7 Farmer Jones and Farmer Smith graze their cattle in the same field. If there are 20 cows grazing in the field, each cow produces $4000 of mil k over its lifetime. If there are more cows in the field, then each cow can eat less grass and its milk production fal ls. With 30 cows in the field, each produces $3000 of milk; with 40 cows, each produces $2000 of milk. Cows cost $1000 each.

a Assume that Farmer Jones and Farmer Smith can each purchase either 1 0 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 Fill in the pay-offs in a 2 x 2 decision box.

c What is the likely outcome of this game? What would be the best outcome? Explain.

d There used to be more common grazing land than there is today. Why? (For more discussion of this topic, reread Chapter 11.)