Please help with questin 4

Question 4. Consider the same set-up as in question #3, but now we have only two firms (n=2), and the two firms have the following cost functions: C1(q1) = c191 and C2(q2) = C292. [17 TOTAL POINTS] a. Set up the profit maximization problem for firm 1, taking as given the quantity level for firm 2 as given and find the FOC (you can assume that SOC is satisfied). [5 points] b. Find the expression for the best reaction /response function for firms 1, qf*(q2), and 2, q2 *(q1), and find the Cournot Nash equilibrium. [6 points] c. Find total market quantity (q,*), equilibrium price (p *) and equilibrium firm profits (of* and 72*). [6 points]Question 3. In this question, we will generalize the Cournot model discussed in class for the case with n identical firms. The inverse demand function is: p(qr) = a - bqr, where qr = _(=1) qi . Each firm has a constant marginal cost c and there are no fixed costs. [17 TOTAL POINTS] a. Set up the profit maximization problem for firm , taking as given the quantity levels of all the other firms as given (i.e., qiz;) and find the FOC (you can assume that SOC is satisfied). [5 points] b. Find the expression for the best reaction/ response function for firm i and the Cournot Nash equilibrium. (Hint: use the best response function and symmetry: q,* C* = 90* = . .. an* = qc*) [6 points] c. Find total market quantity (qf*), equilibrium price (p*) and equilibrium firm profit (7(*). [3 points]