# Equation for Marginal Revenue: Formula, Examples, MR=MC

Published: 2026-04-19
Author: Warren Team
URL: https://www.heywarren.com/blog/marginal-revenue-formula

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A bakery owner stares at her spreadsheet wondering whether to bake one more tray of croissants. A SaaS founder debates accepting a bulk deal at half price. An airline algorithm decides whether to drop the last middle seat to $89. Every one of these decisions hinges on a single, deceptively simple question: what does the next unit actually add to revenue? That number has a name — [marginal revenue](/blog/marginal-revenue-calculation-formula) — and the equation for marginal revenue is one of the most useful tools in all of microeconomics.

The problem is that most explanations of marginal revenue either drown you in calculus or oversimplify it into a one-liner that breaks the moment your demand curve isn't horizontal. The truth sits in the middle: there's a discrete version, a calculus version, and an elasticity version, and each one answers a different real-world question. Knowing which to reach for is the difference between pricing like a pro and pricing by gut.

This guide walks through every form of the marginal revenue equation, shows worked examples in both discrete and continuous form, and connects MR to the profit-maximization rule that drives almost every pricing decision in modern business. By the end you'll know exactly how to compute it, when MR diverges from price, and how to use the MR=MC framework to decide whether the next unit is worth producing.

## What Marginal Revenue Actually Measures

Marginal revenue (MR) is the additional [total revenue](/blog/how-do-we-calculate-total-revenue) a firm earns from selling one more unit of output. Formally, it's the change in total revenue divided by the change in quantity sold. MR is the "next dollar in" — the incremental cash that one more sale brings into the business, before any costs are subtracted.

Why does it matter? Because rational producers don't think in averages — they think at the margin. If the next unit brings in $90 of revenue but costs $70 to make, you produce it. If it brings in $40 and costs $70, you don't. Average revenue and total revenue can mislead; marginal revenue tells you what the next decision is worth. That's why every introductory micro course builds the entire theory of the firm around MR and its cost twin, [marginal cost](/blog/marginal-cost) (MC).

## The Equation for Marginal Revenue

The equation for marginal revenue has three standard forms, each suited to a different situation. The discrete version uses arithmetic on a price-quantity table. The continuous version uses calculus on a revenue function. The elasticity version translates MR into a function of price and the price elasticity of demand — useful for monopolists and any firm with pricing power.

![The three standard forms of the marginal revenue equation and when to use each.](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%3EDiscrete%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%3E%CE%94TR%20%2F%20%CE%94Q%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%3EContinuous%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%3EdTR%20%2F%20dQ%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%3EElasticity%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%3EP%281%20%2B%201%2FE%29%3C%2Ftext%3E%3C%2Fsvg%3E)

*The three standard forms of the marginal revenue equation and when to use each.*

