Total, Average and Marginal Revenue: Tables and Curves

A seller reduces the price of a notebook from Rs 90 to Rs 80 and sells one more notebook. Has revenue increased by Rs 80?

It is tempting to say yes. But if the lower price applies to all the notebooks sold, some revenue is lost on the other notebooks too. The extra money earned may be much less than Rs 80. It may even be negative.

That small detail explains most of the confusion around total revenue, average revenue and marginal revenue. Once you understand it, the formulas and curves begin to tell the same story.

We will work with a single product, one common price at each quantity, and sales during the same period. Where a question says “output”, assume that output is sold unless it says otherwise.

What do TR, AR and MR actually measure?

Think of a shopkeeper asking three different questions after a day’s sales.

Measure	Question it answers	Formula
Total revenue, TR	How much did sales earn altogether?	TR = P x Q
Average revenue, AR	How much revenue was earned per unit sold?	AR = TR / Q
Marginal revenue, MR	How much did revenue change per additional unit?	MR = Change in TR / Change in Q

Here, P means price per unit and Q means quantity sold. TR is measured in rupees; AR and MR are measured in rupees per unit.

If 12 notebooks sell at Rs 50 each, TR is Rs 600 and AR is Rs 50. You cannot calculate the revenue change from those two facts alone unless you also know the relevant earlier revenue or how price behaves as quantity changes.

Total revenue is sales revenue, not profit

Revenue is calculated before subtracting costs.

Suppose sales earn Rs 600 and the total cost is Rs 430. Revenue is Rs 600; profit is Rs 170. If cost is Rs 650, revenue is still Rs 600, but the seller has a loss of Rs 50.

Do not subtract wages, rent or the purchase cost of goods when asked only for TR.

Why average revenue equals price

With one common price:

AR = TR / Q = (P x Q) / Q = P, provided Q is greater than zero.

This is true whether price stays fixed or changes between possible sales quantities. If all five notebooks sell at Rs 60, their average revenue is Rs 60. If all six sell at Rs 55, their average revenue is Rs 55.

The price changes between the two possibilities, but AR still equals the price in each one.

How to calculate marginal revenue

If quantity increases by exactly one unit:

MR of the nth unit = TR at n units - TR at n - 1 units.

If quantity increases by several units, divide by the quantity change. An increase in TR of Rs 300 across five extra units gives MR of Rs 60 per unit over that interval.

At zero sales, TR is zero. AR is undefined because you cannot divide by zero. In a table, write a dash or “not defined” for AR at Q = 0. A quoted price can still exist even when nobody buys.

These definitions and the price-taking case are developed in NCERT’s chapter on the firm under perfect competition.

Revenue under perfect competition

A perfectly competitive firm takes the market price as given. Its own output decision is too small to change that price.

Suppose the price is Rs 40 per unit. The firm earns Rs 40 on its first unit, Rs 40 more on its second, and Rs 40 more on its third.

Quantity sold	Price / AR (Rs)	TR (Rs)	MR (Rs)
0	Not defined as AR	0	Not applicable
1	40	40	40
2	40	80	40
3	40	120	40
4	40	160	40
5	40	200	40

Check the fourth row of positive output yourself:

• TR = 4 x 40 = Rs 160.
• AR = 160 / 4 = Rs 40.
• MR = 160 - 120 = Rs 40.

Because adding a unit does not reduce revenue on the other units, P = AR = MR.

How to draw the curves

Use quantity on the horizontal axis in both diagrams.

For the TR diagram, put total revenue on the vertical axis. Plot (0, 0), (1, 40), (2, 80), and the remaining points. Join them with a straight rising line through the origin. Equal increases in quantity produce equal increases in revenue.

For the AR and MR diagram, put revenue per unit on the vertical axis. Draw one horizontal line at Rs 40 and label it AR = MR = P. Drawing two lines at different heights would contradict the table.

Keep the diagrams separate because total revenue and revenue per unit are different measurements.

Firm demand and market demand are different

The horizontal line describes demand facing one price-taking firm. It does not mean that the entire market’s demand curve is horizontal.

Market demand and market supply determine the price. The individual competitive firm then treats that price as given when choosing its output. If market conditions change, the price line can move to a different height. “Constant price” here means constant as this firm’s quantity changes along the given line, not a price that can never change over time.

See OpenStax’s explanation of competitive output decisions for the connection between the price line and marginal revenue.

Revenue under imperfect competition

In the usual introductory case, the firm faces downward-sloping demand. To sell a larger quantity, it must accept a lower price.

For now, assume the firm charges the same price for every unit sold at a particular output. This is the standard single-price model, not a situation in which different customers pay different prices.

