# Marginal Revenue: Formula, Calculation, and How It's Used in Economics

Published: 2026-02-11
Author: Warren Team
URL: https://www.heywarren.com/blog/marginal-revenue-calculation-formula

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Marginal revenue (MR) is the additional revenue a firm earns from selling one more unit of output. The marginal revenue formula is simply the change in [total revenue](/blog/how-do-we-calculate-total-revenue) divided by the change in quantity sold: MR = ΔTR ÷ ΔQ. Understanding marginal revenue is the foundation of profit-maximisation theory: a firm maximises profit by producing up to the quantity where marginal revenue equals [marginal cost](/blog/marginal-cost) (MR = MC). Beyond this point, each additional unit costs more to produce than it brings in revenue, and profit falls. Marginal revenue behaves differently under [perfect competition](/blog/perfect-market-competition-examples) (where MR equals price) and monopoly (where MR falls below price) — a distinction that drives much of microeconomic and antitrust analysis.

## The Marginal Revenue Formula

> **Marginal Revenue = ΔTotal Revenue ÷ ΔQuantity**

Or equivalently:

> **MR = (TR₂ − TR₁) ÷ (Q₂ − Q₁)**

**Example** (unit-by-unit calculation):

| Units Sold (Q) | Price | Total Revenue | Marginal Revenue |
|---|---|---|---|
| 1 | $100 | $100 | $100 |
| 2 | $95 | $190 | $90 |
| 3 | $90 | $270 | $80 |
| 4 | $85 | $340 | $70 |
| 5 | $80 | $400 | $60 |

In this example, the firm must lower its price to sell more units (a downward-sloping demand curve). Marginal revenue is falling and is less than the price — this is characteristic of a monopoly or monopolistically competitive firm.

**MR from the total revenue formula**:
If TR is a function of Q (e.g., TR = 120Q − 5Q²), then:
> MR = d(TR)/dQ = 120 − 10Q

At Q = 5: MR = 120 − 50 = $70

## MR Under Perfect Competition

In a **perfectly competitive market**, each firm is a price-taker — it can sell as many units as it wants at the market price without affecting price. Therefore:

- Price is constant regardless of quantity sold
- Total revenue = Price × Quantity (a straight line)
- Marginal revenue = Price (the price never changes as Q increases)

**Example**: Wheat farmer sells wheat at $5/bushel:
- Sells 100 bushels: TR = $500
- Sells 101 bushels: TR = $505
- MR = $5 (equals the market price)

In perfect competition: **MR = P** at all output levels.

## MR Under Monopoly and Imperfect Competition

A **monopolist** faces the entire market demand curve — to sell more units, it must lower price for all units. This means:

- As Q increases, the revenue gained from the new unit is partially offset by the lower price now paid on all existing units
- **MR < Price** for all quantities above the first unit
- The MR curve lies below and is steeper than the demand curve

**MR formula for linear demand** (P = a − bQ):
> MR = a − 2bQ

The MR curve has twice the slope of the demand curve (same intercept, twice the slope).

**Example**: Demand: P = 100 − 2Q
> TR = P × Q = (100 − 2Q) × Q = 100Q − 2Q²
> MR = d(TR)/dQ = 100 − 4Q

At Q = 10: P = 80, MR = 60 — MR is $20 below price.

## Profit Maximisation: MR = MC

The fundamental rule of profit maximisation:

