Question

lcoa 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.

1.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?

2.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?

3.Will Kaiser cooperate or cheat? Explain.

4.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

Sol:- Given that kaiser and Alcoa having both high price and low price • Alcoa and Kaisey have been cooperating for the past two now both have been setting high prices Kaiser = $ 400 Alcoa = $ 500 V what is monthly gain to Kaiser from cheating : it baiser cheats, they will get set low prices, leading to the below payoffs Kaiser = $ 525 Alcoa = $ 200 Monthly gain to Kaisex = 525- 400 = $ 125 Present value of benefit from cheating for a months = 2x $185 why = $250 2 what is the monthly cost of Punishment to kaiser:- if Kaiser cheats, they will get punishment for the next few months that is arcou will also set low prices. Kaiser = $ 273 Alcoa = $ 250 Monthly loss to Kaiser = 400-273 = $127 Cross) present value of 1095 from cheating for 2 months = px $ 127 present value of loss $ 254 is more than the present rare of benefit So in case of cheating. So kaisey will continue to cooperate