![Marginal revenue formula derivation](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHZpZXdCb3g9IjAgMCA2MDAgMzAwIiBmb250LWZhbWlseT0ic3lzdGVtLXVpLCBzYW5zLXNlcmlmIiBmb250LXNpemU9IjE0Ij48cmVjdCB3aWR0aD0iNjAwIiBoZWlnaHQ9IjMwMCIgZmlsbD0iI2YxZjVmOSIvPjx0ZXh0IHg9IjMwMCIgeT0iMzIiIHRleHQtYW5jaG9yPSJtaWRkbGUiIGZvbnQtc2l6ZT0iMTciIGZvbnQtd2VpZ2h0PSI3MDAiIGZpbGw9IiMxZTI5M2IiPlRocmVlIEZvcm1zIG9mIHRoZSBNYXJnaW5hbCBSZXZlbnVlIEVxdWF0aW9uPC90ZXh0PjxyZWN0IHg9IjQwIiB5PSI2MCIgd2lkdGg9IjE3MCIgaGVpZ2h0PSIyMDAiIHJ4PSIxMCIgZmlsbD0iI2ZmZiIgc3Ryb2tlPSIjM2I4MmY2IiBzdHJva2Utd2lkdGg9IjIiLz48dGV4dCB4PSIxMjUiIHk9Ijg2IiB0ZXh0LWFuY2hvcj0ibWlkZGxlIiBmb250LXdlaWdodD0iNzAwIiBmaWxsPSIjM2I4MmY2Ij5EaXNjcmV0ZTwvdGV4dD48dGV4dCB4PSIxMjUiIHk9IjEzMCIgdGV4dC1hbmNob3I9Im1pZGRsZSIgZmlsbD0iIzFlMjkzYiI+TVIgPSDOlFRSIC8gzpRRPC90ZXh0Pjx0ZXh0IHg9IjEyNSIgeT0iMTYwIiB0ZXh0LWFuY2hvcj0ibWlkZGxlIiBmaWxsPSIjNjQ3NDhiIiBmb250LXNpemU9IjEyIj49IFRSKG4pIOKIkiBUUihu4oiSMSk8L3RleHQ+PHRleHQgeD0iMTI1IiB5PSIxODAiIHRleHQtYW5jaG9yPSJtaWRkbGUiIGZpbGw9IiM2NDc0OGIiIGZvbnQtc2l6ZT0iMTIiPndoZW4gzpRRID0gMTwvdGV4dD48dGV4dCB4PSIxMjUiIHk9IjIyMCIgdGV4dC1hbmNob3I9Im1pZGRsZSIgZmlsbD0iIzY0NzQ4YiIgZm9udC1zaXplPSIxMiI+VXNlIHdpdGggdGFibGVzPC90ZXh0Pjx0ZXh0IHg9IjEyNSIgeT0iMjQwIiB0ZXh0LWFuY2hvcj0ibWlkZGxlIiBmaWxsPSIjNjQ3NDhiIiBmb250LXNpemU9IjEyIj5vZiBwcmljZSAmYW1wOyBxdWFudGl0eTwvdGV4dD48cmVjdCB4PSIyMjAiIHk9IjYwIiB3aWR0aD0iMTcwIiBoZWlnaHQ9IjIwMCIgcng9IjEwIiBmaWxsPSIjZmZmIiBzdHJva2U9IiMxMGI5ODEiIHN0cm9rZS13aWR0aD0iMiIvPjx0ZXh0IHg9IjMwNSIgeT0iODYiIHRleHQtYW5jaG9yPSJtaWRkbGUiIGZvbnQtd2VpZ2h0PSI3MDAiIGZpbGw9IiMxMGI5ODEiPkNvbnRpbnVvdXM8L3RleHQ+PHRleHQgeD0iMzA1IiB5PSIxMzAiIHRleHQtYW5jaG9yPSJtaWRkbGUiIGZpbGw9IiMxZTI5M2IiPk1SID0gZFRSL2RRPC90ZXh0Pjx0ZXh0IHg9IjMwNSIgeT0iMTYwIiB0ZXh0LWFuY2hvcj0ibWlkZGxlIiBmaWxsPSIjNjQ3NDhiIiBmb250LXNpemU9IjEyIj5JZiBQID0gYSDiiJIgYlE6PC90ZXh0Pjx0ZXh0IHg9IjMwNSIgeT0iMTgwIiB0ZXh0LWFuY2hvcj0ibWlkZGxlIiBmaWxsPSIjNjQ3NDhiIiBmb250LXNpemU9IjEyIj5NUiA9IGEg4oiSIDJiUTwvdGV4dD48dGV4dCB4PSIzMDUiIHk9IjIyMCIgdGV4dC1hbmNob3I9Im1pZGRsZSIgZmlsbD0iIzY0NzQ4YiIgZm9udC1zaXplPSIxMiI+VXNlIHdpdGggc21vb3RoPC90ZXh0Pjx0ZXh0IHg9IjMwNSIgeT0iMjQwIiB0ZXh0LWFuY2hvcj0ibWlkZGxlIiBmaWxsPSIjNjQ3NDhiIiBmb250LXNpemU9IjEyIj5kZW1hbmQgZnVuY3Rpb25zPC90ZXh0PjxyZWN0IHg9IjQwMCIgeT0iNjAiIHdpZHRoPSIxNzAiIGhlaWdodD0iMjAwIiByeD0iMTAiIGZpbGw9IiNmZmYiIHN0cm9rZT0iI2Y1OWUwYiIgc3Ryb2tlLXdpZHRoPSIyIi8+PHRleHQgeD0iNDg1IiB5PSI4NiIgdGV4dC1hbmNob3I9Im1pZGRsZSIgZm9udC13ZWlnaHQ9IjcwMCIgZmlsbD0iI2Y1OWUwYiI+RWxhc3RpY2l0eTwvdGV4dD48dGV4dCB4PSI0ODUiIHk9IjEzMCIgdGV4dC1hbmNob3I9Im1pZGRsZSIgZmlsbD0iIzFlMjkzYiI+TVIgPSBQKDEgKyAxL0UpPC90ZXh0Pjx0ZXh0IHg9IjQ4NSIgeT0iMTYwIiB0ZXh0LWFuY2hvcj0ibWlkZGxlIiBmaWxsPSIjNjQ3NDhiIiBmb250LXNpemU9IjEyIj5FID0gcHJpY2UgZWxhc3RpY2l0eTwvdGV4dD48dGV4dCB4PSI0ODUiIHk9IjE4MCIgdGV4dC1hbmNob3I9Im1pZGRsZSIgZmlsbD0iIzY0NzQ4YiIgZm9udC1zaXplPSIxMiI+KG5lZ2F0aXZlIG51bWJlcik8L3RleHQ+PHRleHQgeD0iNDg1IiB5PSIyMjAiIHRleHQtYW5jaG9yPSJtaWRkbGUiIGZpbGw9IiM2NDc0OGIiIGZvbnQtc2l6ZT0iMTIiPlVzZSB0byBsaW5rIE1SPC90ZXh0Pjx0ZXh0IHg9IjQ4NSIgeT0iMjQwIiB0ZXh0LWFuY2hvcj0ibWlkZGxlIiBmaWxsPSIjNjQ3NDhiIiBmb250LXNpemU9IjEyIj5kaXJlY3RseSB0byBwcmljaW5nPC90ZXh0Pjwvc3ZnPg==)

