Y=5

2. Two firms produce identical products and compete by choosing a price between 0 and 1 in a single period. There is a unit mass of consumers (i.e. the size of the market is 1). Let a = Y/100, where Y is the number you calculated based on your SID. A fraction o of consumers always buy from Firm 1, a fraction o always buy from Firm 2, and the remaining fraction 1 - 20 are shoppers who buy from the cheapest firm (and buy from each firm with equal probability if the prices are equal) Firms have constant marginal costs of c = 0.1 and no fixed costs. (a) Find the market share of each firm as a function of the prices set by both firms. [3 marks] (b) Suppose the firms play pure pricing strategies. i. Solve for the reaction function of each firm. [5 marks] ii. Is there a Nash equilibrium in pure strategies? Explain. [2 marks] (c) Suppose the firms play mixed pricing strategies. Solve for the symmetric Nash equilibrium in mixed strategies. Explain carefully. [10 marks]