How to Calculate Marginal Revenue Using Price Elasticity of Demand?
The concept of marginal revenue and price elasticity of demand explains how a firm’s revenue changes with each extra unit sold, depending on how sensitive buyers are to price changes. This topic is crucial for school and competitive exams, as well as for understanding basic business pricing strategies.
| Elasticity Type | Ed (Elasticity Value) | Marginal Revenue (MR) Sign | Revenue Implication |
|---|---|---|---|
| Elastic Demand | Ed > 1 | Positive | MR > 0; Firm benefits from selling more |
| Unitary Elastic Demand | Ed = 1 | Zero | MR = 0; Total revenue at maximum |
| Inelastic Demand | Ed < 1 | Negative | MR < 0; Selling more reduces total revenue |
Marginal Revenue and Price Elasticity of Demand: Definition
Marginal revenue (MR) is the extra revenue a firm earns by selling one more unit of its product. Price elasticity of demand (Ed) measures how much quantity demanded changes when price changes. The relationship between marginal revenue and price elasticity of demand helps firms decide how to price goods for maximum revenue.
Formula for Marginal Revenue and Price Elasticity of Demand
The key formula showing this relationship is:
MR = P(1 + 1/Ed)
Where MR is marginal revenue, P is the price, and Ed is the price elasticity of demand (usually expressed as a negative number, so 1/Ed is negative).
Derivation of the Marginal Revenue–Elasticity Formula
Total Revenue (TR) = P × Q, where P is price and Q is quantity.
Marginal Revenue (MR) is the change in TR when Q increases by one unit: MR = d(TR)/dQ.
Using calculus: MR = d(P × Q)/dQ = P + Q × (dP/dQ).
From elasticity: Ed = (dQ/dP) × (P/Q) or rearranged, dP/dQ = 1/(Ed) × (P/Q).
Substitute dP/dQ into the MR formula, simplifying to get: MR = P[1 + 1/Ed].
Interpretation: MR and Elasticity Types
The sign of marginal revenue depends on elasticity:
- When demand is elastic (Ed < -1 or |Ed| > 1): MR is positive. Selling extra units increases total revenue.
- When demand is unitary elastic (Ed = -1): MR is zero. Total revenue is at its peak.
- When demand is inelastic (Ed > -1 or |Ed| < 1): MR is negative. Selling extra units lowers total revenue.
Diagram: Marginal Revenue and Price Elasticity of Demand
In a standard diagram, the MR curve lies below the average revenue (demand) curve. MR is positive on the upper (elastic) part of the demand curve, zero at the midpoint (unitary), and negative on the lower (inelastic) segment. This is why firms always aim to operate where demand is elastic and marginal revenue is positive.
Examples of Marginal Revenue and Price Elasticity of Demand
| Scenario | Price (P) | Elasticity (Ed) | MR Calculation | MR Result |
|---|---|---|---|---|
| Elastic: Luxury Shoes | ₹2000 | -2.5 | 2000 × (1 + 1/(-2.5)) | ₹1200 |
| Unitary: Daily Groceries | ₹100 | -1 | 100 × (1 + 1/(-1)) | ₹0 |
| Inelastic: Salt | ₹20 | -0.5 | 20 × (1 + 1/(-0.5)) | ₹-20 |
Market Structure Implications
In monopoly markets, the relationship between marginal revenue and price elasticity of demand affects pricing directly. A monopolist never operates where MR is negative (i.e., inelastic demand). In perfect competition, Ed is infinite (demand is perfectly elastic) and MR equals price.
Real-World Application
Suppose a firm selling branded perfumes finds that lowering price increases quantity sold slightly. This weak response (inelastic demand) means MR becomes negative. The firm should not lower prices further, as this would reduce total revenue. Such analysis helps businesses set optimal prices and maximize profits.
