(1) Two rms produce goods that are imperfect substitutes. If rm 1 charges price p1 and rm 2 charges price 192, then their respective demands are q1 = 12 2p1 He and Q2 = 12+p1 2192. So this is like Bertrand competition, except that when p1 > 102, rm 1 still gets a positive demand for its product. Regulation does not allow either rm to charge a price higher than 20. Both rms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for rm 1. That i8, :01 = BR1(p2) is the optimal price for rm 1 if it is known that rm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justication. (b) Notice that for any given price 391, rm 1's demand increases with 192, so rm 1 is better off when rm 2 charges a high price 192. What is the best reply to 392 = 20? What is the best reply to p2 = 0? (c) What prices for rm 1 are not strictly dominated? What prices would survive two rounds of strict dominance? Provide a reason for each strategy that you eliminate. (d) Challenge question: If you continue the iterative elimination of strictly dominated strategies, what strategies will survive