4. (3DPD) Suppose that a local monopolist car rental company estimates that the student demand for its car is: P; = 100 45/ 2 and nonstudent customer demand is given by: PM = 150 qNs/ 2. The marginal cost of renting out a car is estimated to be $25 per car. a. Assume that monopolist cannot differentiate individuals in these two groups. Monopolist is thinking to use uniform pricing to meet the demands of both groups. That is, to charge single profit maximizing price for both groups. i. Derive inverse total market demand (Hint Total market demand Q = q; + 4N5). Clearly state the market price range to serve both student and nonstudent population. ii. Use the inverse demand in part i) and derive marginal revenue. Then plot market demand, marginal revenue, and marginal cost. 1ii. Use the inverse demand in part i) and calculate prot maximizing price and quantity. Does the price satisfy the range you dened in part i)? iv. Calculate the prot of the monopolist. V. Calculate the consumer surplus. b. Now assume that monopolist is thinking about thirddegree price discrimination (3DPD). i. What price should this rm charge students and what price should it charge nonstudents? Find prot maximizing quantity under both scenarios. ii. Calculate the consumer surplus of two type of buyers. 5. (2DPD) A streaming service provider is designing a monthly subscription package, that is specically designed for students and nonstudent adult customers. The rm estimates that the student demand is described by P = 18 Q, and nonstudent demand is given by P = 20 Q. The marginal cost of the rm is constant at $2. Assume that the rm is not able to differentiate its customers, hence does not know how much they are willing to pay. Currently, student package costs $160, and it includes 16 months of streaming subscription. Now, this rm is thinking about how to use the concepts from 2DPD and price the package for non-student customers with 18-month subscription. a. Calculate how much adults are willing to pay for 16 months of subscription (Him? Calculate adult czm'amer z'oz'al willingness to payfor 76 Mill"). b. How much surplus will adult (nonstudent) customer get if they purchase a package designed to students? c. The streaming service provider wants to nonstudent customers to purchase a package with 18 months of subscription. What should be the price of such subscription? P P 20 15 P = 20- Q $18 ( P = 18 - Q $2 MC $2 MC D ( WTP ) D ( WTP ) 20 0 18