Quick Exam-Ready Summary
- Marginal Revenue (MR) = Price × (1 + 1/Ed)
- MR is positive when demand is elastic (|Ed| > 1)
- MR is zero at unitary elasticity (|Ed| = 1; total revenue is at its maximum)
- MR is negative when demand is inelastic (|Ed| < 1)
- For monopoly, firm always produces on elastic segment of demand curve
- Use this relationship to solve exam problems and for effective pricing in business
At Vedantu, we make commerce concepts like marginal revenue and price elasticity of demand simple, practical, and exam-ready for all students and business enthusiasts. For deeper study, see Price Elasticity of Demand and Concepts of Total Revenue, Average Revenue and Marginal Revenue.
In summary, understanding the relationship between marginal revenue and price elasticity of demand is vital for exams and real business decisions. This concept explains how firms can maximize revenue by choosing the right price and quantity combination based on consumer responsiveness.
FAQs on Marginal Revenue and Price Elasticity of Demand: Concept, Formula & Examples
1. What is the relationship between marginal revenue and price elasticity of demand?
Marginal revenue (MR) and price elasticity of demand (Ed) are inversely related. MR is positive when demand is elastic (Ed > 1), zero when demand is unitary elastic (Ed = 1), and negative when demand is inelastic (Ed < 1). This relationship is crucial for firms in determining optimal pricing strategies.
2. How do you calculate marginal revenue using price elasticity of demand?
The formula to calculate marginal revenue (MR) using price elasticity of demand (Ed) is: MR = P(1 + 1/Ed), where P is the price. This formula helps firms predict revenue changes based on elasticity and price adjustments. Remember that this equation assumes a linear demand curve. For non-linear curves, calculus would be required.
3. What is the relationship between marginal cost and elasticity of demand?
While not directly linked by a single formula, marginal cost (MC) and elasticity of demand influence profit maximization. Firms aim to produce where marginal cost equals marginal revenue (MC = MR). The elasticity of demand determines the shape of the marginal revenue curve, influencing the profit-maximizing output level and price.
4. What is the relationship between marginal revenue and demand?
Marginal revenue is the change in total revenue resulting from selling one more unit of a good. The relationship between marginal revenue and demand is determined by the price elasticity of demand. For example, if the demand is elastic, marginal revenue will be positive and vice-versa.
5. How does the marginal revenue curve relate to the demand curve?
The marginal revenue curve always lies below the demand curve (except in perfect competition). This is because to sell more units, a firm must lower the price on all units, reducing the additional revenue from each extra unit sold. The relationship's slope depends on the price elasticity of demand.
6. What does negative marginal revenue indicate about demand?
A negative marginal revenue indicates that demand is inelastic (Ed < 1). This means that to sell more units, the firm must lower its price so much that the increase in quantity sold is not enough to offset the decrease in price per unit; total revenue falls. In such cases, profit maximization requires a reduction in output.
7. Why is marginal revenue zero when elasticity is unitary?
When the price elasticity of demand is unitary elastic (Ed = -1), a change in price results in an exactly proportionate change in quantity demanded, leading to no change in total revenue. Therefore, marginal revenue is zero at this point. This represents the point of revenue maximization on a demand curve.
8. How does the relationship between marginal revenue and price elasticity of demand differ in different market structures?
The relationship between marginal revenue and price elasticity varies across market structures. In perfect competition, firms are price takers (MR = Price), while in a monopoly, the firm's marginal revenue is always less than the price. In monopolistic competition and oligopoly, the relationship lies somewhere between these two extremes and depends heavily on the nature of competition.
9. How does a linear demand curve's MR relate to elasticity throughout its length?
A linear demand curve has a marginal revenue curve that is twice as steep. The marginal revenue is positive where the demand is elastic, zero where it is unitary elastic (at the midpoint of the demand curve), and negative where it is inelastic.
10. What is the significance of the MR = P(1 + 1/Ed) formula in determining a firm’s pricing strategy?
The formula MR = P(1 + 1/Ed) is crucial for firms to understand how changes in price affect marginal revenue given the price elasticity of demand. By understanding this relationship, firms can determine the optimal price to maximize profits. This is particularly relevant for firms with some market power (not perfect competition).
