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3. Farmer Jones and Farmer Smith graze their cattle on the same field. If there are 20 cows grazing in the field, each cow produces $4000 of milk over its lifetime. If there are more cows in the field, then each cow eats less grass, and its milk production falls. With 30 cows on the field, each produces $3000 of milk; with 40 cows, each produces $2000 of milk. Cows cost $1000 apiece. (a) Assume Farmer Jones and Farmer Smith can each purchase either 10 or 20 cows but that neither knows how many the other is buying when he makes his purchase. Calculate the payoffs of each outcome; (b) What is the likely outcome of this game? What would be the best outcome? Explain.

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