Question 1. [20 pts] Consider a Cournot duopoly game in which rms 1 and 2 simultaneously choose quantities to produce (q1 and q2 respectively), that need to be nonnegative. The market price is given by p = 100 2q1 2q2. Suppose that each rm's marginal cost is 20. Firms want to maximize their prots. a) [4 pts] Derive the rms' best response functions. What is the set of never best response strategies for each rm? b) [3 pts] What is the set of strategies for each rm that survive two rounds of elimination of never best response strategies? (2) [6 pts] What is the Nash equilibrium of the game? d) [7 pts] Now suppose rm 1's marginal cost is reduced to 10 (while rm 2's marginal cost remains 20). What is the new best response function of Firm 1, and what is the new Nash equilibrium of the game