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CBSEArts (English Medium) Class 12
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पाठ्यक्रम

Revenue Concepts

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Topics

Maharashtra State Board: Class 12

Key Points: Marginal Revenue

  • Extra revenue from selling one more unit
  • MR = Change in Total Revenue
  • Formula: MR = TRₙ − TRₙ₋₁
  • Example: ₹4200 − ₹4000 = ₹200
CISCE: Class 12

Total Revenue

Meaning

  • Total Revenue is the total income a firm earns by selling its output.
  • It is equal to the price per unit multiplied by the number of units sold.

Formula

TR = P × Q

Where:

  • P = price per unit

  • Q = quantity of output sold

Example

  • A shop sells notebooks at ₹100 each.
  • If it sells 20 notebooks:
    TR = 100 × 20 = ₹2000
  • So, the total income from selling 20 notebooks is ₹2000.
Maharashtra State Board: Class 12

Key Points: Total Revenue

  • Total Revenue (TR) = total sales income of a firm.
  • Formula: TR = Price×Quantity.
  • Example: Price = ₹200, Quantity = 15 → TR = ₹3000.
 
Maharashtra State Board: Class 12

Key Points: Average Revenue

  • Average Revenue (AR) = revenue per unit sold.
  • Formula: \[AR=\frac{TR}{TQ}\]
  • Example: TR = ₹3000, Quantity = 15 → AR = ₹200.
CISCE: Class 12

Meaning of revenue

  • Revenue is the money (receipts) a firm gets by selling its output in a given time period.
  • Here, three main concepts are used:
    1. Total Revenue (TR)
    2. Average Revenue (AR)
    3. Marginal Revenue (MR)
CISCE: Class 12

Average Revenue

Meaning

  • Average Revenue is the revenue earned per unit of output sold.
  • It is equal to total revenue divided by the number of units sold.
  • For a firm, AR is the same as the price per unit.

Formula

\[AR=\frac{TR}{Q}\]

Since TR = P × Q,

\[AR=\frac{P\times Q}{Q}=P\]

So, AR = Price.

Example

  • Suppose total revenue from selling 20 notebooks is ₹2000.
    \[AR=\frac{TR}{Q}=\frac{2000}{20}=\mathrm{र}100\text{ per notebook}\]
  • This is the same as the price per notebook.

Important point

  • Because AR is equal to price, the AR curve of a firm is also its demand curve.
  • As more units are sold, the price usually has to be reduced, so AR generally falls when output increases.
CISCE: Class 12

Total Revenue (TR)

a) Definition

  • Total Revenue is the total income a firm receives from selling a given quantity of a good.
  • It is also called total sales receipts of the firm.

b) Formula

  • TR = P × Q
  • TR: Total Revenue
  • PP: Price per unit
  • QQ: Quantity sold in a given period

c) Example

  • If a firm sells 15 units at ₹20 per unit:
    TR = 20 × 15 = ₹300
  • If price stays the same and the firm sells more units, TR will increase.

d) TR and consumers’ expenditure

  • From the firm’s side, this is total revenue.
  • From consumers’ side, the same amount is total expenditure on that good.

e) TR as sum of MR

  • Total Revenue can also be written as the sum of marginal revenues of all units sold:
    TR = MR1 + MR2 + MR3 +⋯+ MRn

Key points on TR

  • TR depends on both price and quantity.
  • With constant price, TR increases at a constant rate as output rises.
  • If price changes with quantity, TR may increase at an increasing, constant, or decreasing rate.
CISCE: Class 12

Marginal Revenue

Meaning

  • Marginal Revenue is the additional revenue a firm earns by selling one more unit of output.

Formula (discrete units)

For the nth unit:

MRn = TRn − TRn−1

Where:

  • TRn = total revenue from selling n units
  • TRn−1 = total revenue from selling (n − 1) units

General formula

\[MR=\frac{\Delta TR}{\Delta Q}\]

  • When output changes by 1 unit, MR is just the change in TR when one more unit is sold.

