Relationship between AR, MR and elasticity of demand is represented by:

Question

Accepted Answer

The correct option is 2:
The relationship between Average Revenue (AR), Marginal Revenue (MR), and the Price Elasticity of Demand (e) is a fundamental concept in the theory of the firm, connecting a firm's pricing power to its revenue generation. The correct formula, MR = AR(1 - 1/e), is derived using differential calculus, relating the slope of the Average Revenue (or demand) curve to the marginal revenue. Since AR is equal to price (P) in all market structures, this formula is often written as MR = P(1 - 1/e). This relationship is universally true, regardless of whether the firm is a monopoly, operates under monopolistic competition, or is a price taker in perfect competition. For instance, in perfect competition, demand is perfectly elastic (e = infinity), and substituting infinity into the formula yields MR = AR(1 - 1/infinity) = AR(1 - 0) = AR. This confirms the well-known rule that AR = MR in perfect competition. This formula is critical because it allows a firm to determine its profit-maximizing output where MR = Marginal Cost (MC), provided the firm knows the price elasticity of demand for its product.

The incorrect option is 1:
The formula MR = e(1 - 1/AR) is mathematically incorrect. Since AR represents the price (P), this formula incorrectly attempts to multiply the elasticity by a term that should involve the reciprocal of elasticity, not the reciprocal of AR, failing to define the correct geometric relationship.

The incorrect option is 3:
The formula e = (AR-MR)/AR is a manipulation of the correct relationship, but it incorrectly isolates the elasticity term. The correct algebraic rearrangement of the fundamental formula, MR = AR(1 - 1/e), should result in e = AR / (AR - MR), not the inverse.

The incorrect option is 4:
The equation e = AR(MR-1) is fundamentally incorrect. Elasticity (e) is a pure number (a ratio) and does not typically equate to a revenue term (AR) multiplied by a difference that includes a unit quantity (MR-1), which lacks conceptual basis in the mathematical derivation of the AR, MR, and e relationship.