Consider a Cournot model with 2 firms, where market demand is given by 50-Q if Q50 otherwise 0 P(Q)= = Assume that the firms have different technologies. Firm 2 operates with a modern technology that leads to a constant marginal cost c = 10. Firm 1, however, has an outdated technology that leads to a higher marginal cost c = 20. (a) Derive the best response functions of the firms. (b) Graph them in an appropriately labeled diagram. (c) Find the unique Cournot -Nash equilibrium of the game. (d) Calculate the equilibrium profits obtained by each firm. [8] [5] [4] [4] (e) Now assume that firm 1 is willing (and able) to invest in acquiring the modern technology which would reduce its marginal cost to the same level as firm 2. What is the maximum it is willing to spend for this purpose? [4] What if the disparity in technology between the 2 firms is more pronounced than in the previous problem?