Compare the nash equilibrium against social optimum

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Question: Suppose there are I farmers, each of whom has the right to grace cows on the village common. The amount of milk a cow produces depends on the total number of cows, N, grazing on the green. The revenue produced by ni cows is niv(N) for N <>, and v(N) a 0 for N ≥ N, where r(0) > 0. v'< 0,="" and="" v"="">≤ 0. Each cow costs c, and cows are perfectly divisible. Suppose v(0) > c. Farmers simultaneously decide how many cows to purchase; all purchased cows will graze on the common.

(a) Write this as a game in strategic form.

(b) Find the Nash equilibrium, and compare it against the social optimum.

(This exercise, constructed by R. Gibbons, is based on a discussion in Hume 1739.)

Reference no: EM131449717

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