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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 = q1 + q2 is the total quantity produced by the two firms and a is a parameter). The firms have differentmarginal costs: c1 for Firm 1 and c2 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.
Suppose that between January 2011 and January 2012 the total number of people employed and the unemployment rate both fell. Briefly explain how this is possible. [2 marks]
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