Consider two quantity-setting firms that produce a homogeneous good. The inverse demand function for the good is p = A - (q₁+q₂). Both firms have a cost function C = q²

(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 C₁= F + q²/2. The cost function of firm 2 remains C = q². 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?