1. [40 marks] Consider a Cournot oligopoly with two firms. The market demand curve is

given by 𝑝 = 10 − 𝑄, where p is price and Q is market output.

Consider a case when marginal costs for all firms are constant and equal two. That is,

𝒄𝟏 =𝒄𝟐 =𝟑.

(a) Find the Nash equilibrium of the one-period model.

Consider a case when marginal cost 𝒄𝒊 = 𝒊 where 𝑖 is number of the firm. That is, the marginal costs for firm 1 are 𝒄𝟏 = 𝟐 and marginal costs for the firm 2 are 𝒄𝟐 = 𝟒.

(b) Find the Nash equilibrium of the one-period model.

Consider a case when marginal cost 𝒄𝒊 = 𝒊 where 𝑖 is number of the firm. That is, the

marginal costs for firm 1 are 𝒄𝟏 = 𝟐 and marginal costs for the firm 2 are 𝒄𝟐 = 𝟒.

Assume that the firms compete for an infinite number of periods. Each firm’s discount factor is 𝛿 ∈ (0,1). Assume that in a case of collusion firms split outputs (shares of the market) equally.

(c) Define the stage game for the collusion problem among the firms

(d) Assume that firms use trigger strategies. Find for which values of discount factors collusion can be sustained.

2. [60 marks] Consider a multimarket contact between 2 firms competing on price on 2 markets. The demand curve for each market is given by 𝑄 = 1 − 𝑝, where Q is the total demand and p is the market price. Marginal costs are zero for all firms.

(a) Show that 𝑝∗ = 0 for all firms enumerated by 𝑖 is the Nash equilibrium for the one-

shot game.

From now on, assume that the firms compete for an infinite number of periods. Each

firm’s discount factor is 𝛿 ∈ (0,1).

(b) Find the minimal discount factor that would sustain collusion for the case when all

firms sell to all markets.

(c) Find the minimal discount factor that would sustain collusion for the case when each firm is present in only one market.

(d) Which type of collusion is easier to sustain?

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