Price-match guarantees are commitment to consumers that a store will match the price of its competi- tors whenever it is lower. These types of announcements are generally well-received by consumers, who interpret them as signals that firms are competing more intensely on prices. In this question we are going to analyze price-match guarantees and try to understand their impact on prices. For the rest of this exercise, assume we are considering competition between two firms, say Amazon and Target. Let C (Qi) = 10Q; for both firms, and let overall demand in the market be Q = 100 - P. 1. Assume that price-match guarantees are credible commitments. For example, by announcing a price- match guarantee with Amazon, Target is committing to always match the prices of any items also sold on Amazon. (Imagine that the commitment is credible because if Target then refuses to match, it risks alienating many customers, and lose profits as a result). We are going to model price-match guarantees using a sequential move game where firms choose prices as their strategic variable (i.e. a dynamic version of the static Bertrand competition model we saw in class). Discuss why the model is appropriate in this case. 2. Assume that Target moves first, and announces a "price-match guarantee". In other words, they commit to setting Pr = PA = P (remember that in Bertrand competition we assumed that when two firms set the same price, they split demand equally). Write down Amazon's profit maximization problem and solve it. What is the equilibrium price? What is the total quantity sold by each firm and what are profits? 3. Discuss your results. Among all the models we covered in class (from perfect competition to monopoly, to Cournot and Bertrand oligopoly), which one is this equilibrium closest to? (You can use math if you'd like, but no math is needed for full credit).