Marginal Revenue Formula

What does the marginal revenue formula measure?

Marginal revenue measures how total sales revenue changes when quantity sold changes. A total-sales figure tells you the revenue at one quantity; marginal revenue compares two quantities. It remains a revenue measure, so it does not include costs or show whether the change was profitable.

How is marginal revenue different from related measures?

Several related measures use the same sales or production data but answer different questions. Total revenue is the sales income at a given quantity. Average revenue is total revenue divided by quantity sold. It equals price when one price applies to every unit in the total. Marginal revenue measures the change in total revenue as quantity changes. OpenStax explains total revenue and the price-times-quantity relationship, while its discussion of output decisions distinguishes average revenue from marginal revenue. OpenStax, Principles of Economics 3e

Measure	Question it answers	Calculation or focus
Total revenue	How much sales income does this quantity generate?	Sales income for the quantity; in a single-price model, TR = P × Q.
Average revenue	How much revenue is there per unit across the quantity sold?	TR / Q; equal to price under the single-price assumption.
Marginal revenue	How much does total revenue change as quantity changes?	Change in total revenue per change in quantity over the measured interval.
Marginal cost	How much does total cost change as output changes?	Change in total cost per change in output.
Marginal profit	How does profit change with a marginal increase in output?	Marginal revenue minus marginal cost in the marginal model.
Marginal product	How much extra output comes from an additional input?	Additional output from one more unit of an input, such as a worker.
Marginal benefit	What extra benefit comes from a marginal change?	Incremental benefit in the decision being analyzed; it is broader than a seller's sales revenue.

Revenue, cost, and profit require separate calculations. Marginal cost covers the cost side. Marginal profit combines the revenue and cost effects and, in the standard marginal representation, equals MR − MC. Positive marginal revenue therefore does not prove that added output is profitable: its marginal cost may be higher. OpenStax's calculus text separates revenue, cost, and profit functions and gives marginal profit as MR − MC.

Marginal product and marginal benefit address other parts of a decision. Marginal product concerns production, such as the additional output associated with one more worker. Marginal benefit concerns the extra benefit from a change, as defined for the consumer, firm, or social decision under review. Neither measures the change in a seller's total revenue. OpenStax defines marginal product as additional output from one more worker and treats marginal benefits separately from marginal costs in its analysis of environmental choices. OpenStax, Principles of Microeconomics 3e

How do you calculate marginal revenue?

Start with two comparable observations of quantity and total revenue. Subtract the earlier values from the later values, then divide the revenue change by the quantity change.

What inputs belong in the formula?

For an earlier and a later observation, use:

MR = ΔTR / ΔQ

• MR is marginal revenue for the stated interval.
• ΔTR is the change in total revenue: later total revenue minus earlier total revenue.
• ΔQ is the change in quantity sold: later quantity minus earlier quantity.

If total revenue is measured in dollars and quantity in units, the result is dollars per unit over the measured interval. OpenStax calculates marginal revenue from successive rows by dividing the change in total revenue by the change in quantity sold.

You need a total-revenue value and its matching quantity for each observation. When one price applies to every unit in an observation, calculate total revenue as TR = P × Q, where P is price and Q is quantity. OpenStax defines total revenue as price times quantity. If transactions use different prices or another revenue basis, use consistently defined observed total revenue instead of multiplying one listed price by all units.

Both observations must use the same quantity unit, currency, revenue definition, and time or decision frame. A ratio can still look like a valid currency-per-unit result when those bases differ, but it will not isolate the intended revenue change.

ΔTR / ΔQ is a finite difference: it gives the exact average rate of revenue change over the stated interval. If revenue is instead represented by a differentiable function of continuous quantity, point marginal revenue is written as MR(Q) = R′(Q). The derivative is a point-level rate. A finite difference approaches that rate only as the interval becomes suitably small. OpenStax distinguishes the derivative of revenue from an actual finite revenue change.

How do you calculate marginal revenue from a sales table?

Treat two rows as the endpoints of one interval. The following hypothetical schedule uses values from an OpenStax example. OpenStax's monopoly tables show these price, total-revenue, and marginal-revenue values.

Quantity sold	Price per unit	Total revenue
4 units	$900	$3,600
5 units	$800	$4,000

For the move from 4 to 5 units:

1. Calculate total revenue in each row: 4 × $900 = $3,600 and 5 × $800 = $4,000.
2. Find the revenue change: $4,000 − $3,600 = $400.
3. Find the quantity change: 5 − 4 = 1 unit.
4. Divide the changes: MR = $400 / 1 unit = $400 per added unit.

The $400 result belongs to the interval from 4 to 5 units. It comes from the two rows together, rather than from either row by itself.

How should you interpret a result for more than one added unit?

