Question 2 Three farmers (labeled i = 1, 2, 3) have recognized that any fertilizer sprayed in their neighborhood is a public good to them. Fertilizer costs p = 3 per gallon. The farmers' profits, as functions of the amount r of fertilizer sprayed, are given by the functions mi(x) = 0, In(x) -t, (2) where of = 1, 02 = 2 and as = 3 and where t; is farmer i's payment to cover the cost of r. a) Show that the Pareto efficient level of the fertilizer is x* = 2. (15 marks) b) Show that under an equal cost sharing arrangements (whereby t, = (Pri) /3), the level of a most preferred by farmer i is given by of. (15 marks) c) Based on (b), argue that if the farmer's were to decide on r using majority voting with equal cost sharing, the outcome would be efficient. (20 marks)