It is an extremely hot and sunny day on Far Rockaway beach. However, there is only one shop selling non-dairy ice cream; the shop is a monopolist retailer of ice cream. There are two types of people on the beach: the ones who prefer dairy ice cream, and those who prefer alternative ice cream. This suggests that they have a different willingness to pay for non-dairy ice cream. The dairy ice cream group has demand q = 210-p and the alternative ice cream group one has demand q2 = 300 - P2. The supplier has marginal cost MC(q) = 4q, where q = q1 +92 is the total amount sold at the beach. (a) Suppose that the owner of the shop is able to distinguish whether each customer prefers milk or oat milk. Hence, she can separate the customers into the two groups discussed above (third degree price discrimination). She prepares two different ice creams and sells them at different prices. In this way, each group will pay its own price per unit. How many units does the shop sell to each group? At what prices? (b) Suppose that the owner of the shop knows every person in Far Rockaway very well. She can first degree price discriminate her customers by charging each his/her full willingness to pay for every unit. How many units does she sell to each group? (c) Finally, assume that the owner of the shop is new in town and so she is not able to distinguish among the two groups; she can only set a single price for everyone. Compute the total market demand the supplier is facing (quantity as function of the price; remember, here the two different groups have different price intercepts). Then, compute the marginal revenue as function of the total quantity and the optimal quantity and price set by the monopolist. Are customers from both groups buying the goods? Please provide a graphical representation of the analysis.