Revenue and Its Derivations

Revenue

Revenue can be defined as the amount collected by a producer by selling his production.

According to Dooley, “The revenue of a firm is its sales receipts or money receipts from the sale of a product.”

There are three types of revenue: Total Revenue, Average Revenue, and Marginal Revenue

Total Revenue (TR)

Total revenue is the total earning of a firm from its output. It is calculated by multiplying the price per unit of the product with the total number of units of the product sold to customers.

Mathematically, TR = Price per unit \(\times\) Total number of units of the commodity sold

TR = P \(\times\) Q

Where,

TR = Total revenue

P = Price

Q = Quantity sold

Average Revenue (AR)

Average revenue is the total revenue divided by the quantity sold. Thus average revenue is the revenue per unit of the commodity sold.

AR = \(\frac{TR}{Q}\)

Where,

AR = Average Revenue

TR = Total Revenue

Q = Output sold

Marginal Revenue (MR)

Marginal revenue is the increase in revenue that results from the sale of one additional unit of output.

MR = \(\frac{ΔTR}{ΔQ}\)

Where,

MR = Marginal Revenue

TR = Change in total revenue

Q = Change in quantity sold

Derivation of Revenue Curve under Perfect Competition

Under perfect competition, price remains constant. The price of a commodity is determined by the industry as a whole. Marginal revenue equals to the price as the different units are sold at the same price rate. The relationship between TR, AR and MR can be shown by a schedule as follows:

Here, price per unit is same for all units sold. Total revenue increases with a constant increasing rate as more and more units are sold. If the price per unit is constant AR is also constant and as the AR is constant MR also remains constant as AR. It can be further explained with the following figure:

In the fig (A), Quantity sold is measured on x–axis and TR is measured on the y-axis. As the price of a commodity remains constant total revenue is also constant. Due to this total revenue slopes upward to the right proportionally and uniformly which means, that increase in total revenue is exactly proportionate to the increase in quantity sold.

In the fig (B), Quantity is measured in x-axis and AR and MR is measured in the y-axis. The Marginal Revenue curve coincides with the Average Revenue because additional units are sold at the same price as before. In that case AR = MR.

Derivation of Revenue Curves under Imperfect Monopoly Competition

Monopoly is opposite to perfect competition. It is also called imperfect competition. In a monopoly market, there is only one producer or seller and a large number of consumers. A firm can sell a lot of goods at a lower price or a smaller quantity of goods at a higher price. When monopolist lowers the price AR starts falling. Thus MR also starts to fall as the AR falls but the rate of decrease MR remains higher than decrease AR. But in the case of TR, it reaches maximum at first and then declines. The relation between TR, AR and MR can be shown by a schedule as follow:

On the given table, when the price increases both the TR and MR decline. Marginal revenue decreases at the higher rate than the Average revenue. Marginal revenue falls till zero and becomes negative. Average revenue also falls but remains positive. Total revenue increases continuously to reach a maximum point and decline. The derivation of TR, AR and MR curves has been shown in the following figure.

In the above figure, x-axis measures the quantity sold and y-axis measures TR, AR and MR. Total revenue increases with the increase in rate reach maximum and decline. Average revenue and Marginal revenue curves both slopes downward to the right. The sloping rate of Marginal revenue is greater than the Average revenue.

Relation between Average Revenue and Marginal Revenue under Monopoly

Under monopoly, the relation between average revenue and marginal revenue is very important. Both the average revenue and marginal revenue declines under monopoly competition whereas marginal revenue lies below the average revenue. The additional sales earn less than the average revenue when the average revenue falls, therefore, the marginal revenue is below than the average revenue.

In the figure, AR and MR represent average revenue and marginal revenue curve MR curve cuts a perpendicular AD drew to the Y -axis at its middle point C. In this case, the distance of AC is equal to the distance of CD.

(Jha, Bhusal and Bista)(Karna, Khanal, and Chaulagain)

Bibliography

Jha, P.K., et al. Economics II. Kalimati, Kathmandu: Dreamland Publication, 2011.

Karna, Dr.Surendra Labh, Bhawani Prasad Khanal and Neelam Prasad Chaulagain. Economics. Kathmandu: Jupiter Publisher and Distributors Pvt. Ltd, 2070.