Question

A firm's market power can be measured by its ability to raise price above marginal cost. Relative to the level of marginal cost, this measure is \((P-M C) / P\). How do you expect this to be related to the elasticity of demand for the monopolist's output?

Short answer

The Lerner Index is inversely related to demand elasticity; as elasticity increases, market power decreases.

Step-by-step solution

Understanding the Formula

The firm's market power is measured by the term \((P-MC)/P\). Here, \(P\) is the price set by the firm and \(MC\) is the marginal cost. This expression is often known as the Lerner Index of market power.

Relating Market Power to Elasticity

The elasticity of demand, \(E_d\), is another key concept. It describes how quantity demanded responds to price changes. For monopolists, the relationship between the Lerner Index and elasticity of demand is expressed by \((P-MC)/P = 1/E_d\).

Deriving the Relationship

Re-arranging the above expression, we see that the market power (Lerner Index) of the firm is related inversely to the elasticity of demand. The formula is \((P-MC)/P = 1/E_d\), indicating that as the elasticity of demand increases (becomes more elastic), the market power (Lerner Index) decreases, and vice versa.

Conclusion on Elasticity's Impact

Therefore, a monopoly has more market power (can set a higher price over marginal cost) when the demand for its product is inelastic (\(E_d\) is low). If the demand is elastic (\(E_d\) is high), the monopolist has less market power and thus, less ability to set prices above marginal cost.

Key concepts

Lerner Index

The Lerner Index is a measure of a firm's market power—its ability to set and maintain prices above marginal cost. It is defined by the formula \((P-MC)/P\), where \(P\) represents the price of the product set by the firm, and \(MC\) stands for the marginal cost of producing the product. The difference between the price and the marginal cost, divided by the price, provides insight into how much leeway a firm has to charge over the basic cost of production.

• A high Lerner Index indicates significant market power, allowing the firm to set prices much higher than costs. This typically happens in monopolistic or less competitive markets.
• A low Lerner Index suggests that the firm’s ability to mark up prices is limited, often due to competitive pressures.

Understanding the Lerner Index is important as it helps in evaluating how competition or lack thereof affects pricing strategies and consumer choice.

Elasticity of Demand

Elasticity of demand explains how sensitive the quantity demanded of a good is to changes in price. It's quantified by the elasticity coefficient, \(E_d\), which tells us the percentage change in quantity demanded resulting from a one percent change in price.

• If \(E_d > 1\), demand is considered elastic, meaning consumers are highly responsive to price changes, and a price increase could lead to a significant drop in sales.
• If \(E_d < 1\), demand is inelastic, meaning consumers are less responsive to price changes, allowing firms more freedom to increase prices without losing many sales.
• When \(E_d = 1\), we have unitary elasticity where percentage change in price equals the percentage change in quantity demanded.

For monopolists, understanding demand elasticity is crucial as it informs strategic decisions on pricing and potential revenue outcomes. An inelastic demand curve gives monopolies more pricing power because consumers remain relatively loyal even as prices rise.

Monopolist Pricing Strategy

In a monopoly, the firm has the unique ability to influence prices due to lack of competition. A monopolist uses its knowledge of the Lerner Index and elasticity of demand to optimize pricing strategies. The relationship is captured by the equation \((P-MC)/P = 1/E_d\).

• When demand is inelastic (\(E_d\) is low), the firm can charge higher prices since customers' purchasing behavior remains largely unchanged. The Lerner Index will be high in this scenario.
• Conversely, if demand is elastic, the firm must lower prices to maintain sales volume, as consumers are more price-sensitive. The Lerner Index is lower here.

The key is to identify the demand elasticity and adjust pricing accordingly to maximize profits without losing significant market share. This strategic pricing under monopoly conditions can lead to higher profits but may also attract regulatory scrutiny if perceived as exploitative toward consumers.