2. Min is a monopolist in the economics tutoring market in Hyde Park. There are two types of students who demand his services. Type 1's demand curve is P = 30 -=Q and type 2's demand curve is P = 30 - Q. Min's marginal cost of tutoring is $10 (i.e., it costs him $10 to provide each unit of Q) and he has no fixed costs. For simplicity, we will assume there's one student of each type in the market. (NB: a monopolist facing a linear demand curve P = a - b Q has a marginal revenue curve given by P = a - 2bQ). [47 TOTAL POINTS] 3. On the same graph represent the demand curves of both types of students. Find the mathematical expression for the market demand curve. [5 points] b. Assuming Min cannot distinguish between the two types of students, but he knows the market demand curve (e.g., your answer in part a.). Find his profit maximizing price and quantity. [4 points] c. Calculate Min's profits and the deadweight loss (DWL). Also draw a graph showing Min's optimal decision, labeling the areas representing the profits and deadweight loss. [6 points] d. Now suppose Min can identify the two types of students (and he knows their individual demand curves) but he has to charge a uniform price to each type (i.e., he has to choose a per unit price for each type)- What price should Min charge to each type to maximize profits? [6 points] e. Assume that Min can distinguish the two types AND can also engage in first degree price discrimination. Describe in detail how he should implement such a scheme. [6 points] Assume that Min cannot distinguish between the two types of students and he decides to build two packages (and these two packages are the only options available to the students). Package #1 has 40 hours of tutoring for $800 (this is what the consumer pays for all 40 hours; the student cannot buy partial hours!) while package #2 has 20 hours of tutoring for $400 (this is what the consumer pays for all 20 hours). Min's goal is for type 1 to buy package #1 and type 2 to buy package #2. For type-1 student, Will Min achieve his goal? Justify your answer in detail. (Hint: consider the situation where type-1 student buys package #2) [8 points]