### Discrete form

When you have a table of prices and quantities, MR is just the change in total revenue between two adjacent rows: MR = (TR_n − TR_{n-1}) / (Q_n − Q_{n-1}). If quantity moves up by one unit at a time, the denominator drops out and MR is simply the difference in total revenue.

### Continuous form

When demand is given as a smooth function P(Q), total revenue is TR = P(Q) × Q, and MR is the derivative dTR/dQ. For a linear demand curve P = a − bQ, total revenue equals aQ − bQ², and the derivative gives MR = a − 2bQ. The MR curve is a straight line with the same intercept as demand but twice the slope.

### Elasticity form

Using calculus and the definition of elasticity, MR can be rewritten as MR = P × (1 + 1/E), where E is the price elasticity of demand (typically negative). This form is powerful because it links the next-dollar decision directly to how price-sensitive your customers are.

## A Worked Discrete Example

The cleanest way to see MR is in a table. Suppose your [demand schedule](/blog/demand-schedule) looks like this — drop price by $5, sell one more unit. Total revenue = price × quantity. Marginal revenue = the change in TR from the previous row. Notice how MR falls faster than price, because to sell the extra unit you also accepted a lower price on the units you would have sold anyway.

![At the fifth unit, price is $80 but marginal revenue is only $60 — the $20 gap is the discount given on the four prior units.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20800%20210%22%20width%3D%22800%22%20height%3D%22210%22%20role%3D%22img%22%3E%3Ctitle%3EComparison%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Ctext%20x%3D%22230%22%20y%3D%2257.5%22%20text-anchor%3D%22end%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%3EPrice%20%28P%29%3C%2Ftext%3E%3Crect%20x%3D%22240%22%20y%3D%2225%22%20width%3D%22450%22%20height%3D%2255%22%20rx%3D%226%22%20fill%3D%22%232563eb%22%2F%3E%3Ctext%20x%3D%22702%22%20y%3D%2257.5%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22%232563eb%22%3E%2480%3C%2Ftext%3E%3Ctext%20x%3D%22230%22%20y%3D%22152.5%22%20text-anchor%3D%22end%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%3EMarginal%20Revenue%3C%2Ftext%3E%3Crect%20x%3D%22240%22%20y%3D%22120%22%20width%3D%22337.5%22%20height%3D%2255%22%20rx%3D%226%22%20fill%3D%22%237c3aed%22%2F%3E%3Ctext%20x%3D%22589.5%22%20y%3D%22152.5%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22%237c3aed%22%3E%2460%3C%2Ftext%3E%3C%2Fsvg%3E)

*At the fifth unit, price is $80 but marginal revenue is only $60 — the $20 gap is the discount given on the four prior units.*

| Quantity | 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 |

The fifth unit is priced at $80, but it only adds $60 to revenue. Why? Because dropping price from $85 to $80 also gave a $5 discount to each of the four units you were already selling. That's the core insight: for any firm with downward-sloping demand, marginal revenue is less than price.

