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 'η' 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 '(s x α)' , where 's' > 0 and 'α' is uniformly distributed between 0 and 1.
a. The unloyal consumers can choose to research on the prices or not. If they don't research, they will randomly choose for a supplier. If they have 0.25 probability to choose firm A and 0.75 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.
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