Question

Suppose that a monopoly sells its product in a market with 10 identical consumers. Each consumer has an individual demand given by P = 30 − 2y, where y is the individual quantity demanded at price P. The firm has no fixed costs and a constant marginal cost equal to 5. a) Show that the aggregate inverse market demand is given by P(Y ) = 30 − Y /5, where Y is total quantity demanded in the market. b) First, assume that the monopolist can’t price discriminate. i. compute the firm’s profit function π(Y ), ii. compute the monopoly’s profit-maximizing quantity Ym and price Pm . 8 iii. determine the implied consumer surplus and deadweight loss. Show them on a graph. c) Assume now that the firm decides to use two-part tariff. i. compute the optimal two-part tariff. 9 ii. compute the total quantity produced by the firm, and determine the firm’s profits. iii. compute the implied consumer surplus and deadweight loss. d) Compute the quantity produced and the consumer surplus if the firm uses perfect price discrimination. Compare the implied consumer’s welfare (as measured by the consumer surplus) to the one you found in (c)

Answer 1

d)

In the case of perfect price discrimination, the firm charges different prices for each unit sold. The firm produce up to P=MC level or Y=125 in this case and sell each unit from 0 to 125 at willingness to pay price. This way the consumer extract all the consumer surpluses and still generates efficient outcome in the market. Then in terms of CS and DWL the two-part tariff and perfect price discrimination generate the same results.