## A Worked Linear Demand Example

For a continuous demand curve, calculus gives a clean answer in two lines. Take the linear demand P = 100 − Q. Multiply both sides by Q to get total revenue: TR = 100Q − Q². Take the derivative with respect to Q to get marginal revenue: MR = 100 − 2Q. The MR line shares the $100 intercept of the demand curve but falls twice as fast.

Now add a marginal cost of MC = $20 (assume constant for simplicity). The profit-maximizing firm produces until MR = MC, so set 100 − 2Q = 20, giving Q* = 40. Plug Q* back into the demand curve to find the price: P* = 100 − 40 = $60. Profit per unit is P* − MC = $60 − $20 = $40, and total profit before fixed costs is 40 × $40 = $1,600.

![MR equals MC profit maximization](data:image/svg+xml;base64,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)

## Perfect Competition vs. Monopoly: Why MR Sometimes Equals Price

In perfect competition, MR equals price; in monopoly, MR is strictly less than price. The reason is the demand curve facing the firm. A perfect competitor is a price taker — its individual demand curve is horizontal at the market price, so selling one more unit doesn't move the market and the marginal dollar in is exactly P. A monopolist faces the downward-sloping market demand curve, so each extra unit requires a lower price on every unit.

For a monopolist with linear demand, the rule is sharp: MR has the same intercept but twice the slope of the demand curve. Visually, MR sits below demand at every positive quantity. That gap is the "revenue penalty" you pay for having to discount inframarginal units to move the marginal one — and it's why monopolists restrict output relative to competitive firms.

![MR vs price in two market structures](data:image/svg+xml;base64,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)

## The Elasticity Form: MR = P(1 + 1/E)

The elasticity equation MR = P × (1 + 1/E) ties marginal revenue directly to price and the price elasticity of demand. Because elasticity E is negative for normal goods, the term 1/E reduces MR below P whenever demand isn't perfectly elastic. This form is the workhorse for monopoly and oligopoly pricing — and it produces a striking benchmark: a profit-maximizing firm will never operate where demand is inelastic.

