Can i please get help for this question? Thanks

Quution 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. - Firms can produce the good at a marginal cost of zero1 and hence make a prot of p. o a fraction H of consumers have a discount factor 51 (type-l consumers}, and a fraction 1 E! of the consumers have a discount factor 62 (type-2]. - 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 consumer1 so the proportions of the two types of consumers remain constant across periods. a You are told that in equilibrium, a fraction 11' of the rms charge a price of 331 and the remaining 1 1r charge a higher price pg 2} 15-1.2 a. Suppose type-2 consumers are indifferent between stopping rules that correspond to the two prices. Use this information to nd a relationship that must hold between 1:11 and 332. (This will involve .5 and 11' as well.} b. Suppose 1 :5 452. 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). 'I'ype-l consumers follow their optimal stopping rule. c. Consider a rm that sells at 1:13. 'What is the probability that a consumer that arrives at this rm will buy from it? d. In this market, ll (-5. 11' r: 1, i.e.1 there are rms that sell at both prices 1511 and pg. What is the relation between the two prices that must hold for this to be true? e. Using your answers above1 nd the equilibrium value of r in terms of the 45s, 3 and the prices