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 = q1 +q2 +q3 and qi >= 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 2 (0; a) is a constant. A banks prot from loans is (r-c) qi. (a) [10 points] Suppose the banks engage in Cournot competition. Find the symmetric Nash equilibrium. How much prot does each bank make? (b) [10 points] Now suppose banks compete in the following sequential manner: Bank 1 rst chooses q1. Then banks 2 and 3 observe q1 and then simultaneously choose q2 and q3, respectively. Find the subgame perfect equilibrium. How much prot does each bank make here? Does bank 1 enjoy an advantage being the rst mover