# Payoff Matrix and Equilibrium

Firm A's price

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$20 $15

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Firm B's Price $20 Firm A earns Firm A earns

$40 profit $35 profit

Firm B earns Firm B earns

$irm 37 profit $39 profit

$15 Firm A earns Firm A earns

$49 profit $38 profit

Firm B earns Firm B earns

$30 profit $35 profit

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a. Firm A and B are members of an oligopoly. Explain the interdependence that exits in oligopolies using the payoff matrix facing the two firms.

b. Assuming that the firms cooperate, what is the solution to the problem facing the firms?

c. Given your answer to part b, explain why cooperation would be mutually beneficial and then explain why one of the firms might cheat.

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#### Solution Preview

a. There is a clear interdependence between the two firms. Firm A earns the maximum when it prices at $20 while Firm B prices at $15. The profits of Firm A are dependent on Firm B's price. Similarly, Firm B earns the maximum when it prices at $20 while Firm A prices at $15. It is clear that it is in the best interest of both firms to price their product at $20 each. However, if both firms price at $20, then none of the firms will obtain the highest profit. Thus, there is a ...

#### Solution Summary

The solution goes into a great amount of detail regarding the question being asked. Step by step explanation is provided for each part of the question which makes it very easy to follow along for anyone with just a basic understanding of the concepts. Overall, an excellent response to the question being asked.

Answers to three common Microeconomics review questions. The topics covered are:

1. Payoff Matrix and Dominant Strategy

2. Nash Equilibrium

3. Pricing Decisions

Question 5

The figure shows the payoff matrix for two producers of bottled water, Blue Spring and Purple Rain. Each has two strategies available to it: a high price and a low price. The dominant strategy for Purple Rain is to ...

a) always charge a low price.

b) always charge a high price.

c) always adopt the same strategy as Blue Spring.

d) Purple Rain does not have a dominant strategy.

Question 6

The figure shows the payoff matrix for two producers of bottled water, Blue Spring and Purple Rain. Each has two strategies available to it: a high price and a low price. Which outcomes are Nash equilibrium(s) in this game?

Answer

a) Blue Spring : low and Purple Rain : high

b) Two Nash equilibriums:

1. Blue Spring : low and Purple Rain : high; and

2. Blue Spring : high and Purple Rain : low

c) there are none here

d) every outcome is a Nash equilibrium in this game

Question 7

Your friend Iskander owns a coffee shop in a town with many competing coffee shops in a monopolistically competitive industry. One day Iskander tells you (a trusted economic advisor) that he is earning an economic profit and is currently setting his price equal to his marginal cost. Is Iskander producing the profit-maximizing amount of coffee? What should he do?

See the attached file for the diagrams.

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