Q24 — Relation between AR and MR & Importance of Revenue

Introduction

In the theory of the firm, the revenue side is as important as the cost side. While cost tells us what the firm has to sacrifice to produce a given output, revenue tells us what the firm receives from selling that output. Producer’s equilibrium (profit-maximising output and price) is ultimately determined by the interaction of Marginal Revenue (MR) with Marginal Cost (MC). Hence, a clear understanding of the relationship between Average Revenue (AR) and Marginal Revenue (MR) and the importance of revenue is essential for any serious student of microeconomics, especially at B.Com Semester I level under Panjab University.

I. Meaning of Average Revenue (AR) and Marginal Revenue (MR)

1. Average Revenue (AR)

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

AR = TR / Q

Since total revenue (TR) is equal to price (P) multiplied by quantity (Q), i.e. TR = P × Q, we have:

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.

2. Marginal Revenue (MR)

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

In calculus form, MR is the first derivative of TR with respect to Q:

MR = d(TR) / dQ

MR therefore measures how fast total revenue is changing as output increases.

II. Basic Relation between AR and MR

The relationship between AR and MR depends on the nature of the demand (AR) curve and therefore on the type of market structure in which the firm operates. We discuss the two main cases separately.

1. Under Perfect Competition: AR = MR

Under perfect competition, the firm is a price-taker. It can sell any quantity at the prevailing market price, which is determined by industry demand and supply.

Price (P) is constant for the firm.
TR = P × Q increases proportionately with Q.
AR = TR / Q = P (constant).
MR = ΔTR / ΔQ = P (also constant).

Therefore, under perfect competition:

AR = MR = P
The AR and MR curves coincide, forming a horizontal straight line parallel to the X-axis at the level of market price.

2. Under Imperfect Competition: AR > MR

Under imperfect competition (monopoly, monopolistic competition), the firm faces a downward sloping demand curve. To sell more units, it must reduce the price on all units sold. Consequently:

AR (which is equal to price) falls as Q increases.
When price is reduced to sell an extra unit, the firm loses some revenue on the previous units as well.
Hence the extra revenue from the last unit (MR) is less than its price.

Therefore, under imperfect competition:

MR is less than AR at all positive levels of output, i.e. MR < AR, and both AR and MR curves slope downward from left to right. The MR curve lies below the AR curve and falls more rapidly.

III. Numerical Illustration of AR–MR Relation (Imperfect Competition)

Consider a firm which can sell different quantities of a product at different prices as follows:

Output (Q)	Price (P = AR)	Total Revenue (TR = P × Q)	Marginal Revenue (MR = ΔTR / ΔQ)	Relation between AR and MR
1	10	10	10	AR = MR initially
2	9	18	8	AR (9) > MR (8)
3	8	24	6	AR (8) > MR (6)
4	7	28	4	AR (7) > MR (4)
5	6	30	2	AR (6) > MR (2)
6	5	30	0	MR becomes zero
7	4	28	-2	MR becomes negative

From this schedule we observe:

AR equals price and falls as output increases.
MR starts equal to AR for the first unit but then falls faster and remains below AR.
MR becomes zero when TR reaches its maximum (between 5 and 6 units here).
When MR becomes negative, TR actually starts declining.

This numerical illustration confirms that under imperfect competition, for all positive outputs beyond the first unit, we have AR > MR, and MR eventually may fall to zero and become negative while AR remains positive.

IV. Geometric and Algebraic Relation between AR and MR (Straight-line Demand)

In the traditional textbook treatment (as in T.R. Jain & V.K. Ohri), the relation between AR and MR is very neat when the AR (demand) curve is a straight line.

1. Algebraic Form

Suppose the AR curve is a straight line given by:

AR = P = a − bQ

where a and b are positive constants. Then:

Total Revenue: TR = P × Q = (a − bQ)Q = aQ − bQ²
Marginal Revenue: MR is the derivative of TR with respect to Q: MR = d(TR)/dQ = a − 2bQ

Thus MR has the same intercept as the AR curve on the price axis (a) but twice the slope (−2b instead of −b). As a result, MR cuts the quantity axis at exactly half the distance at which AR cuts it.

2. Geometric Properties

When the AR curve is a straight downward sloping line:

The MR curve is also a straight line, starting from the same point on the price axis.
The MR curve lies entirely below the AR curve (except at the price axis intercept).
MR meets the quantity axis at a point where output is half of the output at which AR meets the quantity axis.

