Q23 — Concepts of Revenue & Relation between AR, MR and TR

Introduction

In the theory of the firm, revenue occupies a position parallel to that of cost. While the cost side explains the sacrifice incurred by the firm, the revenue side explains the receipts obtained from selling output. Producer’s equilibrium regarding output and price is ultimately determined by the interaction of revenue curves with cost curves. Therefore the concepts of Total Revenue (TR), Average Revenue (AR) and Marginal Revenue (MR) and their mutual relationship form a very important and high-scoring part of the B.Com (Sem I) Microeconomics syllabus as presented in the prescribed text “Microeconomics” by T.R. Jain & V.K. Ohri.

In this answer we first explain the basic concepts of revenue, and then analytically and diagrammatically examine the relation between TR, AR and MR under different market conditions, particularly under perfect competition and imperfect competition.

1. Meaning and Concepts of Revenue

In simple language, revenue means the money receipt of a firm from the sale of its output. In economics, we are concerned not only with total revenue but also with revenue per unit and the extra revenue from additional units.

Revenue (in general):
Revenue is the price multiplied by quantity sold. When the firm sells Q units of output at price P per unit, its total revenue is TR = P × Q.

From this basic idea we derive three central concepts:

Total Revenue (TR)
Average Revenue (AR)
Marginal Revenue (MR)

2. Total Revenue (TR)

Definition

Total Revenue is the total money receipts of a firm from the sale of a given quantity of output. Algebraically:

TR = P × Q

where P is the price per unit and Q is the quantity sold.

Behaviour of TR

Under perfect competition, price remains constant; hence TR increases proportionately with Q and the TR curve is a straight line from the origin.
Under imperfect competition (monopoly, monopolistic competition), price falls as more is sold; hence TR first increases at an increasing rate, then at a diminishing rate, attains a maximum, and may finally fall. The TR curve becomes a hill-shaped curve.

3. Average Revenue (AR)

Definition

Average Revenue is the revenue per unit of output. It is obtained by dividing total revenue by quantity sold:

AR = TR / Q

Since TR = P × Q, it follows that:

AR = (P × Q) / Q = P

Thus AR is nothing but price itself. Therefore the demand curve faced by a firm is also its AR curve.

Shape of AR Curve

Under perfect competition, price is constant; hence AR is constant and the AR curve is a horizontal straight line parallel to the X-axis.
Under imperfect competition, the firm faces a downward sloping demand curve; hence the AR curve is downward sloping from left to right.

4. Marginal Revenue (MR)

Definition

Marginal Revenue is the addition to total revenue when one more unit of output is sold. It is the change in TR resulting from a one-unit change in quantity sold:

MR = ΔTR / ΔQ

Shape of MR Curve

Under perfect competition, each unit is sold at the same price; hence the extra unit adds exactly the same amount to TR, so MR = AR = P and the MR curve coincides with the AR curve as a horizontal straight line.
Under imperfect competition, to sell more units the firm must reduce the price on all units. Hence the extra revenue from the last unit (MR) is less than the price at which it is sold. Therefore the MR curve lies below the AR curve and falls faster.

Illustration: Suppose the firm must reduce price from ₹10 to ₹9 to increase sales from 5 to 6 units. TR₅ = 5 × 10 = ₹50; TR₆ = 6 × 9 = ₹54; MR₆ = 54 − 50 = ₹4. AR (price) on the 6th unit is ₹9 but MR is only ₹4, which is less than AR. This is typical under imperfect competition.

5. Numerical Relation between TR, AR and MR

The relation between TR, AR and MR can be made very clear with the help of a simple numerical example under imperfect competition (downward sloping demand):

Output (Q)	Price (P)	Total Revenue (TR = P × Q)	Average Revenue (AR = TR / Q)	Marginal Revenue (MR = ΔTR / ΔQ)
1	10	10	10.0	10
2	9	18	9.0	8
3	8	24	8.0	6
4	7	28	7.0	4
5	6	30	6.0	2
6	5	30	5.0	0
7	4	28	4.0	-2

From the above schedule we observe:

TR increases up to 5–6 units, reaches a maximum at Q = 5 or 6 (TR = ₹30), then starts decreasing.
AR is equal to price and falls steadily as more units are sold.
MR falls faster than AR and becomes zero when TR is maximum (Q = 6).
When MR becomes negative (Q > 6), TR actually falls.

Key Relations from the Schedule:
(i) As long as MR is positive, TR is rising.
(ii) When MR is zero, TR is at its maximum.
(iii) When MR is negative, TR is falling.
(iv) Under imperfect competition, AR falls and MR falls faster than AR, lying below it.

