 # Revenues and their Curves

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## Revenues and their Curves

First, we need to define revenue. The revenue of a firm constitutes the receipts of money from the sale of goods and services over a given time period. Some textbooks also refer to the revenue of a firm as its turnover.

Many students confuse revenue with profit (see the next Learn-It). It is easy to mistakenly talk about revenue as the amount of money that the firm 'makes'. The amount of money that a firm 'makes' is the profit; it is the amount of money left after costs are taken away from revenue.

#### Total, marginal and average revenues

Now we need to look at specifics: total, average and marginal revenue.

Total revenue (TR). This is the total receipts of money received by a firm from the sale of its good or service in a given time period. It can be calculated by multiplying the quantity sold by the price at which the goods were sold, or TR = P × Q.

Average revenue (AR). This is the amount of money received, on average, for each good sold. If you think about it, this is effectively the price. We know that TR = P × Q, so we can substitute this into the equation above: Marginal revenue (MR). Marginal cost is the cost of producing one more unit of output. Marginal revenue is the revenue received from selling one more unit of output. It is the extra revenue at the margin (i.e. by selling the marginal unit of output).

As with the Learn-It on costs, it is worth looking at these relationships in more detail. Look at the table below. Q, which was output in the cost table, now represents sales for our laser printer firm. All revenue figures are in pounds.

Sales (Q) Average revenue (AR) Total revenue (TR) Marginal revenue (MR)
1 300 300 300
2 280 560 260
3 260 780 220
4 240 960 180
5 220 1100 140
6 200 1200 100
7 180 1260 60
8 160 1280 20
9 140 1260 -20
10 120 1200 -60

The first column shows the progressive units of output sold.

The second column shows average revenue. Notice that this figure falls as the quantity sold (or demanded) rises. Remember also that AR = price. So in essence as the price falls, demand rises. As you will see when we draw the diagrams in the next sub-section, the AR curve is the demand curve!

The third column shows total revenue. As we said earlier, TR = P × Q. So the figures in this column were calculated by multiplying the number in the first column (Q) by the corresponding number in the second column (P). So, TR = Q × AR.

The final column shows marginal revenue. Using the same method as we did for marginal cost and marginal product, the marginal revenue for, say, the seventh good sold is the difference between the total revenue received from selling 7 units and the total revenue received from selling 6 units. Algebraically, MR7 = TR7 − TR6 = 1260 − 1200 = 60.

Now try and work out the answers to the table below. Click on the relevant sections in the table to reveal the answers. #### The total, marginal and average revenue curves

In the last section, an important fact was revealed. The AR curve is, in fact, the firm's demand curve. Demand curves tell you how much of a good is demanded at any given price. But they can also tell you the price for a given level of demand. So if the AR curve is the price curve, then it must also be the demand curve.

In the topic called 'Market structure', you will see that firms in most market structures have 'normal' downward sloping demand curves. In the unique market structure of perfect competition, firms have a horizontal, or perfectly elastic demand curve. There are two sets of diagrams below. The first set looks at the case where the firm in question has a downward sloping demand (AR) curve. The second set looks at the more unusual case where the demand (AR) curve is perfectly elastic.

#### When the AR curve is a 'normal' downward sloping demand curve The diagrams are just sketches, this is totally acceptable with examiners. They are more bothered about the quality of your written analysis that goes with the diagram (although the diagram itself is always very important)!

In the top diagram, we have the downward sloping demand curve (AR) and a marginal revenue curve that is falling twice as fast. If you look at the figures in the tables above, this is what you should expect. Do you remember the relationship between all marginals and averages outlined in the 'Costs and their curves? Learn-It? If the marginal is below the average (regardless of whether the marginal is rising or falling), then the average will fall. This is also true with the revenue curves.

I have deliberately put the total revenue curve underneath the other two curves. Notice that the TR curve is at a maximum when the MR curve cuts the x-axis (i.e. when MR = 0). This makes sense.

As MR falls, the extra revenue gained from the sale of the last unit is falling with every unit sold, but it is still positive. This is why the TR curve keeps rising, albeit at a declining rate.

When MR hits the x-axis, the last unit sold added no revenue to the total, so the TR curve remains unchanged (it is momentarily flat).

As successive marginal revenues are negative, the total does finally fall.

#### When the AR curve is a flat demand curve Why is the firm's demand curve (AR curve) the same as its marginal revenue curve? Again, it's down to the relationship between averages and marginals. Do you remember the example with the money you and your friends have on you as you wait at the bus stop? If, on average, all nine of you have £20 each, and a tenth friend turns up with £20, then the average for the ten of you is still £20 each.

In the diagram above, the perfectly elastic AR curve is flat, so the value for average revenue stays the same. If the average is always the same, then the marginal must be constant and the same value as the average. So the two curves are the same.

As the marginal revenue is constant, the extra revenue added to the grand total every time a unit is sold is the same for every unit. Hence, total revenue is continually rising and at a constant rate.

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