Demand, Total Revenue, and Consumer Surplus
1 Introduction
A demand curve shows the relationship between the price of a good and the quantity consumers are willing and able to buy. It can also be interpreted as a marginal willingness-to-pay curve: at each quantity, the height of the curve shows the maximum amount consumers are willing to pay for the next unit.
This interpretation helps distinguish three related ideas:
- total consumer expenditure;
- total revenue received by firms; and
- the total value consumers place on the goods they purchase.
The distinction can be illustrated by looking at this example of the market for personal computers (PCs).
2 Demand and total revenue
Suppose the market price of a PC is \(P_0\) and the equilibrium quantity sold is \(Q_0\). On a standard demand-and-supply diagram, the equilibrium point identifies both the price and quantity exchanged.
Consumers’ total expenditure is:
\[ \text{Total expenditure} = P_0 \times Q_0. \]
This is represented graphically by the rectangle with:
- height \(P_0\); and
- width \(Q_0\).
The same amount is the firms’ total revenue, provided that every PC is sold at the same market price:
\[ \text{Total revenue} = P_0Q_0. \]
For example, if the price of a PC is $800 and 10,000 PCs are sold, then:
\[ \text{Total expenditure} = \$800 \times 10{,}000 = \$8{,}000{,}000. \]
The consumers’ expenditure is the firms’ revenue because the payment made by buyers is received by sellers.
Important: The rectangle \(P_0Q_0\), not the entire area under the demand curve, represents actual expenditure and total revenue.
3 Meaning of the area under demand curve
The demand curve can be interpreted as a marginal-benefit or marginal-willingness-to-pay curve. The height of the curve at a particular quantity indicates the maximum amount consumers are willing to pay for the next unit.
Consider a simplified market in which the maximum willingness to pay for successive PCs is:
| PC | Marginal willingness to pay |
|---|---|
| 1st | $1,200 |
| 2nd | $1,100 |
| 3rd | $1,000 |
| 4th | $900 |
The total willingness to pay for four PCs is the sum of these marginal values:
\[ \text{Total willingness to pay} = \$1{,}200 + \$1{,}100 + \$1{,}000 + \$900 = \$4{,}200. \]
On a graph, adding the values of all successive units corresponds to adding the rectangles under the demand curve. With a continuous demand curve, the sum is represented by an integral:
\[ \text{Total willingness to pay} = \int_0^{Q_0} P(Q)\,dQ, \]
where \(P(Q)\) is the price indicated by the demand curve at quantity \(Q\).
Thus, the entire area under the demand curve, from zero to the quantity purchased, represents consumers’ total willingness to pay or total benefit.
4 Numerical example
Suppose the inverse demand function for PCs is:
\[ P = 1{,}500 - 100Q, \]
where \(P\) is the price of a PC and \(Q\) is the quantity measured in thousands of PCs.
If 10 thousand PCs are sold, then:
\[ P = 1{,}500 - 100(10) = \$500. \]
The demand curve runs from \(P=\$1{,}500\) at \(Q=0\) to \(P=\$500\) at \(Q=10\). The area under the demand curve is a trapezium:
\[ \text{Total willingness to pay} = \frac{1}{2}(1{,}500+500)(10) = \$10{,}000. \]
Because quantity is measured in thousands, this represents \(\$10\) million.
Actual consumer expenditure and firm revenue are:
\[ \text{Expenditure} = \$500 \times 10 = \$5{,}000, \]
or \(\$5\) million.
Therefore, the area under the demand curve is not the same as actual expenditure. It is the total value consumers place on the PCs, whereas the rectangle formed by the market price and quantity is the amount actually paid.
5 Consumer surplus
Consumer surplus is the difference between what consumers are willing to pay and what they actually pay:
\[ \text{Consumer surplus} = \text{Total willingness to pay} - \text{Actual expenditure}. \]
Using the numerical example:
\[ \text{Consumer surplus} = \$10{,}000 - \$5{,}000 = \$5{,}000, \]
or \(\$5\) million.
Graphically, consumer surplus is the area above the market-price line and below the demand curve, up to the quantity purchased.
The relevant areas can be distinguished as follows:
| Graphical area | Economic meaning |
|---|---|
| Entire area under the demand curve | Total willingness to pay or total benefit |
| Rectangle \(P_0Q_0\) | Actual consumer expenditure and firms’ total revenue |
| Area above price and below demand | Consumer surplus |
The relationship can be written as:
\[ \text{Total willingness to pay} = \text{Actual expenditure} + \text{Consumer surplus}. \]
6 Intuitive interpretation
Suppose four customers each want one PC. Their maximum willingness to pay is:
| Customer | Maximum willingness to pay |
|---|---|
| A | $1,200 |
| B | $1,000 |
| C | $800 |
| D | $600 |
The total willingness to pay is:
\[ \$1{,}200 + \$1{,}000 + \$800 + \$600 = \$3{,}600. \]
This means that, collectively, the customers value the four PCs at \(\$3{,}600\). It does not necessarily mean that firms actually receive $$3{,}600.
If the firm charges a uniform price of $$600, all four customers buy and the firm’s revenue is:
\[ \text{Revenue} = \$600 \times 4 = \$2{,}400. \]
Consumer surplus is:
\[ \text{Consumer surplus} = \$3{,}600 - \$2{,}400 = \$1{,}200. \]
The surplus of each customer is:
| Customer | Willingness to pay | Price paid | Consumer surplus |
|---|---|---|---|
| A | $1,200 | $600 | $600 |
| B | $1,000 | $600 | $400 |
| C | $800 | $600 | $200 |
| D | $600 | $600 | $0 |
| Total | $3,600 | $2,400 | $1,200 |
Customer A, for example, would have been prepared to pay up to \(\$1{,}200\) but pays only \(\$600\). The customer does not receive \(\$600\) in cash. Instead, the \(\$600\) represents the additional benefit obtained from buying the PC for less than its maximum valuation.
7 Perfect price discrimination
The interpretation in the previous example can be taken one step further. If a firm could identify every customer’s maximum willingness to pay and charge each customer exactly that amount, it could collect the total willingness to pay as revenue.
In the example, the firm would charge:
- Customer A: \(\$1{,}200\);
- Customer B: \(\$1{,}000\);
- Customer C: \(\$800\); and
- Customer D: \(\$600\).
Its revenue would then be:
\[ \$1{,}200 + \$1{,}000 + \$800 + \$600 = \$3{,}600. \]
This situation is called perfect price discrimination. Under it:
\[ \text{Revenue} = \text{Total willingness to pay}, \]
and consumer surplus is zero.
However, ordinary markets generally use a common price, or a limited set of prices. Therefore, firms usually collect only the rectangle \(P_0Q_0\), while consumers retain the area between the demand curve and the price as consumer surplus.
8 Final distinction
The demand curve supports three different interpretations:
- Marginal willingness to pay: the height of the curve shows the value of the next unit.
- Total willingness to pay: the area under the curve shows the combined value of all units purchased.
- Total expenditure or revenue: the rectangle \(P_0Q_0\) shows the amount actually paid by consumers and received by firms.
The most useful identity is:
\[ \boxed{ \text{Total willingness to pay} = \text{Total expenditure} + \text{Consumer surplus} } \]
Therefore, total willingness to pay is best understood as the total economic value consumers attach to the PCs. It would equal firms’ revenue only in the special case where firms could charge every buyer exactly that buyer’s maximum willingness to pay.