Consider a model of Cournot competition as studied in class, with 2 firms and a linear inverse demand function P(Q) = a - Q (where Q = q_{1} + q_{2} is the total quantity produced by the two firms and a is a parameter). The firms have differentmarginal costs: c1 for Firm 1 and c^{2} for Firm 2.(a) Find the Nash equilibrium.
(b) Assume Firm 1's marginal cost is larger (c1 > c2). Which firm produces more in equilibrium? How do the quantities produced in equilibrium change if Firm 1 improves its technology, leading to a lower c1 (while c2 is unchanged)?
(c) Find the total quantity produced and each firm's profit in equilibrium. Describe what happens to these when Firm 1 changes its technology as above.