2. "Nikie" is a famous sportswear brand. For simplicity, assume that Nikie only sells one product, the popular "Air Jon" basketball shoes, and that Nikie is a monopolist. Suppose there are two groups of consumers for Air Jon. The total demand coming from the first group is characterized by the demand curve P = 900Q: The total demand by the second group is characterized by a constant willingness to pay of $70/pair for up to 50 pairs. In other words, the demand for the second group is 50 pairs of Air Jon as long as the price is no higher than $70/pair and zero otherwise. Suppose the marginal cost of producing Air Jon is $10. a) Suppose Nikie could set tow prices, one for each group of consumers. To maximize profit, what price should it charge the first group of consumers (P1) and what price should it charge the second group of consumers (P2)? What is the total profit? (Show your steps) b) Now suppose Nikie cannot charge different prices to different consumers. The company can only charge one price for all consumer. Please calculate which price leads to the highest total profit. (Show your steps) Nikie discovered that two types of consumers have very different time costs. Nikie is considering setting up two shops, one to be conveniently located in the downtown area where everyone lives and the other one to be located in a remote suburban area. Suppose the time cost of going to the downtown shop is zero for everyone. While the time cost of going to the suburban shop is still zero for the first group of consumers (with demand P = 90 0 Q), the time cost is equivalent to $30 for the second group consumers (with willingness to pay of $70). Resale is impossible. c) Suppose each consumer either buys one or zero pair of shoes. Would Nikie be able to achieve the total profits in question (a) by charging different price in the two shops? Explain your