V. Diagrams: Relation between AR and MR under Different Market Forms

Fig. — Relation between AR and MR: under perfect competition AR and MR coincide; under imperfect competition AR slopes downward and MR lies below AR, falling more steeply.

VI. Importance of Revenue and AR–MR Relationship

Revenue concepts, and in particular the AR–MR relationship, are extremely important in microeconomic analysis. Their main uses can be summarised as follows:

1. Basis of Equilibrium of the Firm (Profit Maximisation)

The fundamental condition for profit maximisation of a firm in all market forms is:

MR = MC

This condition cannot even be stated without the concept of MR, which itself is derived from TR and AR. Therefore, AR and MR are indispensable for determining the firm’s equilibrium output and price.

2. Distinguishing Different Market Structures

The pattern of AR and MR curves varies across market forms:

Under perfect competition: AR = MR and both are horizontal.
Under monopoly and monopolistic competition: AR > MR, both are downward sloping.

Thus, the AR–MR relationship helps us to identify and distinguish different types of market structures and to analyse equilibrium in each case (perfect competition, monopoly, monopolistic competition).

3. Guidance for Pricing and Output Decisions

The firm’s pricing and output decisions are ultimately guided by the behaviour of revenue:

AR tells the firm the price it can charge at different output levels.
MR tells the firm the extra revenue it gains from selling one more unit.
Comparing MR with MC at each level of output helps the firm decide whether increasing or decreasing output will increase profit.

Without AR and MR, rational pricing policy and output adjustment would not be possible.

4. Understanding Effect of Price Changes on Total Revenue

The way total revenue (TR) changes when price changes is crucial for taxation policy, discount policy and sales strategy of firms. TR, AR and MR together show:

Whether cutting price will increase or decrease revenue.
At which output TR is maximum (where MR = 0).
When further reduction in price makes MR negative and causes TR to fall.

Although the detailed relation between MR, AR and price elasticity of demand is taken up in a separate question, the foundation is laid by the AR–MR relationship.

5. Evaluation of Selling Costs and Non-price Competition

In monopolistic competition and modern marketing, firms incur heavy selling costs (advertising, sales promotion, branding). The success of such expenditure is judged by its impact on:

Shifting the AR (demand) curve to the right.
Making the AR curve less elastic, which changes the MR schedule and may increase revenue at a given price.

Thus, revenue concepts provide a basis for cost-benefit analysis of selling activities.

6. Importance in Public Policy and Welfare Economics

For the government, knowledge of revenue behaviour helps in:

Designing indirect taxes so as to raise maximum revenue with minimum excess burden.
Understanding how monopolies and oligopolies exploit their market power through pricing.

Again, these issues rest on the relationship between AR, MR and the underlying demand conditions.

7. Examination Importance (Panjab University)

In the B.Com (Sem I) Microeconomics paper of Panjab University, the question “What is the relation between AR and MR? Explain the importance of revenue.” is a standard 15-marks theoretical question. A good answer must:

Define AR and MR clearly.
Explain the AR–MR relation under perfect and imperfect competition.
Support with a numerical example and neat diagram(s).
Discuss at least 5–6 points showing the importance of revenue concepts in theory and practice.

Exam Tip (for 15 marks): Start with definitions of AR and MR, then explain the AR–MR relation separately for perfect competition (AR = MR) and imperfect competition (AR > MR, MR below AR). Provide a small numerical table and a diagram with two panels for perfect and imperfect competition. Afterwards, give a well-structured list of the importance of revenue: firm’s equilibrium, market-structure distinction, pricing and output policy, TR behaviour, selling-cost decisions and public policy relevance. End with a short conclusion. This pattern matches exactly what Panjab University examiners expect for full marks.

Conclusion

To conclude, the relationship between AR and MR is simple yet powerful. Under perfect competition, the firm is a price-taker and AR = MR = Price. Under imperfect competition, the firm faces a downward sloping demand curve; consequently, AR falls with output and MR falls faster than AR, always remaining below it and eventually becoming zero or negative. This relationship is central to understanding how total revenue behaves and how a profit-maximising firm chooses its output through the MR = MC rule. Because of this, revenue concepts play a foundational role in the microeconomic theory of the firm and occupy a prominent place in the B.Com Semester I syllabus of Panjab University.

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.