5 . Suppose the demand curve for a homogeneous commodity produced in a duopolistic market is given by P = a - bQ, where P and Q are respectively the price and quantity of the commodity, and a, b > 0. Firm 1 produces at a constant marginal cost 2c > 0 and firm 2 produces at a constant marginal cost c. Moreover, assume that firm 1 is the Stackelberg leader and firm 2 is the follower. (a) Find the profit-maximizing quantities of firm 1 and firm 2, and the market price. (b) Find the condition of a, b and c under which the leader will produce less output than the follower. ( c) Does firm 2's profit-maximizing quantity increase or decrease in c? Provide the mathematical reasoning and the intuition