2. In country X, only one firm sells smartphones. Currently, that firm only makes one model, which costs $400 per phone to produce. There are two groups of consumers who might want to buy phones in country X. There are 100 consumers, who we'll call type As, who are willing to pay up to $800 for one of the firm's phones. There are 200 consumers, who we'll call type Bs, who are willing to pay up to $500 for one of the firm's phones. The firm knows how many there are of each type of consumer, and what they are willing to pay, but can't tell which type a given consumer is, and so can't charge the types different prices. (a) What price should the firm charge for a phone in country X to maximize its profit? Your answer should compare the profits of two particular prices, to show definitively that you have found the best price for the firm to charge. (8 points) (b) Technicians at the firm invent a smartphone model that is more basic than their standard model. This new model costs $200 per phone to produce. A type A consumer in country X would be willing to pay up to $450 for a new model, as well as being willing to pay up to $800 for the standard model as before and would not buy two phones). A type B consumer in country X would be willing to pay up to $300 for a new model, as well as being willing to pay up to $500 for a standard model, as before and would not buy two phones). Find a way for the firm to produce both models for sale in country X, with different prices for the two models, that would carn it more profit than the best profit you found in part (a). Calculate the firm's profit to show that you are right. Whatever prices the firm charges, a consumer must make the purchase that maximizes her consumer surplus; when a consumer gets the same surplus from buying either kind of phone, or the same surplus from buying a phone or not buying a phone, you may assume that the consumer makes the choice that yields more profit for the firm. (12 points)