Suppose that individual demand for a product is given by Qd = 1000 5P. Marginal revenue, 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 with the consumer buy in total? b. Show that this second-degree price-discrimination scheme is more profitable than a single monopoly price.