Farmer Jones and Farmer MacDonald graze their cattle on the same field. If there are 20 cows grazing in the field, each cow produces $4 000 of milk over its lifetime. If there are more cows in the field, then each cow can eat less grass, and its milk production falls. With 30 cows on the field, each produces $3 000 of milk; with 40 cows, each produces $2 000 of milk. Cows cost $1 000 apiece. (a) Assume that Farmer Jones and Farmer McDonald can each purchase either 10 or 20 cows, but that neither knows how many the other is buying when she makes her purchase. Calculate the pay-offs of each outcome. (b) What is the likely outcome of this game? What would be the best outcome? Explain. (c) There used to be more common fields than there are today. Why?
4. Farmer Jones and Farmer MacDonald graze their cattle on the same field. If there are 20 cows grazing in the field, each cow produces $4 000 of milk over its lifetime. If there are more cows in the field, then each cow can eat less grass, and its milk production falls. With 30 cows on the field, each produces $3 000 of milk; with 40 cows, each produces $2 000 of milk. Cows cost $1 000 apiece.
(a) Assume that Farmer Jones and Farmer McDonald can each purchase either 10 or 20 cows, but that neither knows how many the other is buying when she makes her purchase. Calculate the pay-offs of each outcome.
(b) What is the likely outcome of this game? What would be the best outcome? Explain.
(c) There used to be more common fields than there are today. Why?
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