Example

  • Suppose TR from 4 notebooks is ₹100 and from 5 notebooks is ₹110.
    MR5 = TR5 − TR4 = 110 − 100 = ₹10
  • So, the 5th notebook adds ₹10 to total revenue.
CISCE: Class 12

Average Revenue (AR)

a) Definition

  • Average Revenue is the revenue per unit of output sold.
  • It is the per-unit sales receipt of the firm.

b) Formula

  • \[AR=\frac{TR}{Q}\]

c) Example

  • If TR is ₹300 from selling 15 units:

    • \[AR=\frac{300}{15}\] = ₹20 per unit.

d) AR and price

  • If all units are sold at the same price, AR is equal to the price of the commodity:
    AR = P

Key points on AR

  • AR tells “how much revenue is received on average from each unit.”
  • In usual Class 12 models, the AR curve of a firm is the same as its demand curve.
CISCE: Class 12

Marginal Revenue (MR)

a) Definition

  • Marginal Revenue is the additional revenue earned by selling one more unit of output.
  • It is the change in total revenue when output increases by one unit.

b) Discrete unit formula

  • For the nth unit:
    MRn = TRn − TRn− 1

c) Example

  • A firm sells 15 units and earns TR = ₹300.

  • It then sells 16 units and TR becomes ₹304 (price now ₹19 per unit).
    MR of the 16th unit = 304 − 300 = ₹4

d) General (change) formula

  • \[MR=\frac{\Delta TR}{\Delta Q}\]
    ΔTR: Change in total revenue
    ΔQ: Change in quantity (usually 1 unit)

Key points on MR

  • MR explains “how much extra revenue is earned by selling one extra unit.”
  • When MR is positive, TR is rising; when MR is zero, TR is maximum; when MR is negative, TR starts falling.
CISCE: Class 12

Relationship between TR, AR and MR (Table)

Output (Q) Price (P) = AR (₹) TR (₹) MR (₹)
1 10 10 10
2 9 18 8
3 8 24 6
4 7 28 4
5 6 30 2
6 5 30 0
7 4 28 -2
8 3 24 -4
9 2 18 -6
10 1 10 -8

Observations

  • As price (and AR) falls from 10 to 1, quantity sold rises from 1 to 10 units.
  • TR increases from 10 to 30 as output increases from 1 to 5 units.
  • TR becomes constant at 30 for 6 units and then falls when output increases further (7, 8, …).
  • MR decreases as more units are sold:
    1. MR is positive up to the 5th unit.
    2. MR is zero at the 6th unit.
    3. MR is negative from the 7th unit onwards.
  • When MR is zero (at 6 units), TR is at its maximum.
  • When MR is negative, TR starts falling.
  • At every output level, MR is less than AR, and it falls faster than AR.
CISCE: Class 12

Behaviour under different market structures

a) Perfect competition (price constant)

  • Firm is a price taker; it can sell any quantity at the given market price.
  • Price stays constant as Q changes, so:
    1. AR = MR = Price (horizontal line).
    2. TR increases at a constant rate as output increases.

b) Imperfect competition (price falls as output rises)

  • Firm faces a downward‑sloping demand curve.
  • To sell more units, it must reduce price.
  • As output rises:
    1. AR falls.
    2. MR falls faster and lies below AR.
    3. TR first increases at a decreasing rate, reaches a maximum (when MR = 0), and may then fall (when MR < 0).
CISCE: Class 12

Key Points: Types of Revenue

  • TR is the total income from all units sold.
  • AR is revenue per unit and is equal to price, so the AR curve is the demand curve of the firm.
  • MR is extra revenue from selling one more unit.
  • When AR falls, MR also falls and is less than AR at each output level.
  • TR increases as long as MR is positive, is maximum when MR = 0, and falls when MR is negative.
  • MR can be positive, zero or negative, but AR (price) is normally always positive.

Test Yourself

Shaalaa.com | Revenue Part 1

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