Question 3: Search In a market there are many buyers (consumers) and many sellers (rms), and one homogeneous good. a Each consumer wants to buy at most one unit of the good, and receives net utility 1 p when he buys one unit at price p. 0 Firms can produce the good at a marginal cost of zero, and hence make a prot of p. o A fraction 6 of consumers have a discount factor 61 (type-1 consumers), and a fraction 1 0 of the consumers have a discount factor 62 (type-2). o In each period, each consumer visits one rm and nds the price it charges. Then the consumer decides whether to buy from that rm or to visit another rm the following period. A consumer who make a purchase leaves the market and is replaced by an identical new consumer, so the proportions of the two types of consumers remain constant across periods. 0 You are told that in equilibrium, a fraction 1r of the rms charge a price of 391 and the remaining 1 7r charge a higher price 392 > 391.2 a. Suppose type-2 consumers are indierent between stopping rules that correspond to the two prices. Use this information to nd a relationship that must hold between 191 and 132. (This will involve 6 and 11' as well.) b. Suppose 61 > 62. What must the optimal stopping rule for type 1 consumers be? Now assume that type-2 consumers buy from the rst rm that they encounter (note that this is an optimal rule given they are indifferent). Type-1 consumers follow their optimal stopping rule. 0. Consider a rm that sells at p2. What is the probability that a consumer that arrives at this rm will buy from it? d. In this market, 0