(20 marks) Consider a simple search cost model introduced in the lecture. Assume that there are 2 firms, firm A and firm B, who are selling homogeneous products and competing in prices. Firm A is a new entrant and firm B is an incumbent which has numbers of loyal consumers. There are also unloyal consumers in the economy and the size is normalized to 1 . For all types of consumers, they can get utility k from consuming the product. The search cost of consumers are denoted by s, where s>0 and is uniformly distributed between 0 and 1 . a. The unloyal consumers can choose to do a research on the prices or not. If they don't do a research, they will randomly choose for a supplier. If they have 1/4 probability to choose firm A and 3/4 probability to choose firm B, find the consumer who is indifferent in doing a research and randomly choosing for a supplier. b. Derive the demand function of firm A and firm B. c. Calculate the profit maximizing prices of both firms