Consumer surplus

Graph illustrating consumer (red) and producer (blue) surpluses on a supply and demand chart

Consumer surplus or Consumer's surplus (or in the plural Consumers' surplus) is the difference between the price consumers are willing to pay (or reservation price) and the actual price. If someone is willing to pay more than the actual price, their benefit in a transaction is how much they saved when they didn't pay that price. For example, a person is willing to pay a tremendous amount for water since he needs it to survive, however since there are competing suppliers of water he is able to purchase it for less than he is willing to pay. The difference between the two prices is the consumer surplus.

Calculation from supply and demand

The aggregate consumers' surplus is the sum of the consumer's surplus for each individual consumer. This can be represented on a supply and demand figure. The consumer surplus is the area under the demand curve and above a horizontal line at the equilibrium price. If the demand curve is a straight line, the consumer surplus is the area of a triangle:

$CS=1/2Q_{mkt}\left({P_{max}-P_{mkt}}\right)$

For more general demand and supply functions, these areas are not triangles but can still be found using Integral Calculus. Consumer surplus is thus the definite integral of the demand function with respect to price, from the market price to the maximum reservation price (i.e. the price-intercept of the demand function):

$CS=\int _{P_{mkt}}^{P_{max}}D(P)\,dP,$

where $D(P_{max})=0.\,$

The graph shows, that if we see a rise in the equilibrium price and a fall in the equilibrium quantity, then consumer surplus falls.

Distribution of benefits when price falls

When supply of a good expands, the price falls (assuming the demand curve is downward sloping) and consumer surplus increases. This benefits two groups of people. Consumers who were already willing to buy at the initial price benefit from a price reduction, and additional consumers who were unwilling to buy at the initial price but will buy at the new price and also receive some consumer surplus.

File:Supply curve shift.png

Supply curve shift

Consider an example of linear supply and demand curves. For an initial supply curve S₀, consumer surplus is the triangle above the line formed by price P₀ to the demand line (bounded on the left by the price axis and on the top by the demand line). If supply expands from S₀ to S₁, the consumers' surplus expands to the triangle above P₁ and below the demand line (still bounded by the price axis). The change in consumer's surplus is difference in area between the two triangles, and that is the consumer welfare associated with expansion of supply.

Some people were willing to pay the higher price P₀. When the price is reduced, their benefit is the area in the rectangle formed on the top by P₀, on the bottom by P₁, on the left by the price axis and on the right by line extending vertically upwards from Q₀.

The second set of beneficiaries are new consumers, those who will pay the new lower price (P₁) but not the higher price (P₀). Their additional consumption makes up the difference between Q₁ and Q₀. Their consumer surplus is the triangle formed by on the left by the line extending vertically upwards from Q₀, on the right by the demand line, and on the bottom by the line extending horizontally to the right from P₁.

Rule of one-half

The rule of one-half estimates the change in consumers' surplus for small changes in supply with a constant demand curve. Following the figure above,

$\Delta CS=0.5\left({Q_{0}+Q_{1}}\right)\left({P_{0}-P_{1}}\right)$

where:

• CS = Consumers' Surplus
• Q₀ and Q₁ are the quantity demanded before and after a change in supply
• P₀ and P₁ are the prices before and after a change in supply

Comparison to profit

In terms of supply and demand, consumer's surplus is the analog to producer's surplus.

History

The idea of consumer's surplus was due to Jules Dupuit and extended by Alfred Marshall.

See also

• economic surplus
• surplus economics
• induced demand
• utility
• welfare economics
• Price discrimination
• Price support