4. Three oligopolistic banks operate in the loan market with the inverse demand function given by r (Q) = a-Q, where r is the interest rate per unit of loan and Q = 91+92+93 and q 0 is the total amount of loans issued by bank i 1, 2, 3. Also, a > 0 is a constant. The cost of funds for bank i is given by cqi, where c = (0, a) is a constant. A bank's profit from loans is (r- c) qi. = (a) [10 points] Suppose the banks engage in Cournot competition. Find the symmetric Nash equilibrium. How much profit does each bank make? (b) [20 points] Now suppose banks compete in the following sequential manner: Bank 1 first chooses q. Then banks 2 and 3 observe q and then simultaneously choose q2 and 93, respectively. Find the subgame perfect equilibrium. How much profit does each bank make here? Does bank 1 enjoy an advantage being the first mover?