Article — Marginal Revenue Calculator
Marginal Revenue: The MR = MC Rule
Marginal revenue (MR) equals the change in total revenue divided by the change in quantity: MR = ΔTR/ΔQ. It is the extra revenue from selling one more unit, and it is the central decision metric for profit-maximizing firms. The MR = MC rule — produce until marginal revenue equals marginal cost — appears in every microeconomics course and applies in every market structure from perfect competition to monopoly.
The concept dates to Alfred Marshall's 1890 Principles of Economics, which formalized marginal analysis as the foundation of modern microeconomics. Marshall's insight was that decisions about how much to produce, sell, or buy are made at the margin — comparing the next unit's revenue to its cost — not by averaging or summing whole quantities.
What is marginal revenue?
Marginal revenue is the additional money a firm earns by selling one more unit. If a coffee shop sells 100 cups for $500 total, then sells 101 cups for $504 total, the marginal revenue of the 101st cup is $4. The 100 cups before it averaged $5 each, but the extra one was sold at a discount (a happy-hour price, a loyalty discount, a markdown to clear the shelf).
Marginal analysis is what economists mean when they talk about "thinking at the margin." The same approach drives optimal advertising spend, optimal labor hiring, optimal price discrimination, and even individual decisions like "should I take this extra hour of work?" The MR = MC framework generalizes to MB = MC (marginal benefit = marginal cost) for any optimization problem.
The marginal revenue formula
The discrete formula uses two observed revenue-quantity pairs:
MR = ΔTR / ΔQ MR = (TR₂ − TR₁) / (Q₂ − Q₁)linear demand P = a − bQ → MR = a − 2bQMR = MC (profit-maximizing rule)The continuous form, used when the demand function is differentiable, is MR = dTR/dQ. For a linear demand curve P = a − bQ, total revenue is TR = P × Q = aQ − bQ², so MR = a − 2bQ. Notice the slope is twice the slope of demand — a feature of all linear demand cases.
The discrete and continuous forms agree for small changes. For most real business analysis, you have observed data (price changes, sales reports), so the discrete formula is what gets used.
Marginal revenue vs average revenue
Average revenue (AR) is total revenue divided by quantity: AR = TR/Q. It equals the average price received per unit. In a single-price market, AR is just the current price.
The relationship between MR and AR tells you what kind of market the firm faces. If MR = AR, the firm is in perfect competition — a price-taker with no influence over the market price. If MR < AR, the firm has some pricing power: selling more requires lowering the price on all units, which drags MR below the price the marginal unit sells for.
Marginal revenue in perfect competition
A perfectly competitive firm sells in a market where it cannot influence price. Wheat farmers, foreign-exchange traders, and small online sellers of commodity goods all operate this way. The market sets the price; the firm decides how much to produce at that price.
Because the firm can sell any quantity at the market price, the demand curve it faces is horizontal at P. Every additional unit brings in exactly P in revenue, so MR = P. The firm's profit-maximizing decision is simple: produce up to where the marginal cost rises to equal the market price.
- Market price = $50 (given)
- TR at Q = 100 = $5,000
- TR at Q = 101 = $5,050
- MR of 101st unit = $50 (same as price)
- AR at Q = 100 = $50
- Conclusion: MR = AR = P throughout
Marginal revenue in monopoly
A monopoly faces the entire market demand curve, which slopes downward — selling more requires charging less. When the firm reduces price to sell one extra unit, it loses revenue on all the previous units that it could have sold at the higher price. The marginal revenue of the new unit is its sale price minus the lost revenue on prior units.
For a demand curve P = 200 − 2Q (a = 200, b = 2):
With linear demand, total revenue is maximized at exactly half the quantity where demand crosses zero. At Q = a/(2b), MR = 0 and revenue can't grow further by selling more. Beyond that point, MR is negative — selling more cuts total revenue. Profit-maximizing firms always operate where demand is elastic (left of TR-max).
- At Q = 10, P = $180, TR = $1,800, MR = $160
- At Q = 30, P = $140, TR = $4,200, MR = $80
- At Q = 50, P = $100, TR = $5,000, MR = $0 (revenue max)
- At Q = 70, P = $60, TR = $4,200, MR = −$80
- At Q = 100, P = $0, TR = $0, MR = −$200
Notice MR is much steeper than demand — twice the slope (−2b vs −b) in the linear case. This is a general property: any firm with downward-sloping demand has MR < price.
Marginal revenue and marginal cost
The profit-maximizing rule for any firm in any market: produce until marginal revenue equals marginal cost (MR = MC). The intuition is straightforward — if the next unit brings in more revenue than it costs, you want it; if it costs more than it earns, you don't.
MR = MC is the rule for profit maximization, not profit zero. It identifies the quantity where each additional unit just breaks even at the margin. Total profit at that quantity can be positive (firm is profitable), zero (firm breaks even), or negative (firm loses money but minimizes loss). The rule still applies — it just optimizes the firm's position.
This rule is one of the most universally applied concepts in business: pricing analysts use it to set prices, production managers use it to set output, advertising managers use it to set ad budgets (MR of ad = MC of ad), HR uses it to set staffing levels. Anywhere a quantity decision can be made, the marginal rule applies.
Marginal revenue and elasticity
The price elasticity of demand (E_d) links marginal revenue to price via the formula:
MR = P × (1 + 1/E_d)
Where E_d is negative (because demand slopes down). Three cases:
- Elastic demand (|E_d| > 1): MR > 0. Cutting price increases total revenue. A 1% price cut leads to more than 1% quantity gain.
- Unit elastic (|E_d| = 1): MR = 0. Total revenue is maximized at this point. Small price changes don't change TR.
- Inelastic demand (|E_d| < 1): MR < 0. Cutting price reduces total revenue — the quantity gain is too small to compensate.
This is why monopolies never voluntarily operate in the inelastic range of their demand curve — they could cut output, raise price, and increase revenue. The optimal output is always in the elastic range, where MR = MC and the equation has a positive solution.
Marginal revenue pitfalls
- Confusing MR with revenue per unit. Revenue per unit (= price = average revenue) is what each unit sells for. Marginal revenue is the extra revenue from one more unit, accounting for the price cut on previous units.
- Assuming MR = P always. Only true in perfect competition. Most real firms have at least some pricing power.
- Ignoring price effects on existing customers. In digital subscription models or single-price retail, lowering price for new customers usually means lowering it for existing ones too — the textbook monopoly assumption.
- Using MR alone for pricing decisions. MR maximizes revenue at MR = 0, but profit requires MR = MC. Skipping the cost side gives wrong prices.
- Using linear demand for complex markets. Real demand curves are usually not linear, especially at extreme prices. Linear models are useful pedagogically but break down in practice for nonlinear pricing strategies.
- Confusing marginal with average analysis. The MR rule operates at the next-unit level; total or average revenue can move in different directions.