Price discrimination by a monopolist


 Alfred Cobb
 1 years ago
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1 Review Imperfect Competition: Monopoly Reasons for monopolies Monopolies problem: Choses quantity such that marginal costs equal to marginal revenue The social deadweight loss of a monopoly
2 Price discrimination by a monopolist New topic: Capturing surplus by price discrimination Definition: A monopolist charges a uniform price if it sets the same price for every unit of output sold. Definition: A monopolist price discriminates if it charges more than one price for the same good or service. What are examples of price discrimination? 1. Student version of software, various other student/senior citizen discounts. What is the advantage of this?
3 Example Airlines commonly price discriminate, using Saturday night stayovers and other devices. Suppose you live in Dallas and want to spend two weeks in LA, returning only for the weekend. First week: First Monday Dallas to Los Angeles, then First Friday Los Angeles to Dallas Second week: Second Monday Dallas to Los Angeles; and Second Friday Los Angeles to Dallas The approximate combined cost of these two flights was US$2,000. In contrast, another way of arranging exactly the same travel is to have two roundtrips, one of which originates in Dallas, while the other originates in Los Angeles:  Trip One: First Monday Dallas to Los Angeles; then second Friday Los Angeles to Dallas  Trip Two: First Friday Los Angeles to Dallas; then second Monday: Dallas to Los Angeles This pair of round trips involves exactly the same travel as the first pair, but costs less than $500 for both (at the time of this writing). Why?
4 Price discrimination Two important distinctions: Discounts to students depend on the identity of the buyers, discounts to overnight passengers depend on the choices of the buyers. The first is called discrimination. direct price discrimination, and the second is called indirect price In order for a seller to pricediscriminate, the seller must be able to Identify (approximately) the demand of groups of customers Prevent arbitrage
5 Types of discrimination Definition: A policy of first degree (or perfect) price discrimination prices each unit sold at the consumer's maximum willingness to pay. A policy of second degree price discrimination allows the monopolist to offer consumers a quantity discount. A policy of third degree price discrimination offers a different price for each segment of the market (or each consumer group) when membership in a segment can be observed.
6 Uniform pricing In the previous chapter, the monopolist charges a uniform price: p p m MC The monopoly produces a quantity such that marginal costs equals marginal revenue. MR( q) mc( q) But the price P m is given by the demand curve. It is much higher than the competitive price. q m q c MR D q Question: What happens when the monopolist can perfectly price discriminate?
7 First degree price discrimination What is the marginal revenue curve for perfectly price discriminating monopolist? The monopolist will charge the maximal price that the marginal consumer is willing to pay. When the monopolist sells an additional unit, it does not have to reduce the price on the other units it is selling. Key Rule: Under first degree price discrimination the monopolist's marginal revenue equals the demand curve. (Because the marginal revenue for each additional unit is the price of the unit). The monopolist will produce an additional unit as long as marginal cost is below the Price. The monopolist produces a quantity such that: p(q)=mc(q)
8 Example Suppose a monopolist produces at a constant marginal cost: MC = 2, and faces a demand curve given by: P = 20  Q 1. Under uniform pricing: What is the price and quantity charged? What is the monopoly's profit? What is the consumer surplus? 2. Under perfect price discrimination: What is the quantity produced? What is the monopoly s profit? Uniform pricing: MR = 202Q MR = MC => Q* = 9 and P* = 11 Monopoly's profit: 9918=81 ; Consumer surplus: 9*9/2=40.5 Perfect price discrimination: The firm produces q=18 units (or mc(q)=p(q)). As long as q<18, the firm can sell an additional unit for a price p>2. Monopoly's profit: 18*18/2=162; Consumer surplus is 0
9 First degree price discrimination Key point: The monopolist will continue selling units until the reservation price exactly equals marginal cost. Therefore, under perfect price discrimination, a monopolist will produce and sell the efficient quantity of output. The same quantity arises in a perfectly competitive market equilibrium. However, under perfect price discrimination, the consumer surplus is 0. The monopolist extracts the entire social surplus.
10 Indirect price discrimination Definition: A monopolist charges a two part tariff if it charges a per unit price p, and a lump sum fee, F. Examples: Electricity often comes with a fixed price per month and then a price per kilowatthour, which is twopart pricing.  Long distance and cellular telephone companies charge a fixed fee per month, with a fixed number of included minutes, and a price per minute for additional minutes.
11 Two Part Tariff Example: Suppose a monopolist with costs MC = AC = 10 faces 100 identical consumers. Each has an individual demand of: P = 100 Q. What is the optimal two part tariff? 11
12 Two Part Tariff Example: Suppose a monopolist with costs MC = AC = 10 faces 100 identical consumers. Each has an individual demand of: P = 100 Q. What is the optimal two part tariff? 100 P Solution two steps: (1) maximize the benefits to the consumers by charging p = MC = 10. (2) capture this benefit by setting F = consumer benefits = Q
13 Two Part Tariff Main takeaway: When facing identical consumers the monopolist can capture the entire surplus using a two part tariff The monopolist maximizes the size of the "pie", then sets the lump sum fee so as to capture the entire "pie" for itself. The total surplus captured is the same as in the case of perfect price discrimination. 13
14 Third degree price discrimination Definition: A policy of third degree price discrimination offers a different price for each segment of the market (or each consumer group) when membership in a segment can be observed. Example: Movie ticket sales to older people or students at discount The monopolist sets a uniform price for each segment of the market. 14
15 Third degree price discrimination Example: Suppose a monopolist with costs MC = AC = 20 faces two types of consumers: P 1 = Q 1 and P 2 = 802Q 2. The monopolist can charge different prices to each group. What are the optimal prices? MR 1 = 1002Q 1 MR 2 = 804Q 2 Set each equal to marginal cost. Q 1 * = 40 and P 1 * = 60, and Q 2 * = 15 and P 2 * = 50 15
16 Third degree price discrimination MR 1 = 1002Q 1 and MR 2 = 804Q 2 Set each equal to marginal cost. Q 1 * = 40 and P 1 * = 60, and Q 2 * = 15 and P 2 * = 50 P P Market 1 Market Demand Demand MR 1 Q MR 2 Q