Chapter 12 Capturing Surplus

Chapter Twelve Overview Introduction: Airline Tickets Price Discrimination First Degree Second Degree Third Degree Tie-in Sales Requirements Tie-ins Package Tie-ins (Bundling) Chapter Twelve

Uniform Price Vs. Price Discrimination Definition: A monopolist charges a uniform price if it sets the same price for every unit of output sold. While the monopolist captures profits due to an optimal uniform pricing policy, it does not receive the consumer surplus or dead-weight loss associated with this policy. The monopolist can overcome this by charging more than one price for its product. Definition: A monopolist price discriminates if it charges more than one price for the same good or service. Chapter Twelve

Forms of Price Discrimination Definition: A policy of first degree (or perfect) price discrimination prices each unit sold at the consumer's maximum willingness to pay. This willingness to pay is directly observable by the monopolist. Definition: A policy of second degree price discrimination allows the monopolist to offer consumers a quantity discount. 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. Chapter Twelve

“Willingness to Pay” Curve Definition: The consumer's maximum willingness to pay is called the consumer's reservation price. Think of the demand curve as a "willingness to pay" curve. If the monopolist can observe the willingness to pay of each customer (based on, for example, residence, education, "look", etc), then the monopolist can observe demand perfectly and can "perfectly" price discriminate. Chapter Twelve

Forms of Price Discrimination Definition: A policy of first degree (or perfect) price discrimination prices each unit sold at the consumer's maximum willingness to pay. This willingness to pay is directly observable by the monopolist. Chapter Twelve

Uniform Price Vs. Price Discrimination Uniform Price Monopoly 1st Degree P.D. Monopoly CS: E+F 0 PS: G+H+K+L E+F+G+H+J+K+L+N TS: E+F+G+H+K+L E+F+G+H+J+K+L+N DWL: J+N 0 E F PU H MC G J P1 N K L MR D Quantity Chapter Twelve

Is it Reasonable? Buying a Car The monopolist will continue selling units until the reservation price exactly equals marginal cost. Therefore, a perfectly price discriminating monopolist will produce and sell the efficient quantity of output. Note: Only if the monopolist can prevent resale can the monopolist capture the entire surplus. Chapter Twelve

Pricing Surplus – Monopoly MC = 2 P = 20 - Q What is producer surplus if uniform pricing is followed? MR = P + (P/Q)Q = 20 - Q - Q = 20 - 2Q MR = MC => 20 - 2Q = 2 => Q* = 9 P* = 11 PS= Revenue-TVC = PQ-2Q = 11(9)-2(9) = 81 Chapter Twelve

Pricing Surplus – Monopoly What will producer surplus be if the monopolist perfectly price discriminates? P = MC => 20 - Q = 2 =>Q* = 18 Revenue - TVC = [18(20-2)(1/2) + 18(2)]-18(2) = 162 This is a gain in captured surplus of 81! Chapter Twelve

First Degree Price Discrimination What is the marginal revenue curve for a perfectly price discriminating monopolist? When the monopolist sells an additional unit, it does not have to reduce the price on the other units it is selling. Therefore, MR = P. (i.e., the marginal revenue curve equals the demand curve.) 20 11 2 MC D 9 18 20 Quantity MR (uniform pricing) Chapter Twelve

Second Degree Price Discrimination Definition: A policy of second degree price discrimination allows the monopolist to charge a different price to different consumers. While different consumers pay different prices, the reservation price of any one consumer cannot be directly observed. Chapter Twelve

Two Part Tariff Definition: A monopolist charges a two part tariff if it charges a per unit fee, r, plus a lump sum fee (paid whether or not a positive number of units is consumed), F. This, effectively, charges demanders of a low quantity a different average price than demanders of a high quantity. Example: hook-up charge plus usage fee for a telephone, club membership, or the like. Chapter Twelve

Two Part Tariff P 100 Example: 4050 10 Q 90 100 All customers are identical and have demand P = 100 - Q MC = AC = 10 4050 10 Q 90 100 Chapter Twelve

Two Part Tariff What is the optimal two-part tariff? Two steps: (1) maximize the benefits to the consumers by charging r = MC = 10. (2) capture this benefit by setting F = consumer benefits = 4050. Chapter Twelve

