4. (5pts) Suppose there are two kinds of customers for shampoo: grungy and fancy. They each make up 50% ofthe market (you can answer the questions in this problem by imagining that there is just 1 grungy and 1 fancy customer). The marginal benefit (measured in dollars} of the two kinds of customers is described by the following table: m__ 2"d -int of sham -oo _ 3rd int of shamoo __ Suppose the marginal cost of production for the firm is $1 per pint of shampoo. For simplicity, we are going to treat the producer as a monopolist (even though in reality we have monopolistic competition in shampoo markets). The monopolist cannot tell which customers negLunagand which are Fancy. For answering these questions assume that if a customer is indifferent between no shampoo and 1 pint they will buy 1; if they are indifferent between 1 and 2 pints they will buy 2. a. Suppose the monopolist charges a single price per pint of shampoo. What single price gives them the largest profits? [Hint: It will be 1, 2.5, 4, or 5] (1pt} b. The monopolist decides to sell LE bottles and 2 pint bottles of shampoo. They will charge P1 for the Lg bottle and P2 for the two pint bottle. What pair of prices below will give them the largest profits? (1pt) i. P1 = 2.5; P; = 6.5 ii. P1 = 2.5; P; = 7.5 iii. P1 = 4; P2 = 6.5 W. P1 = 4; P2 = 7.5 V. P1 = 5; P2 = 6.5 Vi. P1 = 5; P2 = 7.5 c. Given your answer to the above, who pays most per pint of shampoo (not per bottlelpt) d. What kind of price discrimination is Mlpt) e. How does this price discrimination affect the producer's profits relative to no price discrimination (increase/decrease/unchangedlpt)