Monopoly and Price Discrimination: Advanced Microeconomic Analysis

Monopoly: Market Structure and Analysis

Definition and Characteristics of Monopoly

A monopoly is a market structure where a single firm is the sole producer and seller of a product with no close substitutes. This firm, therefore, is the industry itself and has significant control over the market price.

• Single Seller: The firm is the only provider of the good or service.

• No Close Substitutes: Consumers cannot easily switch to another product.

• High Barriers to Entry: New firms cannot easily enter the market due to legal, technological, or resource-based obstacles.

• Price Maker: The monopolist can set the price, constrained only by the market demand curve.

Sources of Monopoly Power

Monopolies arise due to various barriers that prevent entry of new firms:

• Legal Barriers: Government licenses and patents (e.g., pharmaceutical patents).

• Exclusive Control over Inputs: Ownership or control of essential resources (e.g., De Beers in diamonds).

• Economies of Scale: Large-scale production lowers average total cost, making it difficult for smaller entrants to compete (e.g., natural monopolies like Eskom).

Profit Maximization in Monopoly

The monopolist determines the profit-maximizing output and price by equating marginal revenue (MR) with marginal cost (MC). Unlike in perfect competition, the monopolist's demand curve is the market demand curve, and the MR curve lies below it.

• Demand ≠ MR Curve: The MR curve has the same intercept as the demand curve but twice the slope.

• Example: If $P = 800 - 2Q$, then $MR = 800 - 4Q$.

Marginal Revenue and Elasticity

The relationship between marginal revenue and price elasticity of demand is crucial for monopoly pricing:

• Formula: $MR = P \left[1 - \frac{1}{E_d}\right]$

• If $E_d < 1$, MR is negative; if $E_d > 1$, MR is positive.

• Example Calculations:

  • If $E_d = 3$ and $P = 600$, $MR = 600 \left(1 - \frac{1}{3}\right) = 400$

  • If $E_d = 1$ and $P = 400$, $MR = 400 \left(1 - 1\right) = 0$

  • If $E_d = \frac{1}{3}$ and $P = 200$, $MR = 200 \left(1 - 3\right) = -400$

Monopoly Price and Output Determination

The monopolist maximizes profit where $MR = MC$, and sets price according to the demand curve at that output. The result is typically:

• Output: Where $MR = MC$

• Price: Highest price consumers are willing to pay for that output

• Inefficiency: Price exceeds marginal cost ($P > MC$), leading to allocative inefficiency

Lerner Index, Mark-up, and Market Power

The Lerner Index measures the degree of market power by comparing the difference between price and marginal cost as a proportion of price:

• Formula: $L = \frac{P - MC}{P} = \frac{1}{|E_d|}$

• Value ranges from 0 (perfect competition) to 1 (maximum market power).

• More elastic demand ($|E_d|$ large) means lower mark-up; less elastic demand means higher mark-up.

• Example: If $E_d = -2$, mark-up is $\frac{1}{2}$, so profit-maximizing price is twice the marginal cost.

Monopolist Has No Supply Curve

Unlike competitive firms, a monopolist does not have a unique supply curve. The quantity supplied depends on the demand curve and the monopolist's pricing decision, not just on price.

• When demand shifts, the elasticity at a given price may change, so there is no unique price-quantity relationship.

• The monopolist's supply rule is $MR = MC$.

Price Discrimination in Monopoly

Definition and Types of Price Discrimination

Price discrimination occurs when a monopolist charges different prices to different buyers for the same product, not based on cost differences. The main types are:

• First-degree (Perfect) Price Discrimination: Each unit is sold at the maximum price each consumer is willing to pay.

• Second-degree Price Discrimination: Price varies according to the quantity consumed or purchased (block pricing).

• Third-degree Price Discrimination: Different prices are charged to different consumer groups or markets based on elasticity of demand.

Requirements for Price Discrimination

• The seller must have market power (be a price maker).

• The ability to distinguish between buyers with different willingness to pay (different elasticities).

• Prevention of resale (arbitrage) between buyers.

First-Degree Price Discrimination (Perfect PD)

In first-degree price discrimination, the monopolist captures all consumer surplus by charging each consumer their maximum willingness to pay. This leads to allocative efficiency, similar to perfect competition.

• Allocative Efficiency: Output is produced where $P = MC$ for each unit.

• Comparison: Both perfectly competitive firms and monopolies with perfect PD are allocatively efficient, but the monopolist captures all surplus.

Second-Degree Price Discrimination

Second-degree price discrimination involves charging different prices based on the quantity purchased, often through a pricing schedule. All buyers face the same schedule, but consumer surplus is only partially captured.

• Example: Bulk discounts, utility pricing blocks.

• Limited categories mean not all consumer surplus is extracted.

Third-Degree Price Discrimination

Third-degree price discrimination occurs when the monopolist divides consumers into groups based on observable characteristics (e.g., age, location) and charges each group a different price based on their price elasticity of demand.

• Inelastic Demand: Higher price charged (e.g., business travelers).

• Elastic Demand: Lower price charged (e.g., students, pensioners).

• Example: Movie tickets, airline pricing.

Other Forms of Price Discrimination

• Intertemporal Price Discrimination: Prices differ over time; higher prices when demand is inelastic (short run), lower when demand is elastic (long run).

• Peak-Load Pricing: Higher prices during periods of peak demand when capacity is constrained; objective is to improve efficiency.

• Hurdle Model: Firms offer discounts to buyers willing to overcome a hurdle (e.g., using coupons, rebates). This allows price-sensitive consumers to self-select into lower prices.

Summary Table: Types of Price Discrimination

Type	Basis	Example	Efficiency
First-degree	Individual willingness to pay	Car sales negotiation	Allocatively efficient
Second-degree	Quantity purchased	Bulk discounts	Partially efficient
Third-degree	Consumer group	Student/senior pricing	Depends on segmentation
Intertemporal	Time period	New tech pricing	Improves efficiency
Peak-load	Demand period	Electricity rates	Improves efficiency
Hurdle model	Self-selection	Coupons, rebates	Targets elastic buyers

Additional info: The above notes expand on the brief points in the slides, providing definitions, formulas, and examples for each concept. The summary table is inferred for clarity and exam preparation.