In Lecture 25: Innovation 1, we ran through a simple version of Arrow's analysis comparing the gains of a monopolist and a perfectly competitive firm from the same cost-saving innovation. On slide 20, I suggest as an exercise to try the same analysis with an n-firm Cournot oligopoly in which one firm innovates to reduce cost from c to c/2. For this problem, assume n = 2, and use the demand and cost numbers used in the lecture. That is, let inverse market demand be given by P = 100 - Q, and let marginal cost be constant at 50 per unit before the innovation, and 25 per unit after the innovation. (a) Compute what the duopolist stands to gain from innovating. How does it compare to the perfectly competitive firm and to the monopolist? (b) What can you conclude about the relationship between concentration and innovation