1, (3DPD) Suppose that a local monopolist car rental company estimates that the student demand for its car is: P_S = 100 - q_S/2 and non-student customer demand is given by: P_NS = 150 - q_NS/2. The marginal cost of renting out a car is estimated to be $25per car.

a, Assume that the monopolist cannot differentiate individuals in these two groups. Monopolist is thinking of using 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_S + q_NS). Clearly state the market price range to serve both the student and non-student population.
• ii, Use the inverse demand in part i) and derive marginal revenue.
• iii, Calculate profit maximizing price and quantity. Does the price satisfy the range you defined in part i)?
• iv, Calculate the profit of the monopolist

b Now assume that monopolist is thinking about third-degree price discrimination (3DPD).

• i, What price should this firm charge students and what price should it charge non-students? Find profit maximizing quantity under both scenarios. ii.Calculate the consumer surplus of two types of buyers.

Please include all the calculation steps for every questions.