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.