Lecture 18: Price Discrimination and Monopoly Pricing Strategies

Overview and Learning Objectives

• The primary goal of the session is to examine the methods by which monopolists charge different prices to different consumers.

• It investigates why certain markets or consumer groups pay higher prices than others.

• The analysis includes an evaluation of the welfare effects associated with various pricing behaviors.

Sequential Models of Firm Behavior

• The study of firm pricing behavior has been developed through a specific pedagogical sequence:

  • Price Takers: Firms that take the market price as given (Week 8).

  • Uniform Price Monopolists: A single firm with market power that charges a uniform price for all units and consumers (Week 9).

  • Price Discriminating Monopolists: A single firm with market power that charges different prices for different units or to different consumers (Current Lecture).

  • Strategic Interaction: Multiple firms with market power determining prices through strategic interaction (Next Lecture).

Price Variation and Discrimination Definitions

• Real-World Example (iPhone 16 Pricing):

  • As of April 19, 2024, a 6.1-inch iPhone 16 with 128 GB storage costs $USD\,799$ (approximately $AUD\,1,251$) in the United States.

  • The same product costs $AUD\,1,399$ in Australia.

  • This discrepancy illustrates pricing strategies based on geographic market segmentation.

• Definition of Price Discrimination: This is the practice of charging different consumers different prices for the exact same product.

• The Three Degrees of Price Discrimination:

  • First-degree price discrimination: Charging every consumer an individual-specific price for the same product based on their maximum willingness to pay.

  • Second-degree price discrimination: Utilizing quantity-based pricing schemes. This allows consumers to self-select into different per-unit prices based on their level of consumption.

  • Third-degree price discrimination: Charging different groups of consumers (segmented by specific characteristics) different prices for the same product.

Third-Degree Price Discrimination

• This is the most common form of price discrimination found in the marketplace.

• Common Examples:

  • Senior citizen discounts.

  • Student discounts.

  • International market segmentation (e.g., different prices for the same software or hardware in different countries).

• Feasibility and Market Conditions:

  • To explain international price differences, one must understand how pricing strategies depend on price elasticity of demand.

  • Elasticity Recall: More elastic demand indicates that quantity demanded is highly responsive to price changes. This occurs when consumers have many substitutes available.

• Mathematical Model of the Profit-Maximizing Monopolist (Two Markets):

  • A monopolist sells an identical product in Market 1 and Market 2.

  • Prices are set as $P_1$ and $P_2$.

  • Total output: $Q = Q_1 + Q_2$.

  • Total Costs: $TC(Q)$.

  • Crucially, in this model, the cost of the product does not depend on the destination market.

  • Profit function: $\pi = P_1(Q_1)Q_1 + P_2(Q_2)Q_2 - TC(Q)$.

• Profit Maximization Conditions:

  • Market 1: $MR(Q_1) = MC(Q)$.

  • Market 2: $MR(Q_2) = MC(Q)$.

  • Equilibrium relationship: $MR(Q_1) = MC(Q) = MR(Q_2)$.

  • If MR_1 > MR_2 = MC, the firm would shift sales from Market 2 to Market 1 to increase total profits.

• Analytical Example:

  • Inverse Demand Market 1: $P_1 = 10 - Q_1$.

  • Inverse Demand Market 2: $P_2 = 15 - Q_2$.

  • Constant Marginal Cost: $MC = 2$.

  • Equilibrium in Market 1:

    • Total Revenue ($TR_1$): $(10 - Q_1)Q_1 = 10Q_1 - Q_1^2$.

    • Marginal Revenue ($MR_1$): $10 - 2Q_1$.

    • Setting $MR_1 = MC$: $10 - 2Q_1 = 2$.

    • Resulting quantity and price: $Q_1 = 4$ and $P_1 = 10 - 4 = 6$.

• Price/Elasticity Correlation:

  • The monopolist will charge a lower price in the market with the lower willingness to pay.

  • Calculating Elasticity at equilibrium ($E_d = \frac{dQ}{dP} \times \frac{P}{Q}$):

    • Market 1 Equilibrium ($Q_1=4$, $P_1=6$): $E_{d1} = -1 \times \frac{6}{4} = -1.50$.

    • Market 2 Equilibrium (where $15-2Q_2=2 \rightarrow Q_2=6.5$, $P_2=8.5$): $E_{d2} = -1 \times \frac{8.5}{6.5} = -1.31$.

  • Core Principle: The market with the less elastic demand (Market 2 in this case) pays a higher price.

  • Requirement: This strategy requires the absence of arbitrage opportunities (re-selling from the low-price market to the high-price market).

Second-Degree Price Discrimination

• In this model, firms offer a schedule of prices and let consumers self-select.

• Price Structure Example:

  • The total price paid is defined as: $PT(Q) = A + PQ$.

  • $A$ represents a fixed fee.

  • $P$ represents the price paid per individual unit consumed.

• Average Price Calculation:

  • $\text{Average Price} = \frac{A}{Q} + P$.

• Implication: Consumers who purchase larger quantities ($Q$) pay a lower average price, effectively creating a volume discount.

First-Degree Price Discrimination

• Also known as perfect price discrimination, where consumers are charged individual-specific prices based on their exact willingness to pay.

• Shift in Marginal Revenue:

  • In uniform pricing, the monopolist must lower the price on all units to sell more, causing the $MR$ curve to lie below the demand curve.

  • Under first-degree discrimination, the firm charges each person their specific maximum price. Thus, the incremental revenue for each unit is simply the price paid.

  • The $MR$ curve effectively becomes the Demand curve ($D = MR$).

• Optimal Output and Profit:

  • The monopolist continues to sell as long as $P \ge MC$.

  • Optimal output moves from $Q_M$ (the uniform monopoly quantity) to $Q_{PD}$ (where the Demand curve intersects the $MC$ curve).

  • The firm captures all consumer surplus, converting it into producer surplus ($PS_2$).

Welfare Implications

• Uniform Pricing Baseline:

  • Generates consumer surplus ($CS$), producer surplus ($PS_1$), and a deadweight loss ($DWL$) due to under-production.

• Perfect Discrimination Comparison:

  • Total Surplus ($TS_2$) is equal to Producer Surplus ($PS_2$).

  • $TS_2 = CS + PS_1 + DWL$.

  • Because the $DWL$ is eliminated, TS_2 > TS_1.

• Summary of Effects:

  • Welfare Efficiency: Total surplus increases because the monopolist produces up to the socially efficient quantity ($P = MC$).

  • Distributional Impact: There are distinct winners and losers. The monopolist wins by capturing all surplus, while consumers lose as their surplus is entirely extracted.

Ethical and Practical considerations

• The Pink Tax: This is an example of a potentially pernicious form of price discrimination where female-targeted versions of a product (e.g., razors or personal care items) are priced higher than male-equivalent versions.

• Arbitrage: For any form of price discrimination to be successful in the long term, the firm must be able to prevent consumers from buying at the lower price and reselling to those facing the higher price.