Average and Marginal Revenue: Formulas, Differences

Average and Marginal Revenue: A seller of a commodity is concerned with the demand for that commodity because the demand primarily determines the revenue generated by selling. The price paid by the consumer or customer for the product constitutes the seller’s revenue or income. Total revenue refers to the seller’s total income from selling a specific amount of product.

Thus, we can calculate total revenue by multiplying the quantity of output sold by the product’s market price. The revenue earned per output unit is referred to as the average revenue. It is possible to calculate it by dividing total revenue by the total number of units sold. The net revenue generated by selling an additional product unit is referred to as the marginal revenue. It is the additional revenue generated by selling one additional unit of a product.

Average and Marginal Revenue

A company’s revenue is the money or amount it makes from selling goods and services to customers, which are its normal business activities. It is also called sales or turnover. Revenue can also come from royalties, fees, and interests.

Types of Revenue

We have three types of revenue:

Total Revenue

Total revenue is the total amount a vendor can earn from selling goods or services to a customer. Commodity prices can be expressed as \(P \times Q\), the cost price of the commodities multiplied by the number of commodities sold. Hence, the total revenue is the commodity’s cost price \((P)\) multiplied by the enterprise’s output \((Q)\).
\(TR = P \times Q\)

Average Revenue

The revenue obtained per unit of output sold is represented by the average revenue. The average revenue contributes significantly to the profit of any business. Profit per unit product is calculated by subtracting the average (total) cost from the average revenue.

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

\( = \frac {(p \times q)}{q}\)

\(AR = p\)

Average Revenue Key Points

• The average revenue per unit (ARPU) calculates earnings per user or unit.
• This figure is frequently reported by telecom and media companies. It is especially important for telecommunications and media companies because their businesses are based on subscribers or active users rather than buyers of physical products.
• To calculate ARPU accurately, a standard time period must be defined. For example, ARPU is typically calculated monthly by most telephone and communications carriers. After that, the total revenue generated during the standard time period is divided by the number of units or users.
• Churn rate and subscriber growth rate are two other metrics closely monitored in the telecom and media industries.
• Analysts and investors benefit from comparing AR per unit figures from competitors in the same industry. It indicates which company maximises revenue from its subscribers or users the best.
• Management examines the AR per unit figure to determine which products or business segments perform best and worst.
• The period’s end date is not used for the denominator because it may fail to capture fluctuations throughout the period. Instead, the period’s start and end dates are typically averaged.

Marginal Revenue

The revenue generated from the sale of a new product or unit is referred to as marginal revenue. In other words, it is the revenue generated by a company when it sells an additional unit. Management uses it to analyse customer demands, plan production schedules, and set product prices.

By the law of diminishing returns, the revenue margin remains constant up to a certain output level and then slows as output increases.

\(MR = \frac{{{\text{Change}\;{\text{in}}\;{\text{total}}\;{\text{revenue}}}}}{{{\text{Change}\;{\text{in}}\;{\text{quantity}}}}}\)

Marginal Revenue Key Points

• The increase in the revenue that results from the sale of one additional unit of output is referred to as marginal revenue (MR).
• While marginal revenue can remain constant at a given level of output, it is subject to the law of diminishing returns. It then will eventually slow down as the output level increases.
• According to economic theory, perfect competition occurs when all companies sell identical products, market share has no effect on the price, companies can enter and exit without barriers, buyers have perfect or full information, and companies cannot determine prices.
• Marginal revenue analysis assists a company in determining the revenue generated by one additional unit of production.
• A company seeking to maximise profits will produce until the marginal cost equals the marginal revenue.
• When marginal revenue falls below marginal cost, businesses typically conduct a cost-benefit analysis and cease production.
• Marginal revenue is calculated as the ratio of the change in the total revenue to the change in total output quantity. As a result, the cost of a single additional item sold equals marginal revenue.
• Any advantages gained from adding the extra unit of activity are marginal. One example is when marginal revenue exceeds marginal cost, resulting in a profit on new items sold.
• When the marginal revenue falls below the marginal cost, firms typically apply the cost-benefit principle and cease production, as additional production provides no additional benefits.

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Average and Marginal Revenue

An individual firm’s average revenue (AR) curve slopes downwards in all forms of imperfect competition. When a firm lowers the price of its product, the quantity demanded and sales increase.

The figure depicts the situation in which average revenue decreases as more units of the product are sold in the market. It can be seen that the AR curve is falling, and the MR curve is below it.

Since the MR curve is lower than the AR curve, marginal revenue declines faster than average revenue.

Average and Marginal Revenue Under Perfect Competition

When there is perfect competition in a product market, the demand curve facing an individual firm is perfectly elastic, the price is beyond a firm’s control, and average revenue remains constant. If the price or average revenue of a product remains constant as more units are sold, the marginal revenue equals the average revenue.

This is because if one more unit is sold and the price does not fall, the addition to total revenue made by that unit will be equal to the price at which it is sold, as no revenue loss is incurred on the previous units in this case.

The graph below depicts the case of perfect competition, in which an individual firm’s average revenue (or price) remains constant and marginal revenue equals average revenue. Here, the average revenue curve is a horizontal straight line (i.e., parallel to the \(X\)-axis).

