ECO 2020: Principles of Microeconomics

Spring 2023

Optional Problem Set #4 - Due no later than Wed., 5/10/23 at 11:59 PM

Hello everyone!

The problem set below is optional. Use it for study purposes only, or if you choose to complete it and submit it before the due date, it'll be worth up to 25 extra bonus points for the course.

Follow the same instructions given on previous problem sets.

1.Two gas stations, A and B, are locked in a price war. Each player (i.e., firm) has the option of raising its price (R) or continuing to charge the low price (C) - Raise or Continue. They will choose strategies simultaneously. If both choose C, they will both suffer a loss of $100. If one chooses R and the other chooses C, (i) the one that chooses R loses many of its customers and earns $0, and (ii) the one that chooses C wins many new customers and earns $1000. If they both choose R, the price war ends and they each earn $500.

a. Draw the payoff matrix for this game.

A/B	R	C
R	500, 500	0, 1000
C	1000, 0	-100, -100

b. Indicate the best-response by player A if player B chooses R (raise price).

ANS:

c. Does player A have a dominant strategy? Explain.

ANS: For a strategy to be dominant, the payoff from the dominant strategy has to be greater than the payoff from the dominant strategy irrespective of the other firm's actions. In the given case, neither firm has a dominant strategy. If firm A chooses R, it earns payoffs of 500 and 0, depending on what firm B chooses; if firm A chooses C, it earns payoffs of 1000 and -100, depending on what firm B chooses. Hence, neither strategy provides a strictly greater payoff than the other, irrespective of the other player's strategy. Hence, neither player has a dominant strategy.

d.How many Nash equilibria does this game have?

ANS: The game has two pure-strategy Nash equilibria: (R, C) and (C, R) The corresponding payoffs are:

(0,1000) and (1000,0)

e.Does this game resemble a prisoner's dilemma? Explain why or why not.

ANS:

f. What course of action will players A & B end up choosing?

ANS: Since the game has two pure-strategy Nash equilibria - one for each of the two actions, the players will randomly choose their action. Hence, each player will choose R with a probability of 1/2 and will choose C with a probability of 1/2.

2.The following table represents the sales figures for the eight largest U.S. auto industry firms in 2018.

Company Sales (billions of dollars)

General Motors 94.1

Toyota 83.8

Ford 82.1

Fiat Chrysler 73.5

Nissan 53.0

Honda 52.4

Hyundai/Kia 41.6

Subaru 22.8

Total 503.3

a. Compute the 4-firm concentration ratio (CR4) for this industry.

b. Compute the Herfindahl-Hirschman Index (HHI) for this industry (assuming the industry contains

just these eight firms).

c. According to the CR4 and HHI measures, would you consider the auto industry (above) to be an

oligopoly and why?

d. Assuming the industry is represented by these eight firms, if Ford and Toyota wanted to merge and

you were the head of the Department of Justice, would you permit the merger? Why or why not?

(Hint: Calculate the new values from parts a and b assuming the merger takes place.)

3. Use the diagram below to answer the next three questions.

a. What price and quantity will the firm in the diagram produce?

b. What's the socially-optimal price and quantity?

c. In the absence of government intervention, will this firm produce too much or too little?

P5 P 4 - P3 t - - -. P2 MSc PI MPC - - D QI Q2 Q3 Q4 Q5 MR