Here, v; is a taste parameter for 6 {H, L} with vy = 10 and vz = 6, and q denotes quality. A customer of type i receives the following net utility from purchasing a bicycle of quality q : Ui = vig - t (q) . Here, t (q) denotes the price of a quality q bicycle. Assume that the customers' reser- vation net utility is zero. The cost of producing a bicycle is given by: c (q) = 2q2. You seek to maximize your profits by practicing second-degree price discrimination. (a) Suppose first that you can perfectly observe whether a given customer has a high or a low valuation of bicycle quality. What levels of quality should you produce, and what price should you charge in order to maximize your profits? What are your profits? (b) Assume instead that you cannot observe a given customer's valuation, but you know 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 price-quality bundles? What are your profits? Is it better to only serve one type of the customers? Why/why not? (c) Carefully explain the difference between the answers you found in (a) and (b).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 high-taste customer and a low-taste customer, respectively. More specifically, a customer of type ic { H, L} has the following preferences over bicycle quality