selling an identical good. The demand curve in the market is given by: p = a – b(q 1 + q 2 )

The Cournot Model Each firm chooses independently its output. The price is determined by the demand curve. What outputs do the firms choose?

Profits Let us denote the profit of firm 1 by π 1. Suppose that the total cost function is given by: C(q 1 ) = cq 1. Hence profits are given by: π 1. = pq 1 - cq 1 = [a – b(q 1 + q 2 )]q 1 - cq 1

Isoprofit Curves For firm 1 an isoprofit curve is given by: π 1. = constant Hence [a – b(q 1 + q 2 )]q 1 - cq 1 = constant

Reaction Curves If Firm 1 chooses its output to maximise its profits given a level of output of Firm 2, we get: q 1 = (a-c-bq 2 )/2b …the reaction curve of Firm 1.

The Nash Equilibrium … is given by the intersection of the two reaction curves… Total output = 2(a-c)/3b With monopoly = (a-c)/2b With perfect competition = (a-c)/b The output with a duopoly is between the monopoly output and the competitive output. Let’s go to Maple...

The Bertrand Model Each firm independently chooses its price. The demand all goes to the firm with the lowest price. What prices will the firms choose?

What happens with a duopoly Is very sensitive to the rules of the game…

Summary With quantity-setting rules in the Nash Equilibrium the total output with a duopoly is between the monopoly output and the competitive output. A collusive outcome is better for both firms – but is unstable. For a firm it is better to be the leader. With price-setting the Nash Equilibrium has price equal to marginal cost (and therefore like competition).

Chapter 31 Goodbye!