Derivation of Average Revenue and Marginal Revenue Curves from TR Curve

 

The average revenue and marginal revenue curves can be obtained from total revenue curve. The process is little bit different in perfect competition and monopoly (or imperfect competition). It is because price remains constant under perfect competition. On the other hand, price is reduced to sell more quantities under monopoly. Hence, the derivations of TR, AR, and MR curves in two types of market have been shown separately.

 

Derivation of AR and MR Curves Under Perfect Competition

 

The demand curve of a firm under perfect competition is perfectly elastic. The price is beyond the control of a firm. It is because price is determined by the industry as a whole. The average revenue or price thus remains constant. If different units are sold at same price, marginal revenue equals price. Because, the addition made to total revenue by the sale of one more unit is equal to price. It is presented in table.

 

Table  : Revenues Under Perfect Competition

Quantity     Sold       (Q)	Price or Average       Revenue         (P/AR)	Total           Revenue             (P * Q)	Marginal         Revenue           (MR)
0	Rs 16	Rs 0	-
1	16	16	16
2	16	32	16
3	16	48	16
4	16	64	16
5	16	80	16

As shown in the table, the price is constant at Rs 16 even if more units are sold. Hence, average revenue is also constant at Rs 16.

 

The total revenue goes on increasing as more and more units are sold. But the rate of increase in total revenue is constant, that is, total revenue increases by Rs 16.When two units are sold, total revenue has increased from Rs 16 to Rs 32. The addition made to total revenue or marginal revenue is Rs 16. Similarly when three units are sold total revenue increases to Rs 48 and marginal revenue is 48-32 = Rs 16. Hence, average revenue and marginal revenues are equal even if more units are sold.

 

The derivation of TR, AR and MR curves from above table has been shown in the figure.

 

In figure, 1st TR is the total revenue curve. It begins from point of origin, which shows that total revenue is zero when quantity sold is nil. It rises upwards which means that total revenue increases when quantity sold increases. The total revenue curve is a straight line. Since the price is constant, the rate of increase in total revenue is also constant.

 

In figure 2nd, AR is the average revenue and demand curve. The AR curve is horizontal straight line or parallel to OX axis. The horizontal straight-line shape of AR curve indicates that the price remains constant at Rs 16 even if the quantity sold increases. Since marginal revenue and average revenue are equal, the MR curve coincides with AR curve. In other words, AR curve is also the marginal revenue curve.

 

Derivation of AR and MR Curves Under Monopoly

 

In all forms of imperfect competition including monopoly, the firm reduces to sale more quantity. Due to this the average revenue goes on declining. Hence, the addition to total revenue when more units are marginal revenue also goes on declining. Besides, the marginal revenue declines more rapidly than average revenue. The total revenue goes on increasing, reaches the maximum point and declines thereafter. This can be illustrated by the help of following table.

 

Quantity            Sold            (Q)	Price or Average          Revenue            (P/AR)	Total                    Revenue (TR)	Marginal             Revenue               (MR)
0 1 2 3 4 5 6 7 8 9 10	Rs 11 10 9 8 7 6 5 4 3 2 1	Rs 0 10 18 24 28 30 30 28 24 18 10	- Rs 10 8 6   4 2 0 -2 -4 -6 -8

 

The table shows that price decreases when more units are sold. Due to this both average revenue and marginal revenue decline. But the marginal revenue declines more rapidly than average revenue. The marginal revenue is zero when six units are sold and becomes negative thereafter. The total revenue is maximum when marginal revenue is zero and begins to decline thereafter.

 

The derivation of total revenue, average revenue and marginal revenue curves on the basis of above table has been presented in the figure below.

 

In figure   TR is the total revenue curve. It slopes upward in the beginning, reaches maximum at point M and slopes downward thereafter.

 

As shown in figure the average revenue curve, AR. in the monopoly market is downward sloping. It is because price is reduced to sell more quantity. The marginal revenue curve, MR lies below AR. This means that MR falls more rapidly than AR. When 6 units are sold, marginal revenue is zero and if quantity sold is increased beyond 6 units. MR becomes negative.

 

The MR curve has two crucial features. First, at the outset marginal revenue equals average revenue. In figure, AR = MR at quantity one and price Rs 10. The slight difference in figure is due to convention of plotting MR at the midpoint of each interval on the quantity axis. Second, MR = O when total revenue is maximum. When MR is positive total revenue increases; when marginal revenue is negative, total revenue declines. Naturally when the addition to TR is zero, total revenue must be at its maximum.