# Short Notes: Concepts of Revenue # Concept of Revenue

The money income which a producer gets from the sale of his product is known as revenue of the firm. It is also called sale proceeds of the firm.

 Revenue of a firm are its money receipts consequent upon the sale of its product.

The concept of revenue should not be confused with the concept of profit. Profit of a firm is estimated as the difference between revenue and cost related to the production of a commodity (Profit = Revenue – Cost).

# Total Revenue, Average Revenue and Marginal Revenue

Revenue has three aspects:

• Total Revenue
• Average Revenue
• Marginal Revenue

Total Revenue (TR)

Total revenue refers to money receipts of a firm from the sale of its total output. It is estimated as the multiple of price and quantity of output.

TR = PxQ

(Here, TR = Total revenue, P = Price per unit of output, and Q = Quantity (or units) of output.)

 Total revenue is the sum of money receipts of a producer corresponding to a given level of output.

Average Revenue (AR)

Average revenue is the revenue per unit of output. It is equal to total revenue divided by total output.

AR = TR/Q

(Here, AR = Average Revenue, TR = Total Revenue, and Q = Total Output)

 Average revenue is the per unit revenue corresponding to a given level of output of a firm.

Average Revenue is the same as Price of the Commodity.

Let us see how:

AR = TR/Q

AR = (P x Q)/Q           [Since TR= P x Q]

AR = P

Implying that average revenue is nothing but price of the commodity.

Marginal Revenue (MR)

Marginal revenue is the additional revenue that a producer expects from the sale of one more unit of a commodity. In other words, it is the change in total revenue which results from the sale of one more (or one less) unit of a commodity. It is expressed as:

MR = ΔTR/ΔQ = TRn – TRn-1

(Here, MR = Marginal revenue, ΔTR= Change in total revenue, ΔQ= Change in output, TRn= Total revenue from ‘n’ units of the output and TRn-1= Total revenue from ‘n – 1’ units of the output.)

 Marginal revenue is the addition to total revenue on account of sale of one more unit of output.

Table 1 illustrates the concepts of TR, AR and MR.

Table 1: TR, AR, and MR

 Output (Units) Price = Average Revenue (Rs) Total Revenue (Rs) Marginal Revenue (Rs) 1 20 20 20 – 0 = 20 2 20 40 40 – 20 = 20 3 20 60 60 – 40 = 20 4 20 80 80 – 60 = 20 5 20 100 100 – 80 = 20

Note: Table 1 is drawn on the assumption that price is constant at Rs 20 per unit of output.

Observe the following : # Relation between TR, AR and MR

Relation between TR, AR and MR is discussed with reference to different market situations. Broadly, a producer may encounter either of the two situations:

(a) There is a large number of firms selling a product at a constant price. An individual firm is so small in the market that it cannot change price of the product. Or, it has no control over price of the product. Accordingly, to a firm, price is given of course, it can sell any amount of the product at a given price.

(b) A firm enjoys partial control over price through product differentiation or it has full control over price because it is a monopoly firm. Accordingly, a firm can plan to increase its sale by lowering its price.

The basic difference between the two situations is the following:

(a) When a firm has no control over price, it can sell any amount at a given price. Accordingly, firm’s demand curve (or AR curve) is a horizontal straight line as in Fig. 1.

(b) When a firm has partial or full control over price, it can sell more of a product only by lowering its price. Accordingly, its demand curve (or AR curve) slopes downward, showing a negative relationship between price and output as in Fig. 2. Fig. 1. shows that a firm (having no control over price) sells its product at the given price (= OP). It cannot change the price. Implying that it can sell whatever amount it wishes to sell at the given price.

Fig. 2. shows that a firm (having partial or full control over price) can sell more only if it lowers the price of the product.

We now are discussing the relationship between TR, AR and MR with reference to situation-1 (when firm’s AR curve is a horizontal straight line) and situation-2 (when firm’s AR curve is a downward sloping curve).

Situation-1

Relationship between TR, AR and MR when firm’s AR curve (or firm’s demand curve) is a horizontal straight line.

Note an important fact:

When AR is given to a firm, it implies that AR is constant for a firm.

