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.
Qd = 1000 - 5P
Let P = 120
Qd = 1000 - 5(120)
Qd = 1000 - 600
Qd = 400
At a price of $120, the consumer will buy 400 units.
Let P = 80
Qd = 1000 - 5(80)
Qd = 1000 - 400
Qd = 600
At a price ...
Given the function of the demand curve for a product and a monopolist's Marginal Cost, this solution shows how second degree price discrimination in the form of a quantity discount can increase the firm's profits. All calculations are given and explained in full.