# Review: Payoff Matrix, Nash Equilibrium, and Monopolies

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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#### Solution Preview

5. d

A dominant strategy is one that always gives the best payoff no matter what the other player does. In this game, Purple Rain gets its best payoff by choosing the opposite of Blue Spring's strategy, so Purple Rain does not have a dominant ...

#### Solution Summary

This solution gives answers to three common Microeconomics review questions. The topics covered are:

1. Payoff Matrix and Dominant Strategy

2. Nash Equilibrium

3. Pricing Decisions