When quantity changes by more than one unit, ΔTR / ΔQ is the average incremental revenue per unit across the whole interval. It does not reveal the marginal revenue of every one-unit step inside that interval.

In the same hypothetical schedule, total revenue is $3,000 at 3 units and $4,000 at 5 units:

($4,000 − $3,000) / (5 − 3) = $500 per added unit

The $500 figure is the average for the move from 3 to 5 units. The one-unit steps differ: marginal revenue is $600 from 3 to 4 units and $400 from 4 to 5 units. OpenStax's table supplies these values and the underlying totals.

The interval average is not the later posted price, the revenue from each individual added unit, or a forecast for another range. It is an exact finite change for the two stated observations. A derivative, by comparison, is the point-level rate obtained as a difference quotient approaches an arbitrarily small interval. OpenStax explains this limiting process in its definition of the derivative.

Why can marginal revenue differ from price?

Price is the amount charged per unit. Marginal revenue is the change in total revenue associated with a change in quantity. The two coincide only under particular market and pricing assumptions.

When does marginal revenue equal price?

Marginal revenue equals price in the price-taking model, where changing one firm's output does not noticeably change the market price. If price stays at P, a quantity increase of ΔQ raises total revenue by P × ΔQ. Therefore, ΔTR / ΔQ = P.

Perfect competition is the standard model for this condition. It treats each firm as a small price taker, so price and marginal revenue are equal for the firm's output decision. OpenStax explains why a perfectly competitive firm is a price taker and shows constant price and marginal revenue in its output-decision schedule. OpenStax, Principles of Microeconomics 3e

The equality depends on price remaining fixed as the firm's quantity changes. It does not imply that every seller can sell any quantity at a fixed price.

Why is marginal revenue below price for a price-setting firm?

For a single-price firm facing downward-sloping demand, selling more can require a lower common price on every unit. The added unit brings in revenue at the new price, while the price reduction cuts revenue on units that would have sold at the earlier price. Marginal revenue is the net effect, so it is below the new price in this model.

The move from 4 to 5 units in the table shows the arithmetic. At 4 units, the price is $900 and total revenue is $3,600. Selling 5 units requires a common price of $800, for total revenue of $4,000. The fifth unit brings in $800. The $100 reduction on the first four units removes $400 of revenue. The net change is $800 − $400 = $400, which matches ΔTR = $4,000 − $3,600. Marginal revenue is therefore $400, even though the new price is $800. OpenStax works through this common-price tradeoff and supplies the same schedule values.

This result depends on downward-sloping demand and one common price across all units. It does not automatically apply to price discrimination, separate customer segments, bundles, or a seller whose output does not affect price.

What do zero and negative marginal revenue mean?

Zero marginal revenue means that an increase in quantity leaves total revenue unchanged. Negative marginal revenue means that the increase lowers total revenue. Neither result says that total profit is zero.

In OpenStax's hypothetical schedule, total revenue is $4,200 at both 6 and 7 units, so MR over that one-unit interval is $0. At 8 units, total revenue falls to $4,000:

MR = ($4,000 − $4,200) / (8 − 7) = −$200 per added unit

OpenStax's table reports the revenue, marginal-revenue, and separate profit figures.

Zero MR marks a local total-revenue maximum only when revenue rises before that point and falls after it, or when marginal revenue changes from positive to negative. Zero or negative MR alone does not determine an output decision. Costs and feasible alternatives still matter when the objective is profit.

How does marginal revenue relate to a linear demand curve?

The familiar “same intercept, twice the slope” rule belongs to a specific continuous model. Inverse demand must be linear, quantity must be treated as continuous and differentiable, and the firm must charge one price on all units. If inverse demand is P(Q) = a − bQ, with b > 0, then:

TR(Q) = P(Q) × Q = aQ − bQ²

Taking the derivative gives point marginal revenue:

MR(Q) = R′(Q) = a − 2bQ

The demand and marginal-revenue lines have the same vertical intercept, a. Demand has slope −b, while marginal revenue has slope −2b, so the MR line falls twice as fast. OpenStax describes this relationship for a straight-line demand curve, and its calculus example derives the same result from a revenue function. OpenStax, Calculus Volume 1

A discrete sales table uses the finite difference across its stated interval. Even with linear inverse demand, that interval value need not equal the derivative at either endpoint. For R(Q) = aQ − bQ², the forward finite difference over an interval of width h is:

[R(Q + h) − R(Q)] / h = a − 2bQ − bh

That differs from the derivative at the starting quantity, R′(Q) = a − 2bQ, by bh. In OpenStax's calculus example, point MR is $3 at 100 units, while the actual revenue increase from 100 to 101 units is $2.97. Use the derivative line for the continuous point-level model and ΔTR / ΔQ for a table interval. Assigning an interval value to an endpoint mixes the two quantity conventions.

