Consider a village with a common pasture field and n breeders. The breeder i has a number of oxen, g_i. The value of taking an extra ox to the pasture depends on the total number of oxen and is given by v(G). The cost of purchasing and maintaining an ox is c. There is a maximum number of oxen that can be fed in this pasture, G_max. For G, v'(G)<0 and v''(G)<0. For G>G_max, v(G)=0.

(a) Solve the problem of social optimum and arrive at the expression that implicitly defines G*

(b) Solve the Nash equilibrium of each of the n creators, add the quantities and find the expression that defines G^Nash.

(c) Who is bigger, G* or G^Nash? Provide the mathematical proof and the intuition of this result.