The term ‘revenue‘ or ‘total revenue’ in economics refers to total receipts from the sale of output produced. For instance, suppose 1000 units of a product are produced by a firm. Suppose further that market price of each unit is Rs 20. The revenue realised from the sale of entire output at this price would be Rs 20,000.
This is what is known as the ‘total revenue’. In the numerical illustration here, we have assumed that the market price of each unit is Rs 20 and is the same for all the units offered for sale by all the producers in the market. The case refers to a competitive market, in which, price is constant throughout due to the presence of competition among the large number of sellers each of whom is a price taker.
A price taker is one who sells output at a price fixed by the market forces of demand and supply. The market price determined by the forces of demand and supply is Rs 15,000 per TV set. All the producers have to sell their product at this price. A simple multiplication shows that the total revenue from the sale of 105,000 sets is Rs 157.5 crore.
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If the market price, as fixed by the forces of demand and supply, is, say P, and the units sold are, say Q, total revenue, TR, can be represented as
TR = P × Q
Expressions for average and marginal revenues, in this case, can be obtained as below. Average Revenue (AR), defined as the revenue per unit of output sold, is given as
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AR = TR/Q
= P + Q/Q = P
Marginal Revenue (MR) is defined as a change in total revenue on an additional unit of output sold. If the total revenue from the sale of Q0 units is TR0 and that from the sale of Q1, units, TR1; the marginal revenue is
MR = Change in total revenue/Change in quantity sold
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. TR1 – TR0
Δ (TR)/ΔQ = d (TR) dQ
The last expression refers to change in total revenue, d(TR), caused by an infinitesimally small change, dQ, in quantity sold. Since price is fixed at P,
Fig. 5.15: The market price is P, as determined by market forces of demand and supply in the left panel. The competitive firm, being a price taker, has to adopt this price. As a result, its AR and MR have each to be equal to the market price, P (AR = MR = P), as shown in the right panel. The firm has to be prepared to sell unlimited output at this price. AR and MR curves are both horizontal and coincidental.
A numerical illustration would drive the concept home. Consider the following schedule of sales
| Output, Q | 1 | 2 | 10 | 15 | 20 | 30 | 50 | 60 | 80 | 100 |
| TR | 10 | 20 | 100 | 150 | 200 | 300 | 500 | 600 | 800 | 1000 |
| AR = TR/Q | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |
| MR = ΔTR/ΔQ | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |
AR = MR = 10 at all levels of sales. AR and MR are calculated through the equations 5.12 and 5.13.
When a single producer operates in the market, he tends to dictate price and is known as the price maker. He usually starts with a high price which he lowers only when he feels his sales are stuck up. In other words, he faces a downward sloping demand curve of the type
P = a – bQ
where, a and b are fixed numbers and P is price while Q is quantity demanded. Price is not fixed for this producer, known as monopoly producer. Total revenue
TR = Price x Quantity sold
= P × Q = (a – bQ) × Q
= aQ – bQ2
AR, from equation 5.12
AR = TR/Q = PQ/Q = P
= a-bQ
MR, from equation 5.13 and 5.15
MR = d(TR)/dQ
= d(aQ – bQ2)/dQ
= a – 2bQ (on differentiation)
Comparison of equations 5.16 and 5.17 leads to following observations
(i) The slope of MR curve is (-2b) while that of AR curve is (- b). In other words, MR is twice as steep as the AR curve.
(ii) The value of output at which AR = 0 is (a/b) while that at which MR = 0, is (a/2b). In other words, MR bisects the horizontal intercept between the origin and the point where AR meets quantity axis.
A numerical illustration would help in understanding the concept clearly.
Using AR = TR/Q and MR = Δ(TR)/ΔQ, we calculate AR and MR for data in the table above and observe that MR falls twice as fast as AR. Extending the trend further, AR = 0, when Q = 21 while MR = 0 when Q = 11. Note that AR = MR = 20 at Q = 1. It can be seen that 1/2 of (21 – 1) is equal to (11 – 1).
Note that AR and MR do not initiate from the vertical axis in this illustration. Instead, they initiate from a vertical line through Q = 1. For equations 5.16 and 5.17, the AR and MR are initiated from the vertical axis. Figs. 5.16 and 5.17 demonstrate the fact.