How can marginal revenue guide an output decision?

Marginal revenue informs an output decision when it is compared with the marginal cost of the same change in output. The result depends on the demand, cost, market, and feasibility assumptions used in the model.

How do marginal revenue and marginal cost work together?

For a marginal increase in output:

• MR > MC means the added output raises profit in the marginal comparison.
• MR < MC means the added output lowers profit in that comparison.
• MR = MC means the marginal revenue and marginal cost effects offset each other.

In the standard interior profit-maximization model, the relevant output occurs where MR equals MC. Discrete choices may offer no exact equality; in that case, the relevant choice can be the last feasible output before marginal cost overtakes marginal revenue. OpenStax explains the MR > MC and MC > MR comparisons for competitive output decisions and applies the same logic to a firm facing downward-sloping demand. OpenStax, Principles of Microeconomics 3e

MR = MC is a model-based output condition. Boundary choices, multiple intersections, shutdown conditions, discrete quantities, and the direction in which MC crosses MR can change the conclusion. The condition also does not guarantee positive profit: firms may choose an output that minimizes a loss. OpenStax discusses loss-minimizing output, and its cost chapter explains why output decisions require cost, revenue, and market-structure information. OpenStax, Principles of Economics 3e

Why does MR = MC choose output rather than directly set price?

For a single-price firm facing downward-sloping demand, MR = MC identifies an output quantity. Finding the corresponding selling price requires a second step:

1. Use the marginal-revenue and marginal-cost relationships to identify the relevant quantity.
2. Use the demand relationship to find the price associated with that quantity.

In OpenStax's hypothetical monopoly schedule, the firm selects 5 units where MR equals MC, then uses the demand relationship to find the corresponding price of $800. OpenStax sets out this quantity-then-price sequence. Its monopolistic-competition example follows the same sequence: it finds output at the MR–MC intersection and then reads price from perceived demand. OpenStax, Principles of Microeconomics 3e

This sequence requires a demand relationship connecting quantity to price and assumes a single-price firm with downward-sloping demand. Cost data inform the quantity choice; the demand relationship supplies the price for that quantity. Discrete and boundary choices still matter, and the resulting output need not earn a positive profit.

What can make a marginal revenue calculation misleading?

Correct arithmetic can still produce the wrong conclusion when the inputs answer a different question. Check the numerator, the basis of the observations, and the interval before using the result.

Are you measuring revenue rather than profit?

The numerator must contain the change in total sales revenue. Costs, overhead, margin percentages, and net profit do not belong in the marginal-revenue formula. Profit is total revenue minus total cost; a margin is a separate measure. OpenStax distinguishes total revenue, total cost, and profit.

For a profit decision, calculate marginal cost separately and compare it with MR. In the standard marginal representation, marginal profit is MR − MC. OpenStax separates revenue, cost, and profit functions and defines marginal profit as MR − MC. Positive MR shows that total revenue rose over the interval. It does not show that profit rose, because the cost of the added output may exceed the added revenue.

Are the observations comparable?

Each total-revenue value must match the quantity beside it, and both observations must use the same basis. Before subtracting, align:

• the time window or decision frame;
• the currency and definition of total revenue;
• the quantity definition and unit of measure;
• the product or customer mix; and
• the price or revenue basis in each observation.

Subtracting values in different currencies can still produce a number, but that number has no clear currency-per-unit meaning. A changed product mix or revenue basis likewise changes what the numerator measures. These are analytical validity checks, rather than formal accounting or revenue-recognition rules.

The formula divides a change in total revenue by the corresponding change in quantity, as adjacent entries in one schedule. OpenStax calculates MR from paired rows in a revenue schedule and defines total revenue in relation to sales and quantity. OpenStax, Principles of Microeconomics 3e

Does the calculation describe the decision you are considering?

A historical finite MR describes its observed quantity interval. It does not automatically forecast the revenue effect of a new quantity or price decision. Using it for another interval requires assumptions that connect the old observations to the proposed change.

Check whether demand, price, product or customer mix, sales channel, capacity, competitive conditions, and the pricing rule remain applicable. A change in any of them can change the meaning of the historical ratio. For example, a shift in perceived demand changes total revenue at each output and shifts marginal revenue; short-run capacity depends on available inputs and technology. OpenStax discusses shifts in perceived demand and marginal revenue, while its production chapter explains the role of fixed inputs and technology in short-run capacity. OpenStax, Principles of Economics 3e

Use the historical result as evidence for its stated range, then test the assumptions behind the new decision. Output and price decisions require relevant cost and revenue information plus the applicable market structure; an MR calculation alone does not predict the result. OpenStax's cost analysis explains this broader information requirement.