Wireless Network Pricing Chapter 5: Monopoly and Price Discriminations Jianwei Huang & Lin Gao Network Communications and Economics Lab (NCEL) Information Engineering Department The Chinese University of Hong Kong Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 1 / 39
The Book E-Book freely downloadable from NCEL website: http: //ncel.ie.cuhk.edu.hk/content/wireless-network-pricing Physical book available for purchase from Morgan & Claypool ( http://goo.gl/JFGlai ) and Amazon ( http://goo.gl/JQKaEq ) Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 2 / 39
Chapter 5: Monopoly and Price Discriminations Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 3 / 39
Focus of This Chapter Key Focus: Profit maximization in a monopoly market ◮ One service provider (monopolist) dominates the market Theoretic Approach: Price Theory ◮ The study of how prices are decided and how they go up and down because of economic forces such as changes in supply and demand Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 4 / 39
Price Theory Part I: Monopoly Pricing ◮ The service provider charges a single optimized price to all consumers. Part II: Price Discrimination ◮ The service provider charges different prices for different units of products or to different consumers. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 5 / 39
Section 5.1 Theory: Monopoly Pricing Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 6 / 39
What is Monopoly? “Monopoly” is the only firm (single seller) in its industry. ◮ Question: Is Apple a monopoly? ⋆ It is the only firm that sells iPhone; ⋆ It is not the only firm that sells smartphones. The formal definition of monopoly is based on the monopoly power. Definition (Monopoly) A firm with monopoly power is referred to as a monopoly or monopolist. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 7 / 39
What is Monopoly Power? Monopoly power (or market power) is the ability of a firm to affect market prices through its actions. Definition (Monopoly Power) A firm has monopoly power, if and only if (i) it faces a downward-sloping demand curve for its product, and (ii) it has no supply curve. (i) implies that a monopolist is not perfectly competitive. That is, he is able to set the market price so as to shape the demand. (ii) implies that the market price is a consequence of the monopolist’s actions, rather than a condition that he must react to. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 8 / 39
Profit Maximization Problem P : the market price that a monopolist chooses; Q � D ( P ): the downward-sloping demand curve that the monopolist faces; Definition (Monopolist’s Profit Maximization Problem) The monopolist’s choice of market price P to maximize his profit (revenue) π ( P ) � P · Q = P · D ( P ) . For simplicity, we assume that there is no production cost, hence profit = revenue. In general, profit = revenue - cost. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 9 / 39
Profit Maximization Problem The first-order condition: d π ( P ) = Q + P · d Q d P = 0 d P The optimality condition: P · △ Q Q · △ P + 1 = 0 ◮ △ P is a very small change in price, and △ Q is the corresponding change in demand quantity. How to understand this? Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 10 / 39
Demand Elasticity Price Elasticity of Demand (defined in Section 3.2.5) η � △ Q / Q △ P / P = P · △ Q Q · △ P ◮ The ratio between the percentage change of demand and the percentage change of price. A Closely Related Question: Under a particular price P and demand Q = D ( P ) , how much should the monopolist lower his price to sell additional △ Q units of product? ⇒ Answer: P △ P = Q · η · △ Q Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 11 / 39
Demand Elasticity The monopolist’s total profit change by selling additional △ Q units of product: △ π � ( P + △ P ) · ( Q + △ Q ) − P · Q = P · Q + P · △ Q + △ P · Q + △ P · △ Q − P · Q ≈ P · △ Q − |△ P | · Q � � P � � = P · △ Q − Q · η · △ Q � · Q � � � � � 1 − 1 = P · △ Q · | η | ◮ P · △ Q is the profit gain that the monopolist achieves, by selling additional △ Q units of product at price P ; ◮ |△ P | · Q is the profit loss that the monopolist suffers, due to the decrease of price (by |△ P | ) for the previous Q units of product. ◮ We ignore the higher order term of △ P · △ Q . Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 12 / 39
Demand Elasticity Monopolist’s Total Profit Change: � 1 − 1 � △ π = P · △ Q · | η | ◮ If | η | > 1, then △ π > 0. The monopolist has the incentive to decrease the price. ◮ If | η | < 1, then △ π < 0. The monopolist has the incentive to increase the price. ◮ If | η | = 1, then △ π = 0. The monopolist has no incentive to change the price. The price under | η | = 1 is the optimal price (if no producing cost) ◮ Equivalent to the previous first-order condition. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 13 / 39
Demand Elasticity Now consider the production cost, where profit = revenue - cost. Suppose the unit producing cost is C . Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 14 / 39
Demand Elasticity Now consider the production cost, where profit = revenue - cost. Suppose the unit producing cost is C . The optimal price is given by △ π = C · △ Q , or equivalently, � � 1 − 1 P · △ Q · = C · △ Q . | η | Hence at the optimal price, we have 1 | η | = 1 − C / P > 1 Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 14 / 39
Demand Elasticity Now consider the production cost, where profit = revenue - cost. Suppose the unit producing cost is C . The optimal price is given by △ π = C · △ Q , or equivalently, � � 1 − 1 P · △ Q · = C · △ Q . | η | Hence at the optimal price, we have 1 | η | = 1 − C / P > 1 Recall that ◮ When | η | > 1, we say that the demand curve is elastic. ◮ When | η | < 1, we say that the demand curve is inelastic. Theorem A monopolist always operates on the elastic portion of the demand curve. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 14 / 39
Demand Elasticity When △ Q = 1, then � � ◮ △ π = P · 1 1 − is called the marginal revenue (MR); | η | ◮ C is the marginal cost (MC). In general, MC may not be a constant. We have � 1 − 1 � MR = P · = C = MC . | η | ◮ The optimal production quality equalizes MR and MC. Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 15 / 39
Section 5.2 Theory: Price Discriminations Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 16 / 39
What is Price Discrimination? Price discrimination (or price differentiation) is a pricing strategy where products are transacted at different prices in different markets or territories. Examples: ◮ Charge different prices to the same consumer, e.g., for different units of products; ◮ Charge uniform but different prices to different groups of consumers for the same product. Three types: ◮ First-degree price discrimination ◮ Second-degree price discrimination ◮ Third-degree price discrimination Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 17 / 39
An Illustrative Example How would the monopolist increase his profit via price discrimination? ◮ MR: the marginal revenue curve; ◮ MC: the marginal cost curve; ◮ Demand: the downward-sloping demand curve; Price MC π + P ∗ π ⋆ Demand π ∗ C 0 MR 0 Q ∗ Quantity Q ⋆ Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 18 / 39
Without Price Discrimination Without price discrimination, the monopolist charges a single monopoly price to all consumers: The optimal production quality (and demand) is Q ∗ , which equalizes MC and MR; The optimal monopoly price is P ∗ , which is determined by the Q ∗ and the demand curve. The monopolist’s profit (=revenue - cost) is π ∗ , and the consumer surplus is π + . Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 19 / 39
With Price Discrimination With price discrimination, the monopolist can charge different prices to different consumers: For example, the monopolist can charge each consumer the most that he would be willing to pay for each product that he buys; With the same demand Q ∗ , the monopolist’s profit is π ∗ + π + , and the consumer surplus is 0; When the demand increases to Q ⋆ , the monopolist’s profit is π ∗ + π + + π ⋆ , and the consumer surplus is 0; Huang & Gao ( c � NCEL) Wireless Network Pricing: Chapter 5 September 25, 2018 20 / 39
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