Greg Softie just came up with a new protein powder. He has a very loyal fanbase composed of 100 type Aconsumers, and 50 type B consumers, so he behaves like a monopolist with them. The individual inverse demands of each type is l P4401) = 50 if: and 1 P301} = 50 3'1 where 9 denotes the quantity of protein boxes. Softie's total cost function is given by (3(9) 2 2g. (a) Greg Softie, pretty new in the business, plans to apply a uniform per unit price to his customers, given that he wants both types to consume. What pricelquantity should he set? Call them Qm and Pm. What will his prots 1r,\" be? (5 points} One of his fans teaches him about 2\" degree price discrimination. He cannot tell consumers apart, so he plans on implementing it by proposing two bundles: (qA, TA) and (:13, TB) where q is the quantity and T is the price of the bundle. (b) What quantity q will Softie propose in bundle B? (5 points) (c) Greg now needs to make sure type A consumers will purchase their bundle as opposed to no purchasing anything at all. Compute the consumer surplus ofa type A consumer if he buys bundle A: (qA, TA) and nd TA as a function of qA such that type A consumers are indifferent between buying that bundle and not buying at all. ('1 0 points) (d) Greg now needs to make sure type B consumers will purchase their bundle as opposed to purchasing bundle A. Compute the consumer surplus of a type B consumer when buying bundle B (using your answer (13 from (a)) and the consumer surplus of a type B consumer when buying bundle A. We assume that if a type B consumer is indifferent between the two bundles, he buys bundle B. Find TB as a function of (La. (use the expression of TA as a function of (Li found in (b) as well) (10 points) (e) Write down the prot as a function of {IA only given that each type will consume the bundle made for him. Find the prot maximizing quantity (1:1. Conclude what the two optimal bundles (:13, T) and (9:1 , T3) will be and compute prots ar". ('1 0 points)