Consider the case of two breeders having to decide how many sheep to graze on the communal field. The communal field is relatively small and can quickly succumb to overgrazing. The value per sheep is given by:

v(q1, q2) = 120 (q1 + q2)

The utility of farmer i (i = 1 or 2) is given by ui(q1, q2) = qi(120 (q1 + q2))

a) What is the best response function of breeder i, i.e. what form does qi = BRi(qj ) take? b) What is the number of sheep per farmer in the Nash equilibrium of this game? c) What would be the number of sheep per breeder if they collectively maximized their utilities? d) Show that the utility obtained during the collective maximization is greater than that obtained at the Nash equilibrium.