Question:

For a profit maximising monopolist, the ratio of the profit margin to price (also known as the Lerner Index or the relative mark-up) has a relationship with the price-elasticity of demand at the profit maximising price. Then, which of the following statements is CORRECT?

Updated On: Feb 10, 2025
  • The larger the elasticity of demand at the profit maximising price, the greater is the relative mark-up
  • The power to sustain a price higher than the marginal cost depends only on the profit maximising price
  • At the profit maximising price, given costs are greater than zero, the price elasticity of demand is strictly larger than unity
  • At the revenue maximising price, the price elasticity of demand is greater than unity
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The Correct Option is C

Solution and Explanation

The Lerner Index and Monopolist’s Pricing Power

The Lerner Index, which measures a monopolist’s pricing power, is defined as: 

L = (P - MC) / P = 1 / |Ed|

Where:

  • P = Price
  • MC = Marginal Cost
  • Ed = Price Elasticity of Demand

Profit Maximization Condition

  • For a profit-maximizing monopolist, the demand elasticity must be greater than one in absolute terms, i.e., |Ed| > 1.
  • This ensures that P > MC, meaning the monopolist has pricing power.
  • If |Ed| ≤ 1, then marginal revenue becomes non-positive, which contradicts the requirement for profit maximization.

Implication of |Ed| > 1

  • The condition |Ed| > 1 guarantees that the Lerner Index is positive, meaning:
  • (P - MC) / P > 0, which implies a positive profit margin.

Conclusion

For a monopolist to maximize profit, the absolute value of demand elasticity must be greater than one (|Ed| > 1), ensuring P > MC and a positive Lerner Index.

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