A monopolist faces the market demand curve. A firm selling a differentiated product also commonly faces downward-sloping demand, but its demand is only part of the market. OpenStax’s discussion of monopolistic competition explains that distinction.

Do not infer an exact market structure from a falling price column alone. It supports the downward-demand revenue analysis; it does not prove that the seller is a monopoly. More complex models, including some oligopoly models, need their own assumptions.

A complete revenue schedule

Imagine a notebook seller with these possible weekly sales:

Quantity sold	Price / AR (Rs)	TR (Rs)	MR of extra unit (Rs)
0	Not defined as AR	0	Not applicable
1	110	110	110
2	100	200	90
3	90	270	70
4	80	320	50
5	70	350	30
6	60	360	10
7	50	350	-10
8	40	320	-30

These are alternative price-quantity combinations, not successive batches sold at different prices. The seller can sell three notebooks at Rs 90 each or four notebooks at Rs 80 each. We are comparing the revenue from those alternatives.

At Q = 4:

• All four notebooks sell for Rs 80 each.
• TR = 4 x 80 = Rs 320.
• AR = 320 / 4 = Rs 80.
• MR = 320 - 270 = Rs 50.

Notice that MR is Rs 50 even though the fourth notebook’s price is Rs 80.

Why is MR below AR?

Compare three notebooks at Rs 90 each with four notebooks at Rs 80 each.

The extra notebook contributes Rs 80. However, the other three notebooks now earn Rs 10 less each. The revenue reduction on those three is Rs 30.

Net addition to revenue = 80 - 30 = Rs 50.

That is MR. It is less than the new price of Rs 80, which is also AR.

There is no need to imagine refunds to past customers. We are comparing two possible selling plans for the same period. Under the four-notebook plan, the common price is lower for all four units.

This reasoning is also explained in OpenStax’s treatment of monopoly revenue. The notebook figures here are a separate worked illustration.

In a one-unit table, the first unit has MR = AR when TR starts from zero. There are no earlier units whose price must be reduced. The familiar statement “MR is below AR” applies to subsequent expansions in this table and to positive quantities on the usual smooth downward-demand curves.

How MR tells you what TR is doing

Return to the notebook schedule. MR falls from Rs 90 to Rs 70 to Rs 50, but TR continues to rise.

A smaller positive addition still increases the total. Adding Rs 10 to Rs 350 produces Rs 360, even though Rs 10 is much less than the earlier additions.

MR over an increase in quantity	What happens to TR?
Positive	TR increases
Zero	TR is unchanged across that increase
Negative	TR decreases

If MR is positive and falling, TR rises by progressively smaller amounts. If MR is constant and positive, equal quantity increases produce equal revenue increases.

At seven notebooks, MR is -Rs 10. The seller still earns positive revenue of Rs 350. Negative MR does not mean total revenue is negative, and it does not tell us whether the firm is making a loss. We would need costs to answer the profit question.

Is TR always highest where MR equals zero?

For a smooth, hill-shaped TR curve, its interior maximum occurs where the slope is zero. Since MR measures that slope, MR = 0 there, with MR changing from positive to negative around the maximum.

Tables need a little more care.

In our notebook table, TR is highest at six units, at Rs 360. The listed MR values move from +Rs 10 to -Rs 10. There is no row with MR = 0. That is fine: the observations are whole-unit steps.

A different table might show TR values of Rs 240, Rs 280, Rs 280 and Rs 260 at successive quantities. The middle two quantities tie for the highest revenue, and the move between them has MR = 0.

Drawing AR, MR and TR when price falls

For a straight downward-sloping AR curve, the usual smooth MR curve begins at the same vertical intercept and slopes downward twice as steeply. It reaches the quantity axis halfway to the AR curve’s quantity intercept.

This is a straight-line demand result. Do not apply the twice-the-slope shortcut to every curved demand relationship.

For TR, draw the corresponding rising-then-falling curve. Mark its highest point directly above the quantity at which smooth MR crosses zero. The part before that point has positive MR; the part after it has negative MR.

Our notebook schedule follows:

P = AR = 120 - 10Q.

Multiplying price by quantity gives:

TR = 120Q - 10Q squared.

For the smooth version of this relationship:

MR = 120 - 20Q.

So the AR line reaches zero at Q = 12, while MR reaches zero at Q = 6. Revenue at Q = 6 is 120 x 6 - 10 x 36 = Rs 360.

If you have learned differentiation, the smooth MR expression follows by differentiating TR with respect to Q. If you have not, focus on the graph relationship and the revenue table.

Why does the table show MR = 10 at six units?

This is a useful question, not a mistake in the table.