6. Diagrammatic Relation between TR, AR and MR

(A) TR, AR and MR under Perfect Competition

Under perfect competition, the individual firm is a price-taker. It can sell any quantity at the prevailing market price. Hence:

AR = Price (constant),
MR = Price (constant),
Therefore AR = MR = Price.

Fig. 1 — Under Perfect Competition: TR increases proportionately with Q; AR and MR are equal, constant and coincide in a horizontal line.

(B) TR, AR and MR under Imperfect Competition

Under monopoly or monopolistic competition, the firm faces a downward sloping demand curve. It can sell more only by reducing the price. Hence:

AR curve slopes downward from left to right.
MR curve also slopes downward but lies below the AR curve and falls more rapidly.
TR curve is inverted U-shaped (or hill-shaped), rising at first, reaching a maximum, and then declining.

Fig. 2 — Under Imperfect Competition: TR is hill-shaped; AR slopes downward; MR slopes downward more steeply and lies below AR. TR is maximum where MR = 0.

7. Formal Relationship between AR, MR and TR

We can now summarise the precise relationship between AR, MR and TR.

(i) Basic Identities

TR = P × Q
AR = TR / Q = P
MR = d(TR) / dQ (in calculus form) or ΔTR / ΔQ (in discrete form)

(ii) Under Perfect Competition

Price is constant, so AR = P (horizontal line).
Each extra unit sold adds exactly P to TR, so MR = P.
Therefore: AR = MR = Price, and TR increases proportionately with Q.

(iii) Under Imperfect Competition

The firm faces a downward sloping demand curve; to sell more, it must reduce the price on all units.
Hence AR falls as Q increases.
MR falls faster than AR and lies below AR.
TR increases as long as MR is positive, reaches maximum when MR = 0, and decreases when MR is negative.

Compact Statement:
Under perfect competition, AR = MR and both are constant. Under imperfect competition, AR > MR and both are falling; TR is maximum at the output level where MR becomes zero.

8. Importance of TR, AR and MR in Microeconomic Analysis

The concepts of TR, AR and MR are not mere definitions; they play a crucial role in the theory of the firm:

(a) Basis of Output and Price Determination
The basic equilibrium condition of a profit-maximising firm is MR = MC. Without knowing MR (derived from TR, AR), the firm cannot decide its optimal output under any market form.

(b) Distinguishing Market Structures
The shape and relative position of AR and MR curves differ under perfect competition, monopoly, and monopolistic competition. Hence revenue curves help us to distinguish market structures and to analyse equilibrium under each one (studied in later questions).

(c) Understanding Elasticity and Revenue
The relationship between AR, MR and price elasticity of demand (taken up in Question 25) is essential for understanding how total revenue behaves when price changes. This is widely used in taxation policy and business pricing decisions.

(d) Revenue Maximisation and Pricing Strategy
Some firms may aim at revenue maximisation subject to a minimum profit. TR, AR and MR curves are indispensable for identifying the revenue-maximising output (where MR = 0) and comparing it with profit-maximising output (where MR = MC).

(e) Examination Relevance
For Panjab University B.Com (Sem I), the question “Explain the concepts of revenue. What is the relation between AR, MR and TR?” is a classical 15-marks theory question. A structured answer with clear definitions, numerical illustration, neat diagrams, and a precise summary of relations is highly scoring and fully consistent with the treatment in T.R. Jain & V.K. Ohri.

Exam Tip (for 15 marks): To impress the examiner, begin with a brief introduction, then define TR, AR and MR with formulae. Provide a small numerical table showing how TR, AR and MR are calculated and how MR becomes zero when TR is maximum. Support your explanation with two neat diagrams — one for TR, AR and MR under perfect competition and one under imperfect competition. Finally, summarise the relations (AR = MR under perfect competition; under imperfect competition AR > MR, TR maximum when MR = 0) and briefly mention their importance. This pattern matches the expectations of Panjab University professors.

Conclusion

To sum up, the concepts of revenue — Total Revenue, Average Revenue and Marginal Revenue — provide the analytical foundation for the study of the firm’s behaviour on the revenue side. TR measures total receipts, AR measures receipts per unit (and coincides with the demand curve), and MR measures the addition to revenue from an extra unit sold. Their mutual relationship differs under perfect and imperfect competition, but in all cases MR plays the crucial role in determining equilibrium output through the MR = MC rule. A firm that understands these relations can take rational decisions regarding output, price and market strategy, and a student who presents them clearly in the examination is very likely to secure full marks in this important question.

These notes form part of a carefully curated set of important questions which have frequently appeared in past university examinations and therefore carry a high probability of being reflected, in whole or in part, in future question papers. However, they are intended as high-quality academic support material only and should not be treated as a guarantee or assurance of any specific questions being asked in forthcoming exams.