Question

Use the following game to answer questions 8-10. Be sure to show all of your math step-by-step.

Alcoa and Kaiser, duopolists in the market for primary aluminum ingot, choose prices of their 500 foot rolls of sheet aluminum on the first day of the month. The following payoff table shows their monthly payoffs resulting from the pricing decisions they can make.

Alcoa

High price

Low price

Kaiser

High price

A

$400, $500

B

$175, $575

Low price

C

$525, $200

D

$273, $250

Suppose Alcoa and Kaiser repeat their pricing decision on the first day of every month. Suppose they have been cooperating for the past few months, but now the manager at Kaiser is trying to decide whether to cheat or to continue cooperating. Kaiser’s manager believes Kaiser can get away with cheating for two months, but he also believes that Kaiser would be punished for the next two months after cheating. After punishment, Kaiser’s manager expects the two firms would return to cooperation. Kaiser’s manager ignores the time-value of money and does not discount future benefits or costs.

8. What is the monthly gain to Kaiser from cheating? What is the present value of the benefit from cheating for the two months of cheating?

9. What is the monthly cost of punishment to Kaiser? What is the pres­ent value of the cost of cheating for the two months of punishment?

10. Will Kaiser cooperate or cheat? Explain.

11. Suppose you were asked to manage a golf course that was currently charging a uniform price. Would you suggest that the course continue with this price plan or switch to a two-part pricing plan? Explain your decision and how you would choose the optimal price.

Answer 1

*Answer:

Alcoa and Kaiser have been cooperating for the past two months - both have been setting high prices, leading to a payoff of:

Kaiser = 400$

Alcoa = 500$

8. If Kaiser cheats, they will set low prices, leading to the below payoffs:

Kaiser = 525$

Alcoa = 200$

Monthly gain to Kaiser = 525 - 400 = 125$

Present value of benefit from cheating for 2 months = 125$*2 = 250$ (Ignoring time value of money concept)

9. If Kaiser cheats, they will get punishment for the next two months, i.e. Alcoa will also set low prices, leading to below payoffs:

Kaiser = 273$

Alcoa = 250$

Monthly loss to Kaiser = 400 - 273 = 127$ (loss)

Present value of loss from cheating for 2 months = 127$*2 = 254$ (Ignoring time value of money concept)

10. Present of loss (254$) is more than the present value of benefit (250$) in case of cheating, So Kaiser will continue to cooperate.

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