Question: Barb and Sue are competitors in a local market. Each is trying to decide if it is better to price low, medium or high. If they both price low, each will earn a profit of $5,000. If they price medium, each will earn a profit of $7,000. If they both price high, each will earn a profit of $10,000. If one prices low and the other prices medium, then the one pricing low will earn $8,000 and the other will earn $3,000. If one prices low and the other prices high, then the one who priced low will earn $15,000 and the other will earn $2,000. If Barb prices medium and Sue prices high, Barb will earn a profit of $16,000 and Sue will earn $1,000. If Sue prices medium and Barb prices high, then the Sue will earn $12,000 and the Barb will earn $4,000.

a. Represent this as a game by filling in the game below.

b. What are Sue’s dominant and dominated strategies (if any exist)? How do you know?

c. What are Barb’s dominant and dominated strategies (if any exist)? How do you know?

d. What is the Nash Equilibrium? How do you know?

e. What is the Pareto Solution for Barb and Sue? How do you know?

f. Discuss the difference in the social welfare for society if Barb and Sue end up both pricing low (both acting like a competitive firm and pricing where P=MC) as opposed to them both pricing high (both colluding and acting like a monopolist).