![The three-zone logic of the MR = MC profit-maximisation rule: produce more, hold, or cut output.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20660%20125%22%20width%3D%22660%22%20height%3D%22125%22%20role%3D%22img%22%3E%3Ctitle%3EFlow%20diagram%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Crect%20x%3D%2230%22%20y%3D%2225%22%20width%3D%22170%22%20height%3D%2275%22%20rx%3D%2210%22%20fill%3D%22white%22%20stroke%3D%22%232563eb%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22115%22%20y%3D%2258.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EMR%20%26gt%3B%20MC%3C%2Ftext%3E%3Ctext%20x%3D%22115%22%20y%3D%2278.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3EProduce%20more%3C%2Ftext%3E%3Cline%20x1%3D%22205%22%20y1%3D%2262.5%22%20x2%3D%22237%22%20y2%3D%2262.5%22%20stroke%3D%22%2364748b%22%20stroke-width%3D%222%22%2F%3E%3Cpolygon%20points%3D%22244%2C62.5%20235%2C57.5%20235%2C67.5%22%20fill%3D%22%2364748b%22%2F%3E%3Crect%20x%3D%22245%22%20y%3D%2225%22%20width%3D%22170%22%20height%3D%2275%22%20rx%3D%2210%22%20fill%3D%22white%22%20stroke%3D%22%232563eb%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22330%22%20y%3D%2258.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EMR%20%3D%20MC%3C%2Ftext%3E%3Ctext%20x%3D%22330%22%20y%3D%2278.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3EMax%20profit%3C%2Ftext%3E%3Cline%20x1%3D%22420%22%20y1%3D%2262.5%22%20x2%3D%22452%22%20y2%3D%2262.5%22%20stroke%3D%22%2364748b%22%20stroke-width%3D%222%22%2F%3E%3Cpolygon%20points%3D%22459%2C62.5%20450%2C57.5%20450%2C67.5%22%20fill%3D%22%2364748b%22%2F%3E%3Crect%20x%3D%22460%22%20y%3D%2225%22%20width%3D%22170%22%20height%3D%2275%22%20rx%3D%2210%22%20fill%3D%22white%22%20stroke%3D%22%232563eb%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22545%22%20y%3D%2258.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EMR%20%26lt%3B%20MC%3C%2Ftext%3E%3Ctext%20x%3D%22545%22%20y%3D%2278.5%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3EProduce%20less%3C%2Ftext%3E%3C%2Fsvg%3E)

*The three-zone logic of the MR = MC profit-maximisation rule: produce more, hold, or cut output.*

> **Produce where Marginal Revenue = Marginal Cost**

**Logic**:
- If MR > MC: Producing one more unit adds more revenue than cost → profit increases → produce more
- If MR < MC: Producing one more unit costs more than it earns → profit decreases → produce less
- If MR = MC: No gain from changing output → maximum profit

**Example** (monopolist):
- Demand: P = 100 − 2Q → MR = 100 − 4Q
- Marginal cost: MC = 20 (constant)
- Set MR = MC: 100 − 4Q = 20 → Q = 20
- Price at Q = 20: P = 100 − 2(20) = $60
- Profit = (P − AC) × Q (if AC = MC = 20): ($60 − $20) × 20 = $800

Under perfect competition, the same MC would yield: P = MC = $20, Q = 40 — lower price, higher output. The monopolist restricts output to raise price and capture higher profit.

## Marginal Revenue vs. Average Revenue

| Metric | Formula | Relationship to Price |
|---|---|---|
| Total Revenue | P × Q | — |
| Average Revenue | TR / Q = P | Equals price |
| Marginal Revenue | ΔTR / ΔQ | Equals price (perfect competition); Below price (monopoly) |