Two Part Tariff Any higher usage charge would result in a dead-weight loss that could not be captured by the monopolist. Any lower usage charge would result in selling at less than marginal cost. In essence, 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. Chapter Twelve

Block Tariff Definition: If a consumer pays one price for one block of output and another price for another block of output, the consumer faces a block tariff Chapter Twelve

Block Tariff Example P = 100 - Q MC = AC = 10 Let Q1 be the largest quantity for which the first block rate applies so that p1(Q1) = 100 - Q1. Let Q2 be the largest quantity purchased (so that the second block rate will apply between Q1 and Q2) so that p2(Q2) = 100 - Q2 Chapter Twelve

Block Tariff Example Then:  = p1(Q1)Q1 + p2(Q2)(Q2-Q1) - TC(Q2) = (100 - Q1)Q1 + (100 - Q2)(Q2-Q1) - 10Q2 and we must choose Q1 and Q2 to maximize this profit… MR1 = (100 - Q1) - Q1 - (100 - Q2) = 0 MR2 = (100 - Q2) - Q2 + Q1 = MC = 10 Chapter Twelve

Key Equations These are two equations in two unknowns that can be solved to obtain: Q1* = 30 Q2* = 60 P1* = 70 P2* = 40 (a quantity discount) Chapter Twelve

Block Pricing Quantity Single Price Discrimination Monopoly P P 100 Demand Demand 450 70 1012.5 55 450 40 2700 2025 1012.5 450 MC 10 30 60 100 45 MR 100 Q Q Chapter Twelve

Block Pricing If the monopolist could set a different block price for each customer, it would capture the same amount of surplus as a perfectly price discriminating monopolist. Chapter Twelve

Utility Pricing D - small D - large MC Q Chapter Twelve

Utility Pricing D - small D - large Additional CS P1 Additional PS P2 MC Q1s Q1L Q2L Q Chapter Twelve

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 Suppose that marginal costs for the two markets are the same. How does a monopolist maximize profit with this type of price discrimination? Chapter Twelve

Optimal Pricing Example Set the marginal revenue in each market equal to marginal cost. (i.e., the monopolist maximizes total profits by maximizing profits from each group individually.) This implies that MR1 = MC = MR2 at the optimum. Otherwise, the monopolist could raise revenues by switching sales from the low MR group to the high MR group. MC = AC = 20 P1 = 100 - Q1 P2 = 80 - 2Q2 Example Chapter Twelve

Optimal Pricing Example MR1 = 100 - 2Q1 = MC = 20 Chapter Twelve

Third Degree Price Discrimination Market 1 Market 2 100 Demand 1 80 Demand 2 60 50 20 100 20 40 MR1 Q Q MR2 Chapter Twelve

Tie-in Sales – Requirements Definition: A tie-in sale occurs if customer can buy one product only if they agree to purchase another product as well. Requirements tie-in sales occur when a firm requires customers who buy one product from the firm to buy another product from the firm. A requirements tie-in sale may be used in place of price discrimination when the firm cannot observe the relative willingness to pay of different customers. Chapter Twelve

Tie-in Sales – Bundling Package tie-in sales (or bundling) occur when goods are combined so that customers cannot buy either good separately. Bundling may be used in place of price discrimination to increase producer surplus when consumers have different willingness to pay for the goods sold in the bundle. But bundling does not always pay… Chapter Twelve

Tie-in Sales – Bundling Negatively Correlated Preferences Chapter Twelve

Tie-in Sales – Bundling Optimal Pricing Policy Without bundling: pc = $1500 pm = $600 Profit cm = $800 With bundling: pb = $1800 Profit b = $1000 Chapter Twelve

Tie-in Sales – Bundling Positively Correlated Preferences Chapter Twelve

Tie-in Sales – Bundling Optimal Pricing Policy Without bundling: pc = $1500 pm = $600 Profit cm = $800 With bundling: pb = $2100 Profit b = $800 In general, bundling a pair of goods only pays if their demands are negatively correlated (customers who are willing to pay relatively more for good A are not willing to pay as much for good B). Chapter Twelve

Reservation Price The reason is that the price is determined by the purchaser with the lowest reservation price. If reservation prices for the two goods are negatively correlated, bundling reduces the dispersion of reservation prices and so raises the price at which additional units can be sold. Chapter Twelve

Advertising The firm can capture surplus using nonprice strategies such as advertising. Chapter Twelve