Constant AR implies that MR should also be constant, and equal to AR. This is a mathematical fact. Because, AR is average value of a series. Average value can remain constant corresponding to every level of output only when MR (which is additional revenue or additional value) remains constant corresponding to every level of output. Thus, in case a firm is facing a demand curve which is a horizontal straight line, it should represent both its AR as well as MR curve.

 Important In case a firm is facing a demand curve which is a horizontal straight line, it should represent both its AR as well as MR curve. It is a situation when a firm has no control over price and has to sell its product at the given price.

Now, when AR and MR are constant and are equal to each other, corresponding to every additional unit of output, a firm should be adding a constant amount to its TR (total revenue). Thus, firm’s TR should increase at a constant rate (Note: MR is the rate of TR; constant MR implies that TR increases at a constant rate). Fig. 3 (a and b) illustrates the behaviour of TR, AR and MR in such a situation. Fig. 3

Situation-2

Relationship between TR, AR and MR when firm’s demand curve slopes downward.

Note a fact again:

When AR tends to decline corresponding to every next level of output, MR should be declining even faster. Reason: average value of a series (AR) will decline only when additional value (MR) declines faster than the average value. Take an illustration, as under:

 Output AR TR MR 1 10 10 10 2 9 18 8 3 8 24 6

We find that when AR is declining by 1 unit (corresponding to a unit increase in output), MR is declining by 2 units. Implying the fact that when AR declines, MR should be declining faster than AR.

(Note: The reader may note the fact that in case AR curve is a straight line and slopes downward, the slope of MR curve should be twice the slope of AR curve. No proof is required as it is beyond the scope of the prescribed syllabus.)

Fig. 4 illustrates the relationship between TR, AR and MR when firm’s demand curve (AR curve) slopes downward. Fig. 4

Observations:

(i) When marginal revenue curve declines till point ‘M’ in part ‘B’, total revenue is increasing at diminishing rate as shown by the segment O to B in part ‘A’.

(ii) When marginal revenue becomes zero at point ‘M’ in part ‘B’, total revenue is at its maximum as shown by point ‘B’ in part ‘A’.

(iii) When marginal revenue falls, the average revenue also falls but lies above the marginal revenue curve. Implying that in a situation of falling price, MR falls even faster.

(iv) After point ‘M’, marginal revenue becomes negative. Now total revenue starts diminishing.

(v) A situation of zero AR obviously implies a situation of zero TR. (Zero price situation is not a general phenomenon, but, of course has examples as in government or charitable hospitals where medicines are given to the patients at zero price.)

 Note Carefully Marginal revenue can be positive, zero or negative but average revenue (or price) cannot be negative.

# AR and MR Curves under Different Market Situations

AR and MR Curves under Perfect Competition

A firm facing a perfectly competitive market is a price taker. It sells its product only at the given price, or the price that prevails in the market, as determined by the forces of market supply and market demand. As already discussed, this is a situation when firm’s demand curve (or price line) is a horizontal straight line. Both AR and MR are represented by the same horizontal straight line, as already discussed. Refer to Fig. 3(a) for illustration.

AR and MR Curves under Monopoly and Monopolistic Competition

Both average revenue and marginal revenue curves are downward sloping straight lines from left to right under monopoly as well as monopolistic competition. Implying that a monopolist can sell more units of the output only at lower price. Or, if he desires to charge high price, he will be able to sell less units of the output.

However, the difference is that firm’s AR curve under monopolistic competition is flatter than that under monopoly. Flatter means, it is more elastic. Reason: a firm under monopolistic competition has only a partial control over price, owing to the presence of many competitors in the market (implying higher elasticity of demand for the product). On the other hand, a monopoly firm has complete control over price, owing to the absence of competition (implying lesser elasticity of demand for the product, as consumers do not have options).

AR and MR curves under monopoly are shown in Fig. 5 and under monopolistic competition in Fig. 6. Fig. 5                                                                                     Fig. 6

However, in both the situations, MR curve is below the AR curve. Implying that when AR decreases, MR decreases faster than AR. Hence, AR > MR or AR curve is above MR curve under monopoly and monopolistic competition. This contrasts with AR and MR curves under perfect competition where they happen to coincide and are represented by a horizontal straight line.

 AR curve or firm’s demand curve is more elastic under monopolistic competition than under monopoly, owing to the fact that while a firm under monopolistic competition has a large number of competitors in the market, a monopoly firm has none.

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