Suppose that individual demand for a product is given by QD = 1000 - 5P. Marginal revenue is MR = 200 - 0.4Q, and marginal cost is constant at $20. There are no fixed costs.
a. The firm is considering a quantity discount. The first 400 units can be purchased at a price of $120, and further units can be purchased at a price of $80. How many units will the consumer buy in total?
b. Show that this second-degree price-discrimination scheme is more profitable than a single monopoly price.