(4) Suppose there are two identical firms engaged in quantity competition (Cournot compe- tition). The inverse demand is P = a - Q where Q = q1 + 92. Assume that firm's i total cost of production is TC(qi) = cqi where c the constant marginal cost of production. (a) Find the best response functions using the first-order conditions. Check the second- order conditions. (b) Compute the Cournot-Nash equilibrium (i.e., quantities, price, and profits). (c) Suppose firms could collude. Solve for the quantities and profits under collusion. (d) Is the collusion outcome a Nash equilibrium. Why or why not