![Whether marginal revenue is positive or negative depends on where demand elasticity falls — profit maximizers always stay in the elastic zone.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20720%20480%22%20width%3D%22720%22%20height%3D%22480%22%20role%3D%22img%22%3E%3Ctitle%3EQuadrant%20matrix%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Crect%20x%3D%2290%22%20y%3D%2225%22%20width%3D%22300%22%20height%3D%22190%22%20fill%3D%22%23dbeafe%22%2F%3E%3Crect%20x%3D%22390%22%20y%3D%2225%22%20width%3D%22300%22%20height%3D%22190%22%20fill%3D%22%23d1fae5%22%2F%3E%3Crect%20x%3D%2290%22%20y%3D%22215%22%20width%3D%22300%22%20height%3D%22190%22%20fill%3D%22%23ffedd5%22%2F%3E%3Crect%20x%3D%22390%22%20y%3D%22215%22%20width%3D%22300%22%20height%3D%22190%22%20fill%3D%22%23ede9fe%22%2F%3E%3Cline%20x1%3D%2290%22%20y1%3D%22215%22%20x2%3D%22690%22%20y2%3D%22215%22%20stroke%3D%22%2364748b%22%20stroke-width%3D%222%22%2F%3E%3Cline%20x1%3D%22390%22%20y1%3D%2225%22%20x2%3D%22390%22%20y2%3D%22405%22%20stroke%3D%22%2364748b%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22240%22%20y%3D%22100%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%22700%22%20fill%3D%22%230f172a%22%3EAvoid%3C%2Ftext%3E%3Ctext%20x%3D%22240%22%20y%3D%22120%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%3E%E2%80%A2%20MR%20%26lt%3B%200%3C%2Ftext%3E%3Ctext%20x%3D%22240%22%20y%3D%22136%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%3E%E2%80%A2%20Raise%20price%3C%2Ftext%3E%3Ctext%20x%3D%22540%22%20y%3D%22100%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%22700%22%20fill%3D%22%230f172a%22%3EOperate%20here%3C%2Ftext%3E%3Ctext%20x%3D%22540%22%20y%3D%22120%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%3E%E2%80%A2%20MR%20%26gt%3B%200%3C%2Ftext%3E%3Ctext%20x%3D%22540%22%20y%3D%22136%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%3E%E2%80%A2%20MR%20%3D%20MC%20possible%3C%2Ftext%3E%3Ctext%20x%3D%22240%22%20y%3D%22290%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%22700%22%20fill%3D%22%230f172a%22%3EInelastic%20trap%3C%2Ftext%3E%3Ctext%20x%3D%22240%22%20y%3D%22310%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%3E%E2%80%A2%20Revenue%20falls%3C%2Ftext%3E%3Ctext%20x%3D%22240%22%20y%3D%22326%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%3E%E2%80%A2%20Never%20profit-max%3C%2Ftext%3E%3Ctext%20x%3D%22540%22%20y%3D%22290%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%22700%22%20fill%3D%22%230f172a%22%3EUnit%20elastic%3C%2Ftext%3E%3Ctext%20x%3D%22540%22%20y%3D%22310%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%3E%E2%80%A2%20MR%20%3D%200%3C%2Ftext%3E%3Ctext%20x%3D%22540%22%20y%3D%22326%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%3E%E2%80%A2%20TR%20maximized%3C%2Ftext%3E%3Ctext%20x%3D%2290%22%20y%3D%22425%22%20text-anchor%3D%22start%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3EInelastic%3C%2Ftext%3E%3Ctext%20x%3D%22690%22%20y%3D%22425%22%20text-anchor%3D%22end%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3EElastic%3C%2Ftext%3E%3Ctext%20x%3D%22390%22%20y%3D%22453%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2212%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EPrice%20Elasticity%3C%2Ftext%3E%3Ctext%20x%3D%2280%22%20y%3D%2237%22%20text-anchor%3D%22end%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3EPositive%20MR%3C%2Ftext%3E%3Ctext%20x%3D%2280%22%20y%3D%22405%22%20text-anchor%3D%22end%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2211%22%20fill%3D%22%2364748b%22%3ENegative%20MR%3C%2Ftext%3E%3Ctext%20x%3D%2235%22%20y%3D%22215%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2212%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%20transform%3D%22rotate%28-90%2035%20215%29%22%3EMarginal%20Revenue%3C%2Ftext%3E%3C%2Fsvg%3E)

*Whether marginal revenue is positive or negative depends on where demand elasticity falls — profit maximizers always stay in the elastic zone.*

Walk through the cases:

- **E = −∞** (perfectly elastic): MR = P × (1 + 0) = P. This is the perfect competition case.
- **E = −2** (elastic): MR = P × (1 + (−0.5)) = P/2. Halving price relationship is built right in.
- **E = −1** (unit elastic): MR = P × (1 + (−1)) = 0. Selling one more unit leaves total revenue unchanged.
- **−1 < E < 0** (inelastic): MR is negative. Selling one more unit actually shrinks total revenue, so a profit maximizer would never produce here — they'd raise price and sell less.

Combining this with the profit-max rule MR = MC, and remembering MC ≥ 0, you get the famous markup formula: P = MC / (1 + 1/E). The more inelastic your demand, the higher the markup over marginal cost — which is why luxury brands and patent-protected drugs price at multiples of cost, while commodity producers price near MC.

## Marginal Revenue Across Market Structures

MR's relationship to price is the cleanest way to compare market structures. In perfect competition, MR = P exactly because individual demand is flat. In monopolistic competition, demand slopes down gently (close substitutes exist), so MR sits just below P. In oligopoly, the famous kinked demand model gives MR a discontinuous jump at the prevailing price, which is why oligopolists often hold prices steady. In pure monopoly, demand can be steep and MR is well below P.

This isn't academic taxonomy — it changes how a firm should think. A wheat farmer takes the market price and decides only how much to grow. A patent-holding pharma company sets price first and lets quantity follow. A regional cable monopoly weighs the elasticity of switching customers. The MR equation is the same; the demand curve plugged into it is what differs.

