2. Suppose you are the only producer and seller of bicycles in your area. You know that half of your customers are avid bicyclists and have a valuation of quality, whereas the others value quality less. Normalize the number of customers to unity. Let H and L denote a hightaste customer and a lowtaste customer, respectively. More specically, a customer of type i E {H, L} has the following preferences over bicycle quality: \"1:: ,1}. Here, at; is a taste parameter for 1' E {H, L} with UH = ID and 11;, = IE, and :3 denotes quality. A customer of type i receives the following net utility from purchasing a bicycle of quality q : U1; = \"tilH9} Here, t {1;} denotes the price of a quality :1 bicycle. Assunle that the customers' reser 1ration net utility is zero. The cost of producing a bicycle is given by: C (a) = 3:12. You seek to maximize your prots by practicing seconddegree price discrimination. [a] Suppose rst that you can perfectly observe whether a given customer has a high or a low Tvaluation of bicycle quality. 1What levels of quality should you produoe, and what price should you charge in order to maximize your prots? 'What are your prots? (b) Ansonle instead that you catmot observe a given customer's valuation, but you lcuow that half of them have high valuation and the rest have low valuation. If you want to serve both types of customers, what are the optimal pricequality bundles? 1What are your profits? Is it better to only serve one type of the customers? Viki-by;r why not? [c] Carefully explain the difference between the answers you found in [a] and {b}