A firm’s revenue varies with its output: R(q). Its manager’s income, Y, equals aR(q), where 0 6 a 6 1 is the manager’s share of the firm’s revenue. Use calculus to prove that maximizing aR(q) implies the same output level, q, as maximizing R(q). What does this result imply about the manager’s incentive to maximize the firm’s profit, π(q) = R(q) – C(q)? Would it be better for shareholders if the manager received a share of profit rather than a share of revenue?