Calculating Incentives in a Shared Pasture
A shared pasture is used by 10 herders, each grazing 10 sheep. At this level (100 sheep total), each sheep generates $50 of profit. If an additional 10 sheep are added to the pasture, the land becomes overgrazed, and the profit per sheep for all sheep drops to $45. An 11th herder is considering adding their 10 sheep. Calculate the total profit for this new herder and the total loss in profit for the original 10 herders combined. Explain why the new herder's individual incentive conflicts with the community's collective interest.
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