![How marginal revenue relates to price differs by market structure: equal under perfect competition, below price under imperfect competition.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20600%20211%22%20width%3D%22600%22%20height%3D%22211%22%20role%3D%22img%22%3E%3Ctitle%3EHierarchy%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Crect%20x%3D%22220%22%20y%3D%2220%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22%232563eb%22%2F%3E%3Ctext%20x%3D%22300%22%20y%3D%2254%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22white%22%3EMarginal%20Revenue%3C%2Ftext%3E%3Cpath%20d%3D%22M%20300%2078%20L%20300%20105.5%20L%20120%20105.5%20L%20120%20133%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%20fill%3D%22none%22%2F%3E%3Crect%20x%3D%2240%22%20y%3D%22133%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22white%22%20stroke%3D%22%230891b2%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22120%22%20y%3D%22158%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2213%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EPerfect%20Comp.%3C%2Ftext%3E%3Ctext%20x%3D%22120%22%20y%3D%22176%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3EMR%20%3D%20Price%3C%2Ftext%3E%3Cpath%20d%3D%22M%20300%2078%20L%20300%20105.5%20L%20300%20105.5%20L%20300%20133%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%20fill%3D%22none%22%2F%3E%3Crect%20x%3D%22220%22%20y%3D%22133%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22white%22%20stroke%3D%22%230891b2%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22300%22%20y%3D%22158%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2213%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EMonopoly%3C%2Ftext%3E%3Ctext%20x%3D%22300%22%20y%3D%22176%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3EMR%20%26lt%3B%20Price%3C%2Ftext%3E%3Cpath%20d%3D%22M%20300%2078%20L%20300%20105.5%20L%20480%20105.5%20L%20480%20133%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%20fill%3D%22none%22%2F%3E%3Crect%20x%3D%22400%22%20y%3D%22133%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22white%22%20stroke%3D%22%230891b2%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22480%22%20y%3D%22158%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2213%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EMonopolistic%3C%2Ftext%3E%3Ctext%20x%3D%22480%22%20y%3D%22176%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3EMR%20%26lt%3B%20Price%3C%2Ftext%3E%3C%2Fsvg%3E)

*How marginal revenue relates to price differs by market structure: equal under perfect competition, below price under imperfect competition.*

Average revenue always equals price (TR/Q = P×Q/Q = P). Marginal revenue falls below average revenue (and price) whenever the demand curve slopes downward — the hallmark of pricing power.

## Applications

**Business pricing strategy**: Understanding MR guides managers to set prices where the last unit sold contributes at least as much as its marginal cost. Companies with pricing power (brands, patents, network effects) have MR > 0 across a wider quantity range.

**Antitrust analysis**: Regulators compare monopolist MR = MC output to competitive (P = MC) output to quantify the deadweight loss of monopoly — the welfare cost of restricted output.

**Revenue management**: Airlines use marginal revenue principles to set ticket prices dynamically — the marginal value of an additional seat decreases as the plane fills, informing discounting decisions.

## Authoritative Sources

For deeper background and primary-source data on this topic, the following authoritative sources are useful starting points:

- [Bureau of Economic Analysis](https://www.bea.gov/)
- [Bureau of Labor Statistics](https://www.bls.gov/)

## Conclusion

Marginal revenue — the additional revenue from selling one more unit — is a foundational microeconomic concept that drives profit-maximisation decisions. Under perfect competition, MR equals price; under monopoly or imperfect competition, MR falls below price. The profit-maximising rule (MR = MC) is universal across market structures. For pricing strategy, market analysis, and antitrust economics, understanding how marginal revenue changes with output is essential. For related microeconomic concepts, see our guides on [macro vs. microeconomics](/blog/macro-vs-microeconomics) and [formula of opportunity cost](/blog/formula-of-opportunity-cost).

Warren at [heywarren.com](https://heywarren.com) helps students, business analysts, and economists understand core microeconomic concepts, pricing theory, and the mathematical frameworks behind profit maximisation.

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## Related Reading

**More from Warren**:
- [Macroeconomics vs. Microeconomics: What's the Difference?](/blog/macro-vs-microeconomics)
- [Opportunity Cost: Formula, Examples, and How to Calculate It](/blog/formula-of-opportunity-cost)
- [Diminishing Marginal Benefit: Definition, Examples, and Economic Implications](/blog/diminishing-marginal-benefit)

**Authoritative sources**:
- [CFA Institute — Microeconomics](https://www.cfainstitute.org/en/membership/professional-development/refresher-readings/demand-supply-analysis-introduction)
- [MIT OpenCourseWare — Microeconomics](https://ocw.mit.edu/courses/14-01-principles-of-microeconomics-fall-2018/)
- [Federal Reserve — Competition and Pricing](https://www.federalreserve.gov/econres.htm)