Determine a model of Cornet competition as studied in class, with 2 firms and a linear inverse demand function P(Q) = a - Q (where Q = q1 + q2 is the total quantity formed by the two firms and a is a parameter). The firms have different marginal costs: c1 for Firm 1 and c2 for Firm 2.
1. Identify the Nash equilibrium.
2. Suppose the Firm 1's marginal cost is larger (c1 > c2). Which firm forms more in the equilibrium? Explain how do the quantities produced in equilibrium change if Firm 1 improves its technology, leading to a slightly lower c1?
3. Identify the total quantity produced and each firm's profit in equilibrium. Explain what happens to these when Firm 1 changes its technology as above.