Monopoly and Market Power: Principles of Profit Maximization

The Global Context of AIDS: Worldwide, the AIDS virus has resulted in the deaths of more than $36,000,000\,\text{people}$ .
Impact of Pharmaceutical Innovation: In the United States, AIDS is no longer an automatic death sentence due to the introduction of specialized drugs in the mid-1990s. One prominent example is the drug Combivir.
The Cost Discrepancy of Combivir:
- In the United States, Combivir is priced at approximately $12.00\,\text{dollars}$ to $13.00\,\text{dollars}$ per pill.
- In India, where patents for Combivir are not recognized, the market is competitive. In this competitive environment, the price is approximately $0.50\,\text{dollars}$ per pill.
- The price in the United States is roughly $25\,\text{times}$ higher than the marginal cost of production.
The Role of Monopoly: The high cost in the U.S. is not due to high manufacturing costs, which are actually quite low. Instead, it is a result of a monopoly held by GlaxoSmithKline (GSK). GSK owns the patent on Combivir, which grants them the legal right to exclude all competitors from the market.

Market Power Defined: Market power is defined as the power to raise price above marginal cost without fear that other firms will enter the market.
Economic Basis of Market Power: A firm possesses market power when it sells a unique good and is protected by barriers to entry.
Primary Barriers to Entry:
- Patents: Legal protections that grant a firm exclusive rights to sell a product, as seen with GSK and Combivir.
- Government Regulations: Other forms of legal barriers, such as exclusive licenses granted by the government.
- Economies of Scale: Situations where a single large firm can produce at a lower cost than many small firms, making it difficult for new entrants to compete.
- Exclusive Access to Inputs: Controlling a necessary resource. For example, owning a majority of the world's diamond mines allows a firm to monopolize the diamond market.
- Technological Innovations: Temporary market power can be gained when a firm possesses unique knowledge or abilities that competitors have not yet acquired.

The Fundamental Rule: To maximize profit, a firm should produce at the output level where marginal revenue ( $MR$ ) is equal to marginal cost ( $MC$ ).
Comparison to Competitive Firms: While both competitive firms and monopolists follow the $MR = MC$ rule, their marginal revenue structures differ.
- For a competitive firm, marginal revenue is equal to the market price ( $P$ ).
- For a monopolist, marginal revenue is less than the market price (MR < P).
Why MR is Less Than Price: A monopolist faces the entire downward-sloping market demand curve. To sell an additional unit, the monopolist must lower the price not only for that additional unit but for all previous units sold.

Total Revenue Calculation Example:
- Selling $2\,\text{units}$ at $16.00\,\text{dollars}$ each results in a total revenue of: $16 \times 2 = 32.00\,\text{dollars}$ .
- To sell $3\,\text{units}$ , the price must drop to $14.00\,\text{dollars}$ . Total revenue becomes: $14 \times 3 = 42.00\,\text{dollars}$ .
The Two Components of Marginal Revenue ( $MR$ ):
- Revenue Gain: The revenue from the additional unit sold ( $14.00\,\text{dollars}$ for the third unit).
- Revenue Loss: The loss in revenue from having to lower the price on previous units. In this case, the price on the first two units dropped from $16.00\,\text{dollars}$ to $14.00\,\text{dollars}$ . Loss = $(16 - 14) \times 2 = 4.00\,\text{dollars}$ .
- Final MR Calculation: $MR = \text{Revenue Gain} - \text{Revenue Loss} = 14 - 4 = 10.00\,\text{dollars}$ .
General Rule: Because $MR = P - \text{Revenue Loss}$ , it is mathematically certain that for a monopolist, marginal revenue will always be less than the price.

Inverse Demand Equation: For any linear demand curve represented as: $P = A - B \times Q$
Marginal Revenue Equation: The corresponding marginal revenue curve begins at the same vertical intercept ( $A$ ) but has twice the slope: $MR = A - 2B \times Q$
Horizontal Intercept Relationship: Because the slope is doubled, the marginal revenue curve will hit the horizontal axis at exactly half the distance of the demand curve.
- Example 1: If the demand curve hits the horizontal axis at $500\,\text{units}$ , the $MR$ curve hits at $250\,\text{units}$ .
- Example 2: If the demand curve hits the horizontal axis at $200\,\text{units}$ , the $MR$ curve hits at $100\,\text{units}$ .

Step 1: Determine Profit Maximizing Quantity ( $Q^*$ ): Find the intersection where the marginal revenue curve meets the marginal cost curve ( $MR = MC$ ).
- In the provided example, with marginal cost flat at $0.50\,\text{dollars}$ , this quantity is $80,000,000\,\text{pills}$ .
Step 2: Determine Profit Maximizing Price ( $P^*$ ): Look up from the quantity ( $Q^*$ ) to the demand curve to find the maximum willingness to pay.
- In the example, for $80,000,000\,\text{pills}$ , the price on the demand curve is $12.50\,\text{dollars}$ .
Step 3: Calculate Total Profit:
- Profit is calculated as the difference between price ( $P$ ) and average cost ( $AC$ ) multiplied by quantity ( $Q$ ).
- Formula: $\text{Profit} = (P - AC) \times Q$
- In the example, the profit per unit is $10.00\,\text{dollars}$ (derived from $12.50\,\text{dollars}\text{ price} - 2.50\,\text{dollars}\text{ average cost}$ ).
- Total Profit = $10 \times 80,000,000 = 800,000,000\,\text{dollars}$ . This is represented graphically by the shaded rectangle defined by the price and average cost boundaries.

Upcoming Focus: Future discussions will explore how the markup (the difference between price and marginal cost) varies.
Elasticity Connection: The size of the markup is directly influenced by the elasticity of demand. Firms with less elastic demand can command higher markups over marginal cost.