Firm 1 and Firm 2 sell identical products except for the fact that customers must purchase the good at a physical store location, which differs by firm. Customers face travel costs but are equally distributed throughout the geographic market, with some closer to the location of Firm 1 and others closer to Firm 2. The demand functions for each firm given prices p1, p2 are q1(p1, p2) = 100-p1+1 2p2, q2(p2, p1) = 100-p2+1 2p1. Both firms have constant marginal costs mc1 = mc2 = 20 and zero fixed costs a) Write down the profits of each firm as a function of p1 and p2. (b) Find and graph the best-response functions of each firm to their rival's price. (c) Solve for the equilibrium price and quantity of each firm. (d) Suppose that demand changes and is now given by q1(p1, p2) = 60-p1+3 4p2, q2(p2, p1)=60-p2+3 4p1. i. Are the products now more or less differentiated? ii. Is this consistent with customers travel costs increasing or decreasing? Firm 1 and Firm 2 sell identical products except for the fact that customers must purchase the good at a physical store location, which differs by firm. Customers face travel costs but are equally distributed throughout the geographic market, with some closer to the location of Firm 1 and others closer to Firm 2. The demand functions for each firm given prices p1, p2 are q1(p1, p2) = 100-p1+1 2p2, q2(p2, p1) = 100-p2+1 2p1. Both firms have constant marginal costs mc1 = mc2 = 20 and zero fixed costs a) Write down the profits of each firm as a function of p1 and p2. (b) Find and graph the best-response functions of each firm to their rival's price. (c) Solve for the equilibrium price and quantity of each firm. (d) Suppose that demand changes and is now given by q1(p1, p2) = 60-p1+3 4p2, q2(p2, p1)=60-p2+3 4p1. i. Are the products now more or less differentiated? ii. Is this consistent with customers travel costs increasing or decreasing?