Nash Economics Assingment Help With Solution

Consider two companies competing in a market by choosing their output level.

Assume the inverse demand function is given by p = 28 − q1 − q2 . Where q1 and q2 are production levels for firm 1 and 2 respectively and p the market price.

Assume that firm 1 has a marginal cost of production of c1 = 8 and that firm 2 has a marginal cost of production of c2 = 0 . Further assume that each firm maximizes profits given by π1 = pq1 − c1q1 and π2 = pq2 − c2q2

Find the reaction function for each company and graph.

What is the Nash equilibrium (quantities produced by each firm) and profits at this Nash equilibrium?

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a) If the companies decided instead to collide and act as a single company (Monopoly) what are the profits to each company assuming that they use the efficient cost c2 = 0 to produce?

b) What the profits for each company if firm 1 chooses to produce the monopoly level and firm 2 the level indicated by its reaction function?

c) What are the profits for each company if firm 2 chooses to produce the monopoly level and firm 1 the level indicated by its reaction function?

d) Use the profits found in b) to e) to construct a payoff matrix where the actions for each firm is to collude or to compete.

e) Would you expect collusion to be stable? Is there a level of “trust” (Probability that the game will be repeated) that guarantees collusion for several periods?

f) Assume now that the game is played sequentially. Firm 1 is considered the leader and moves first and firm 2 is considered the follower and moves second. What is the level of output and profits for this game? (Show payoff matrix for sequential game).

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