REVENUE IN ECONOMICS (TOTAL, MARGINAL AND AVERAGE REVENUE)

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Revenue is defined as the income received by a firm or organization from the sales of its product. 

In other words, revenue is defined as the receipt that a firm obtains from selling its goods.

The following revenue calculation is used by economists to analyze the revenue of economic entities.

Total revenue

As the name implies, total revenue is the total receipt that a firm obtains from selling its goods. 

More appropriately, total revenue is the sum of all payments received by a firm or organization from the sales of its goods.

It is computed as price times quantity, like this:

$TR=P\times Q$.

For instance, if a firm was able to sell 500 apples at €30 each, its total revenue will be $500\times 30=€15000$.

As another example, if a firm sells 100 books for €5 per book, then its total revenue would be $5\times100=500$

Average revenue

As the name suggests, average revenue is the per-unit revenue. It is derived by dividing the total revenue of a firm by the quantity sold.

Mathematically, Average revenue is expressed as:

$AR=\frac{TR}{Q}$.

It is important to note that average revenue always equals price. 

Let me show how valid this is, mathematically 😉.

You know,

$AR=\frac{TR}{Q}$

But $TR=P\times Q$, Hence

$AR=\frac{P\times Q}{Q}$

$AR=\frac{P\times\require{cancel}\bcancel{Q}}{\require{cancel}\bcancel{Q}}$

$AR=P$.

Because the average revenue always equals price, the average revenue curve of any firm is the same as its demand curve.

Remember that the demand curve relates to price and quantity while average revenue relates to average revenue and quantity.

Example

If a firm receives a total revenue of €400 from selling 10 apples. Its average revenue is:

$AR=\frac{400}{40}$

$AR=10$

Marginal revenue

This refers to the addition to total revenue as a result of selling one unit of output. 

Simply put, marginal revenue is the change in total revenue as a result of selling an additional unit of sales.

Mathematically, it is represented as

$MR=\frac{∆TR}{∆Q}$

The accompanying illustrations show the relationship between the various revenue calculations. 

Quantity

Sold

Price

TR(P×Q)

AR

(TR÷Q)

MR (∆TR÷∆Q)

1

10

10

10

10

2

9

18

9

8

3

8

24

8

6

4

7

28

7

4

5

6

30

6

2

6

5

30

5

0

7

4

28

4

-2


Analysis

Total revenue is derived by multiplying price and quantity. Hence, for the first unit, Total revenue is $1\times 10=10$.

For the second unit, Total revenue is $2\times 9=18$. The same procedure is done for the other units.

Average revenue is total revenue divided by quantity. So, for the second unit, the average revenue is $18÷2=9$.

The same is done for all other units. Average revenue, as you would observe, is the equal price at every unit. This is consistent with what was said earlier.

Lastly, marginal revenue is the change in total revenue as a result of a unit increase in quantity.

Calculating marginal revenue, for the first unit, the marginal revenue would be $10-0=10$. 

For the next unit, marginal revenue would be $18-10=8$. We derived the other marginal revenue in the same way.

Now, let's visualize the above revenue schedule on a graph


We can observe three things from this diagram.

1.  The total revenue will keep increasing as long as marginal revenue is positive.

2. Total revenue is at a maximum when marginal revenue is zero. In this case, the total revenue is at a maximum of 6 units.

3. When marginal revenue is negative, then total revenue falls. This is the castor of the seven units.

Relationship Between Average And Marginal Revenue

The relationship between average revenue and marginal revenue is such that:

1. Average revenue will fall when marginal revenue is lesser than average revenue.

2. Average revenue will remain constant when marginal revenue equals average revenue (like the case with perfect competition)

3. Average revenue will rise when marginal revenue is above the average revenue

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Relationship Between Price And Marginal Revenue For Various Market Structures.

In the theory of firms, there are only two possible price and marginal revenue relationships.

It is either price equals marginal revenue or price greater than marginal revenue.

In a perfectly competitive market, the price is usually equal to the marginal revenue. 

This is because each firm in perfect competition has to sell its goods and services at the prevailing market-established price.

The accompanying revenue schedule illustrates the relationship between the price and marginal revenue of the perfectly competitive firm. 

Units

Sold

Price

Total revenue

Average revenue

Marginal

Revenue 

1

4

4

4

4

2

4

8

4

4

3

4

12

4

4

4

4

16

4

4

5

4

20

4

4

6

4

24

4

4


As can be seen, the price of the perfectly competitive firm equals marginal revenue at all output.

Hence, the demand curve, as well as the marginal revenue of the perfectly competitive firm, will be horizontal, indicating that it sells all goods at one price.

Firms in imperfect competitions (such as monopoly, oligopoly and, monopolistic competition) will face a downward slopping demand curve.

This is because imperfect competitive firms can affect sales either by increasing price or decreasing price.

You know, imperfect competitive firms, unlike their perfect competitive counterparts, are price makers.

The price of an imperfectly competitive firm is equal to or greater than its marginal revenue.

This is because an imperfectly competitive firm will have to lower the price of outside goods and services to make additional sales (law of demand). Hence its price will be greater than marginal revenue at almost all times.

It is, however, important to note that the price received by the imperfectly competitive will be the same as its marginal revenue at the first unit

This can be observed from the first revenue schedule.

The reason is that, unlike other units, an imperfectly competitive firm does not need to lower the price to sell the first unit. 

In short, the demand curve of a perfectly competitive firm is the same as its marginal revenue curve while the demand curve for an imperfectly competitive firm is different from its marginal revenue curve.

Conclusion

Marginal, total and, average revenues are important economic concepts. No firm can declare profit without knowing its total revenue and total cost.

It is also the same for a firm maximizing profit, which can not make production decisions without knowing its marginal revenue.

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