1. Cournot vs. Stackelberg (35pts) Consider an industry with two firms selling a homogeneous good and competing in quantitics. Both firms face the same inverse demand curve p =100 q1 q2, where @1 denotes the quantity produced by firm 1 and , denotes the quantity produced by firm 2. Both firms also have a constant marginal cost of 10 (i.e., MC\\ = MC3 = 10). (a) Cournot. Suppose firms choose their output level simultaneously. Derive the best response function of each firm. (b) Find the equilibrium quantity and equilibrium price. (c) Calculate each firm's equilibrium profit. (d) Stackelberg. Suppose that firm 1 is the industry leader, which means firm 1 gets to move first and sets its level of output. Using a backward induction, derive the optimal quantity produced by firm 1 and firm 2 and find the equilibrium price. (e) Calculate each firm's equilibrium profit. I (f) Comparison. Compare the individual output for ecach firm, price, and profits in the Cournot competition (where firms simultancously select their output lev- els) and in the Stackelberg competition (where firms sequentially choose their output)