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Question: Suppose two cowboys indexed by i= 1,2who own multiple cows use the samefield (in British English this is sometimes called a "Common") in which their cows graze. Let yi∈R be thenumber of cows (can be continuous, to avoid integer problems and to take derivatives) that cowboy ichooses tolet use the field. Cowboy i's total benefit from letting yinumber of cows graze is yi-0.25 (yi)2-0.1 (y1 y2).(a) What are the equilibrium levels of y1and y2if the cowboys decide the numbers separately?(b) What are the efficient levels of y1and y2from a social (joint benefit maximizing) point of view?
(c) Why are the results different in (a) and (b)?(d) Propose some ways so that the equilibrium levels and the socially efficient levels coincide
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