Aim for FiveMicroeconomics

Short free-response question

A pricing game

  • Unit 4
  • 5 points
  • About 12 minutes

You can use a calculator on this question, just like on exam day.

A shorter question with a few lettered parts on one situation, often built on a table, a payoff matrix or a given or described graph. You make claims, explain them, calculate a value, or describe a labeled graph and show a change on it. On the exam: Questions 2 and 3 of 3 in Section II; 5 points each, a quarter of the section score each. About 12 minutes suggested for each. Four-function calculator allowed.

The question and its sources

Alpha Airlines and Beta Air are the only two airlines flying between two cities. Each must choose to charge a high fare or a low fare, and they choose at the same time without working together. The payoff matrix shows each airline's daily profit for each pair of choices. The first number in each cell is Alpha's profit, and the second number is Beta's profit. Both airlines know all the information in the matrix.

Table 1. Payoff matrix (daily profit in thousands of dollars: Alpha, Beta)

Alpha's choiceBeta charges a high fareBeta charges a low fare
Alpha charges a high fare$60, $50$20, $70
Alpha charges a low fare$80, $20$40, $35

Source: Hypothetical data

Suggested time: 12 minutes

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Part (a)

1 point

Identify whether Alpha has a dominant strategy. If it does, identify the strategy. Explain using the payoffs.

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Part (b)

1 point

Identify the Nash equilibrium of this game.

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Part (c)

2 points

Identify the pair of strategies that would give the two airlines the largest combined profit, and explain why they are unlikely to end up there without an enforceable agreement.

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Part (d)

1 point

Suppose the city where Alpha is based pays Alpha a fixed daily amount whenever Alpha charges the high fare, and Beta's payoffs do not change. Calculate the smallest daily payment, as a whole number of thousands of dollars, that would make charging the high fare Alpha's dominant strategy. Show your work.

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