Question 4. (15 marks) Consider the Stackelberg's duopoly model in which two firms, 1 and 2, sequentially choose the quantities qr and qz, respectively, they will sell on the market. Suppose firm 1 chooses the quantity first, then firm 2 does so, knowing the quantity chosen by firm 1. The price each receives for each unit given these quantities is P(q, q:) = 2 - (qr + q:). Their costs per unit are zero. 4.1 Solve the game by backward induction. What are the quantity decisions of two firms? (5 marks) 4.2 Compared to the Cournot model in which two firms move simultaneously, is firm 2's profit in Stackelberg model lower? Provide proof. (5 marks) 4.3 Compared to the monopoly model, is firm 1's profit in Stackelberg model higher? Provide proof