Differentiated Bertrand competition with two symmetric firms - Suppose there are two firms active in the market—Firm A and Firm B—and they compete on price. Demand for each Firm i (where i is either A or B) is given by: Di(pi:pj) = 115 — 319i + Pj where pi is the price of Firm i and pj the price of the other firm (i.e. Firm j). Suppose that the marginal cost of each firm is c = 15 and its fixed cost F = 100. a) Write down the profit function of Firm A as function of prices 29,1 and p3, so 11A (pA,pB) b) Suppose Firm B charges a price of pH = 80. What is the best response of Firm A? Briefly describe your approach. Hint: first plug p3 = 80 into the profit function. 0) What is the best response of Firm A as a function of any price p3 of Firm B? Briefly describe your approach. Hint: take same steps as above but leave p3 open. You can check your answer by plugging in for p3 = 80 and finding the same number as above. d) What is the market equilibrium outcome in this case? Briefly describe your approach. Hint: you can rely on market symmetry here.