The table’s sixth-unit MR measures the change from five to six: 360 - 350 = Rs 10. The smooth formula measures the slope at exactly six, which is zero.

For this example, the one-unit difference is:

TR(Q) - TR(Q - 1) = 130 - 20Q.

At Q = 6 that gives Rs 10. At Q = 7 it gives -Rs 10. The continuous slope reaches zero between the midpoints of those two intervals, at Q = 6 itself.

Use differences for a discrete table and the smooth formula when working with the continuous curve. Do not replace one with the other halfway through a solution.

The link between revenue and demand elasticity

When price falls, the seller gets less per unit but sells more units. Which effect wins depends on how responsive quantity demanded is.

For small movements along a smooth downward-sloping demand curve with positive price:

• In the elastic portion, a price reduction increases TR, and MR is positive.
• At unit elasticity, the local MR is zero.
• In the inelastic portion, a price reduction decreases TR, and MR is negative.

The total-revenue test is explained in OpenStax’s section on elasticity and pricing.

When your course uses the formula, let e be the positive magnitude of point price elasticity of demand:

MR = AR x (1 - 1/e).

For example, if AR = Rs 90 and e = 3:

MR = 90 x (1 - 1/3) = Rs 60.

If AR = Rs 90 and e = 0.75:

MR = 90 x (1 - 1/0.75) = -Rs 30.

The negative answer says revenue falls when output increases locally. It does not say that the seller charges a negative price.

For a large change between two observations, calculate the actual revenues directly rather than treating a point-elasticity result as exact over the entire interval. You can revisit the basics in our price elasticity of demand guide.

Four solved questions to practise the method

1. Find TR when AR and quantity are given

Question: A firm sells 18 units with AR of Rs 75. Find TR. Can you find MR?

TR = AR x Q = 75 x 18 = Rs 1,350.

MR cannot be found from this information alone. AR gives revenue per unit at this quantity; it does not reveal how TR changes when quantity changes.

If the question additionally states that the firm is a price taker at a fixed price of Rs 75, then MR = Rs 75.

2. Calculate MR when quantity changes by five units

Question: TR is Rs 900 at 15 units and Rs 1,100 at 20 units. Find MR over the interval and AR at 20 units.

Change in TR = 1,100 - 900 = Rs 200.

Change in Q = 20 - 15 = 5 units.

MR = 200 / 5 = Rs 40 per unit.

AR at 20 units = 1,100 / 20 = Rs 55.

The answer Rs 200 is the total revenue increase, not the increase per extra unit. Also, Rs 40 is an interval average; the data do not tell us the separate MR of each of those five units.

3. Reconstruct TR and AR from MR

Question: MR for the first four units is Rs 80, Rs 60, Rs 40 and Rs 20. Find TR and AR at every quantity, assuming TR is zero at zero sales.

Q	MR (Rs)	TR, adding successive MR values (Rs)	AR = TR / Q (Rs)
1	80	80	80
2	60	140	70
3	40	180	60
4	20	200	50

At four units, TR is 80 + 60 + 40 + 20 = Rs 200. Dividing by four gives AR of Rs 50.

Do not add the AR column to obtain TR. Each AR entry belongs to a different possible sales quantity.

4. Explain a negative MR without using a formula alone

Question: A seller can sell eight units at Rs 60 each or nine units at Rs 50 each. Find MR and explain the result.

TR at eight units = 8 x 60 = Rs 480.

TR at nine units = 9 x 50 = Rs 450.

MR = 450 - 480 = -Rs 30.

The extra unit earns Rs 50, but the price reduction costs Rs 10 on each of the other eight units, a reduction of Rs 80. Net change = 50 - 80 = -Rs 30.

That last sentence explains the economics behind the subtraction and makes the answer much stronger.

Revenue maximisation is not profit maximisation

Suppose two possible outputs have these results:

Quantity	TR (Rs)	TC (Rs)	Profit = TR - TC (Rs)
5	350	220	130
6	360	250	110

Six units earn more revenue, but five units earn more profit among these two choices. Producing the sixth unit adds Rs 10 to revenue and Rs 30 to cost, reducing profit by Rs 20.

That is why an answer about maximum revenue must not automatically become an answer about the best output for profit. A full profit decision needs costs and the relevant output conditions. Our producer equilibrium guide takes that next step.

Common mistakes and quick repairs

“AR equals price only under perfect competition.” AR equals the common price whenever TR = P x Q and Q is positive. Perfect competition adds the condition that this price stays constant as the firm’s quantity changes.

“Falling MR means falling TR.” Check whether MR is positive or negative. Falling but positive MR still increases TR.