The horizontal line average revenue curve (AR) indicates that when the quantity increases, the price or average remains constant. Since the marginal revenue equals average revenue, the marginal revenue curve coincides with the average revenue curve.

Solved Examples – Average and Marginal Revenue

Q.1. An individual firm sells \(200,000\) sweet candies in a year. The price per candy is \(₹1\). What’s the firm’s total revenue?
Solution: Total revenue \(=\) the number of candies sold \(\times\) the price per candy
Thus, total revenue \(= 200,000 \times 1 = ₹ 200,000.\)

Q.2. A company that sells microwaves makes \(₹600,000\) in total revenues in a year. The number of microwaves sold that year was \(1,200\). Calculate the average revenue?
Solution: Average revenue \( = \frac{{{\text{total}\;{\text{revenue}}}}}{{{\text{number}\;{\text{of}}\;{\text{microwaves}}\;{\text{sold}}}}}\)
\( = \frac{{600,000}}{{1200}}\)
\(\therefore \,AR = ₹ 500\)
Hence, the company makes \(₹ 500\) on average from selling one microwave.

Q.3. A company has generated \(₹ 5,000\) in total revenue. The total number of output sold was \(400\) units. The following year the firm increased its production to \(500\) units, and then the total revenue was \(₹5,500\). Calculate their marginal revenue?
Solution:
Marginal revenue \( = \frac{{{\text{Change}\;{\text{in}}\;{\text{total}}\;{\text{revenue}}}}}{{{\text{Change}\;{\text{in}}\;{\text{quantity}}}}}\)
Hence, the marginal revenue \( = \frac{{₹ 5,500 – ₹ 5,000}}{{\left( {500 – 400} \right)}}\)
\(= \frac {₹ 500}{100}\)
\(= ₹ 5\)

Q.4. A software company generated a total revenue for the last quarter of about \(₹ 8.2\) million. The number of subscriptions fluctuated regularly for the last quarter, but the weighted average was found to be \(110,500\) users. Find the average revenue.
Solution:
Average revenue \( = \frac{{{\text{total}\;{\text{revenue}}}}}{{{\text{number}\;{\text{of}}\;{\text{users}}}}}\)
\( \Rightarrow AR = \frac{{₹ 8.2\;{\text{million}}}}{{110,500}}\)
\(= ₹ 74.21\)

Q.5. In a company, \(10\) units are sold at \(₹ 9\) each, resulting in total revenues of \(₹ 90\). Then, \(11\) units are sold at \(₹ 8.50\), resulting in the total revenues of \(₹ 93.50\). Find the marginal revenue of the \(11^{th}\) item.
Solution: Total revenue from \(10\) units when sold at \(₹ 9 = ₹ 90\)
Total revenue from \(11\) units when sold at \(₹ 8.50 = ₹ 93.50\)
Therefore, the marginal revenue of the \(11^{th}\) unit is \(= ₹ 93.50 – ₹ 90\)
\(\therefore MR = ₹ 3.50\).

Summary

There are significant distinctions between average revenue and marginal revenue. However, a firm requires both of these economic concepts to determine the optimal production levels for their commodity. They also require these two figures to determine whether the current selling price of their product should be adjusted.

The net revenue generated by selling an additional unit of a company’s product is marginal revenue. It is the extra revenue generated by selling one more unit. Average revenue, on the other hand, refers to revenue earned per output unit. By dividing the total revenue earned by the number of units sold, we will get the average revenue.

The average and marginal revenue are the same when it is a perfectly competitive market. Perfect competition occurs when all companies sell identical products, market share has no effect on the price, companies can enter and exit without barriers, buyers have perfect or full information, and companies cannot determine prices.

Frequently Asked Questions (FAQs)

The frequently asked questions regarding average and marginal revenue are given below:

Q.1. What is the relationship between the average and the marginal revenue?
Ans: Marginal revenue is the net revenue generated by selling an additional unit of a company’s product, whereas average revenue is generated per output unit. Thus, marginal revenue is calculated by dividing the change in revenue by the change in quantity. In contrast, average revenue is calculated by dividing total revenue by units sold.

Q.2. What is meant by total revenue, average revenue and marginal revenue?
Ans: Total revenue is the amount of money earned by a company during a given period from the sale of its goods and services. The average revenue shows how much money is made per unit of output. The increase in the total revenue by increasing one output unit is marginal revenue.

Q.3. What is an average revenue?
Ans: The average revenue shows how much money is made per unit of the output. In other words, it computes how much revenue a company earns on average from each unit of product sold. To calculate the average revenue, divide the total revenue by the number of output units.

Q.4. In which market are average revenue and marginal revenue are same?
Ans: The standard condition for a perfectly competitive firm is that price equals both average revenue and marginal revenue \((P = AR = MR)\). This condition indicates that a firm is a price taker with no market control and is confronted with a perfectly elastic demand curve equal to the market price. The marginal revenue of a competitive firm always equals the average revenue and price because the price remains constant across varying levels of output.

Q.5. What is revenue?
Ans: The total amount of income generated by the sale of goods or services related to the company’s primary operations is revenue.

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