## Using MR=MC in Real Business Decisions

The MR = MC rule is more than a textbook condition; it's a checklist for almost every incremental pricing decision a business makes. Whenever you're deciding "should we produce one more, sell one more, accept one more order, or open one more location," the right framing is to compare the marginal revenue from that action to the marginal cost of taking it.

Concrete applications:

- **Should we accept this large order at a discount?** If the discounted price exceeds your true marginal cost (and doesn't cannibalize full-price sales), MR > MC, so yes.
- **Should we expand capacity?** Forecast the MR of the next slice of output and compare to the MC of building and operating new capacity.
- **Should we cut prices to gain volume?** Compute MR using the elasticity form. If demand is elastic, MR is positive and the cut may pay; if inelastic, you'll lose total revenue.
- **Airline yield management:** every seat is priced to the MR of selling it versus the MC of flying it (close to zero), which is why last-minute fares can swing wildly.
- **OPEC quota decisions:** members debate quotas precisely because MR depends on how much each barrel pulls down the world price.

## Common Mistakes to Avoid

Even seasoned analysts trip over MR. The most common mistake is conflating marginal revenue with average revenue (which equals price). For a downward-sloping demand curve, MR is always less than AR, and the gap grows as quantity rises. A second trap is forgetting that MR can be negative — once you cross into inelastic territory, selling more shrinks total revenue.

A third error is dragging fixed costs into a marginal decision. Fixed costs are sunk relative to the next unit; only marginal cost belongs in the MR = MC comparison. A fourth is misreading the shutdown rule: a firm should produce while MR = MC and price covers average [variable cost](/blog/variable-cost), not stop the moment MR equals AVC. And finally, treating perfect competition's MR = P as universal is the mistake that turns pricing strategy into guesswork — the moment your firm has any pricing power, MR diverges from P and the elasticity form takes over.

## How MR Connects to Other Pricing Concepts

Marginal revenue is the hub of a wider pricing toolkit. Demand elasticity feeds directly into MR via the MR = P(1 + 1/E) identity. [Price discrimination](/blog/price-discrimination) — charging different prices to different segments — is profitable precisely because it lets a firm capture a separate MR curve in each segment, lifting total revenue above what a single price can achieve. Two-part tariffs (a fixed access fee plus a per-unit price) work the same way: the per-unit price is set near MC to maximize quantity, while the fixed fee captures consumer surplus that single-price MR analysis would leave on the table.

Once you internalize the equation for marginal revenue, ideas like peak-load pricing, bundling, and revenue management stop feeling like ad-hoc tricks and start looking like applications of the same incremental logic.

## Authoritative Sources

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

- [IRS](https://www.irs.gov/)
- [SEC](https://www.sec.gov/)
- [Federal Reserve](https://www.federalreserve.gov/)
- [Consumer Financial Protection Bureau](https://www.consumerfinance.gov/)

## Conclusion

The equation for marginal revenue — MR = ΔTR/ΔQ in discrete form, dTR/dQ in continuous form, and P(1 + 1/E) in elasticity form — is one of the highest-leverage formulas in microeconomics. It reframes every output and pricing question as "what does the next unit add?" and it powers the universal profit-max rule: produce until MR = MC.

A few takeaways to anchor:

1. For any firm with downward-sloping demand, MR is always less than price, because each new sale requires a discount on inframarginal units.
2. For linear demand P = a − bQ, MR = a − 2bQ — same intercept, twice the slope.
3. MR = P(1 + 1/E) means a profit maximizer never operates where demand is inelastic; the optimal markup is P = MC / (1 + 1/E).
4. The MR = MC rule is the single most useful test for whether to make, sell, expand, or cut.
5. Don't confuse MR with average revenue, and don't drag fixed costs into a marginal decision.

Whether you're pricing software seats, sizing a new product run, or weighing a discount for a strategic customer, marginal revenue is the lens that turns intuition into arithmetic.

Ready to put this knowledge to work? Try Warren, your AI financial advisor — get personalized, conflict-free guidance at heywarren.com

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## Related Reading

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**Authoritative sources**:
- [SEC Investor.gov — Investing Basics](https://www.investor.gov/introduction-investing/investing-basics)
- [FINRA — Investor Education](https://www.finra.org/investors)