“The price of the extra unit is always its MR.” Account for any price reduction on the other units. Price equals MR in the constant-price case, but not generally under downward demand.

“AR and MR are always half and double each other.” No. In the smooth straight-line case, MR has twice the slope of AR in magnitude. That does not make MR half of AR at every quantity.

“A horizontal revenue line means TR is constant.” First identify the line. Horizontal AR and MR at a positive price mean that TR rises at a constant rate.

“MR = 0 means TR = 0.” Zero MR means no additional revenue locally or across the stated interval. The existing total may be substantial.

Try these questions before checking the answers

1. A price-taking firm sells seven units at Rs 35 each. Find TR, AR and MR.
2. TR increases from Rs 560 to Rs 680 when sales rise from eight units to ten. Find MR over this interval.
3. A firm sells five units with TR of Rs 450. At six units, TR is Rs 480. Find AR at both quantities and sixth-unit MR.
4. MR for four successive units is Rs 100, Rs 80, Rs 60 and Rs 40. With TR at zero sales equal to zero, find TR and AR at four units.
5. TR at successive quantities is Rs 150, Rs 210, Rs 240, Rs 240 and Rs 220. Which listed quantities give maximum TR?
6. A smooth demand curve is P = 80 - 4Q. Find TR, smooth MR and the quantity that maximises TR over 0 to 20 units.
7. A student says, “MR fell from Rs 25 to Rs 15, so TR must have fallen.” Correct the statement.
8. AR is Rs 120 and the positive magnitude of point demand elasticity is 2. Find MR.

Answers with brief working

1. TR = 7 x 35 = Rs 245; AR = Rs 35; MR = Rs 35.
2. MR = (680 - 560) / (10 - 8) = Rs 60 per unit.
3. AR at five units = 450 / 5 = Rs 90. AR at six units = 480 / 6 = Rs 80. Sixth-unit MR = 480 - 450 = Rs 30.
4. TR = 100 + 80 + 60 + 40 = Rs 280. AR = 280 / 4 = Rs 70.
5. The third and fourth listed quantities both give the maximum TR of Rs 240. MR for the move between them is zero.
6. TR = 80Q - 4Q squared; smooth MR = 80 - 8Q. Setting MR to zero gives Q = 10, where TR is Rs 400. MR is positive before and negative after this quantity.
7. Both MR figures are positive, so TR is still rising, but its addition per extra unit has become smaller.
8. MR = 120 x (1 - 1/2) = Rs 60.

Frequently asked questions

What is the difference between total, average and marginal revenue?

TR is the revenue from all units sold. AR divides that total by the quantity sold. MR measures the change in TR per additional unit. They answer different questions: total earnings, earnings per unit, and the extra earnings from increasing sales.

Why are AR and MR equal under perfect competition?

The firm sells additional units at the same market price without reducing the price on other units. Each extra unit adds exactly that price to TR, so P = AR = MR.

Why is the AR curve also called the demand curve?

With a common price, AR equals price. A curve showing AR at each quantity therefore shows the same price-quantity combinations as the demand curve facing the firm.

Why does MR lie below AR under imperfect competition?

In the standard single-price, downward-demand case, selling more requires lowering the price on other units as well. The net revenue addition is therefore less than the new price. In a discrete table starting from zero sales, the first unit is an exception because no earlier units are affected.

Can marginal revenue be negative while average revenue is positive?

Yes. Nine units at Rs 50 give positive AR of Rs 50. If eight units could instead have sold at Rs 60, increasing quantity reduces TR from Rs 480 to Rs 450, so ninth-unit MR is -Rs 30.

Does zero marginal revenue always mean maximum total revenue?

For the usual smooth hill-shaped TR curve, its interior maximum has MR = 0 with a change from positive to negative MR. In a discrete table, a zero MR entry only shows equality with the previous TR entry. Compare all the TR values before identifying the maximum.

How do I calculate MR when quantity increases by more than one unit?

Divide the change in TR by the change in quantity. If revenue increases by Rs 240 across four additional units, MR over that interval is Rs 60 per unit.

Is marginal revenue always twice as steep as average revenue?

The twice-the-slope rule applies to the smooth MR curve derived from a straight downward-sloping AR curve. It is not a general rule for curved demand, nor does it say that the value of MR is twice the value of AR.

Can I find MR from AR alone?

Not usually. You need information about how revenue changes with quantity. If the question establishes a fixed price under perfect competition, MR equals AR. Otherwise, one AR value is insufficient.

Does the output with the highest revenue give the highest profit?

Not necessarily. Profit equals TR minus TC. An output increase may add more to cost than to revenue, so profit can fall while revenue rises. Use cost information whenever the question asks about profit.