Consider two quantity-setting firms that produce a homogeneous good. The inverse demand function for the good is p = A - (q_{1}+q_{2}). Both firms have a cost function C = q^{2}
(a) Compute and describe the Nash equilibrium (quantities, price and profits) in the game in which both firms choose their quantities simultaneously?
(b) Suppose that firm 1 can switch to a new technology under which its cost function becomes C_{1}= F + q^{2}/2. The cost function of firm 2 remains C = q^{2}. What is the largest value of F for which firm 1 will switch when we assume that both firms will continue to produce the equilibrium quantities computed in (a)?
(c) Compute the Nash equilibrium after firm 1 adopts the new technology. What is the largest value of F for which firm 1 will switch to the new technology?
(d) Compare your answers to (b) and (c). Explain the intuition in detail; that is, why is/isn't there a difference between the two answers?