3.3.1 Revenue

Formulae

Total revenue = price x quantity.

Average revenue = total revenue ÷ quantity.

Marginal revenue = the change in revenue for a firm from selling one more unit of a good.

Revenue for a price taking firm

A price taking firm accepts the market price as given.

• If the firm changes the quantity produced, this does not influence the price.
• This is likely to occur in markets with lots of firms and where products are identical. In other words, the perfect competition market structure.

So, for a price taking firm, the revenue curves have the following patterns:

• Total revenue = price x quantity. As the price is fixed, total revenue increases at a constant rate as quantity increases. So, total revenue is an upward-sloping line.
• Average revenue = total revenue ÷ quantity = (price x quantity) ÷ quantity = price. From the point of view of the firm, the price is constant, no matter how the firm changes the quantity. So price, or average revenue, is a horizontal line.
• Marginal revenue is the change in revenue from selling one more unit of the good. For each extra unit sold, the firm receives the price p as extra revenue. So marginal revenue is constant at price p and equal to average revenue.

Numerical table example – price taker

Assume the price per unit is £5 and the firm takes this as given. Then total, average and marginal revenue would be as follows:

Revenue for a price making firm

A price maker can influence the market price.

• This occurs where firms have a sufficiently large market share and/or where there are few substitutes.
• While this means the firm can raise the price, this will come with a fall in the quantity demanded.

Numerical example – price making firm

Consider this numerical example for a price making firm.

We make the assumption that as the price per unit falls, the units sold, the demand, increases.

[In this particular case we assume a one unit fall in price leads to an increase in demand by one unit. But this does not need to be the case]

Output	0	1	2	3	4	5	6
Price per unit (£)	6	5	4	3	2	1	0
Total revenue (£)	0	5	8	9	8	5	0
Average revenue (£)	N/A	5	4	3	2	1	0
Marginal revenue (£)	N/A	+5	+3	+1	-1	-3	-5

Note the following patterns from this numerical example:

• As the number of units sold increases, total revenue at first rises then falls.
  • As output increases by one unit, the firm can earn revenue on this extra unit.
  • However as output increases, the price falls to sell the extra units due to the law of demand. As the price falls, this reduces the revenue earnt on all the previous units that are already being sold.
    • At low levels of output, the positive effect on revenue from selling one more unit outweighs the fact that the lower price reduces the revenue earnt on all previous units. So total revenue rises as output rises.
    • At higher levels of output, the positive effect on revenue from selling one more unit is outweighed by the the fact that the lower price reduces the revenue earnt on all previous units. So total revenue falls as output rises.
• The average revenue is just the price here. So as the number of units sold increases, the price must fall to ensure those units all sell (a version of the law of demand). So average revenue falls.
• As the number of units sold rises, the marginal revenue also falls. However marginal revenue falls twice as quickly as average revenue.

Price maker diagram

The revenue curves for a price maker are below. These can be derived from numerical examples.

Total revenue is maximised at the peak of the TR curve. This also coincides with the output level where MR = 0.

• Suppose MR > 0. This means a one-unit increase in output leads to an increase in revenue. So increasing output leads to higher revenue.
• Suppose MR < 0. This means a one-unit increase in output leads to a fall in revenue. So decreasing output leads to higher revenue.
• Therefore at MR = 0, revenue is maximised.

Also, marginal revenue (revenue change with an extra unit of output) falls more quickly and is twice as steep as average revenue. 

• Average revenue equals the price. As output rises, price falls via the law of demand.
• Marginal revenue is the change in revenue from increasing output by one unit.
  • The firm makes the price p in extra revenue specifically from the extra unit produced.
  • However, in addition to this, the firm must reduce its price on all other units being sold to p. This lowers the change in overall revenue.
  • Overall, this means MR is lower than AR and that MR falls more rapidly than AR.

The link between price elasticity of demand and revenue

According to the law of demand, a fall in price leads to a rise in the quantity demanded.

The effect of a fall in price on total revenue depends on the price elasticity of demand (PED).

• If the PED is elastic, a fall in price leads to an even greater rise in quantity demanded in percentage terms. So overall, revenue rises.
  • This corresponds to the left-hand side of the revenue diagram. For output levels below q, a fall in price (and the corresponding rise in output) lead to higher total revenue. So the demand for the firm’s product is elastic.
• If the PED is inelastic, a fall in price leads to a smaller rise in quantity demanded in percentage terms. So overall, revenue falls.
  • This corresponds to the right-hand side of the revenue diagram. For output levels above q, a fall in price (and the corresponding rise in output) lead to lower total revenue. So the demand curve for the firm’s product is inelastic.

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