Economic surplus

This article is about consumers' and producers' surplus. For information about other surpluses, see Surplus.

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

In mainstream economics, economic surplus, also known as total welfare or Marshallian surplus (after Alfred Marshall), refers to two related quantities. Consumer surplus or consumers' surplus is the monetary gain obtained by consumers because they are able to purchase a product for a price that is less than the highest price that they would be willing to pay. Producer surplus or producers' surplus is the amount that producers benefit by selling at a market price that is higher than the least that they would be willing to sell for; this is roughly equal to profit (since producers are not normally willing to sell at a loss, and are normally indifferent to selling at a breakeven price).

Overview

In the mid-19th century, engineer Jules Dupuit first propounded the concept of economic surplus, but it was the economist Alfred Marshall who gave the concept its fame in the field of economics.

On a standard supply and demand diagram, consumer surplus is the area (triangular if the supply and demand curves are linear) above the equilibrium price of the good and below the demand curve. This reflects the fact that consumers would have been willing to buy a single unit of the good at a price higher than the equilibrium price, a second unit at a price below that but still above the equilibrium price, etc., yet they in fact pay just the equilibrium price for each unit they buy.

Likewise, in the supply-demand diagram, producer surplus is the area below the equilibrium price but above the supply curve. This reflects the fact that producers would have been willing to supply the first unit at a price lower than the equilibrium price, the second unit at a price above that but still below the equilibrium price, etc., yet they in fact receive the equilibrium price for all the units they sell.

Consumer surplus

Consumer surplus is the difference between the maximum price a consumer is willing to pay and the actual price they do pay. If a consumer is willing to pay more for a unit of a good than the current asking price, they are getting more benefit from the purchased product than they would if the price was their maximum willingness to pay. They are receiving the same benefit, the obtainment of the good, with a smaller cost as they are spending less than they would if they were charged their maximum willingness to pay. An example of a good with generally high consumer surplus is drinking water. People would pay very high prices for drinking water, as they need it to survive. The difference in the price that they would pay, if they had to, and the amount that they pay now is their consumer surplus. The utility of the first few litres of drinking water is very high (as it prevents death), so the first few litres would likely have more consumer surplus than subsequent litres.

The maximum amount a consumer would be willing to pay for a given quantity of a good is the sum of the maximum price they would pay for the first unit, the (lower) maximum price they would be willing to pay for the second unit, etc. Typically these prices are decreasing; they are given by the individual demand curve, which must be generated by a rational consumer who maximizes utility subject to a budget constraint. Because the demand curve is downward sloping, there is diminishing marginal utility. Diminishing marginal utility means a person receives less additional utility from an additional unit. However, the price of a product is constant for every unit at the equilibrium price. The extra money someone would be willing to pay for the number units of a product less than the equilibrium quantity and at a higher price than the equilibrium price for each of these quantities is the benefit they receive from purchasing these quantities. For a given price the consumer buys the amount for which the consumer surplus is highest. The consumer's surplus is highest at the largest number of units for which, even for the last unit, the maximum willingness to pay is not below the market price.

Consumer surplus can be used as a measurement of social welfare, first shown by Willig (1976). For a single price change, consumer surplus can provide an approximation of changes in welfare. With multiple price and/or income changes, however, consumer surplus cannot be used to approximate economic welfare because it is not single-valued anymore. More modern methods are developed later to estimate the welfare effect of price changes using consumer surplus.

The aggregate consumers' surplus is the sum of the consumer's surplus for all individual consumers. This can be represented graphically as shown in the above graph of the market demand and supply curves. It can also be said to be the maxim of satisfaction a consumer derives from particular goods and services.

Calculation

As a rule-of-thumb, consumer surplus is typically around 100% at the top of the price. Economist Brad DeLong estimates that in "Andreesenian" (digital) commodities it is at least around 500 – 1000%,because just an ancillary product is sold (and included in GDP). Tim Worstall estimates that when the (real) GDP in rich countries has formally become 8-fold in the 20th century, we are actually maybe 100 times better off.

Calculation from supply and demand

The consumer surplus (individual or aggregated) is the area under the (individual or aggregated) demand curve and above a horizontal line at the actual price (in the aggregated case: the equilibrium price). If the demand curve is a straight line, the consumer surplus is the area of a triangle:

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

where P_mkt is the equilibrium price (where supply equals demand), Q_mkt is the total quantity purchased at the equilibrium price and P_max is the price at which the quantity purchased would fall to 0 (that is, where the demand curve intercepts the price axis). 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):

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

where $D(P_{\mathit {max}})=0.$ This shows that if we see a rise in the equilibrium price and a fall in the equilibrium quantity, then consumer surplus falls.

Calculation of a change in consumer surplus

The change in consumer surplus is used to measure the changes in prices and income. The demand function used to represent an individual's demand for a certain product is essential in determining the effects of a price change. An individual's demand function is a function of the individual's income, the demographic characteristics of the individual, and the vector of commodity prices. When the price of a product changes, the change in consumer surplus is measured as the negative value of the integral from the original actual price (P₀) and the new actual price (P₁) of the demand for product by the individual. If the change in consumer surplus is positive, the price change is said to have increased the individuals welfare. If the price change in consumer surplus is negative, the price change is said to have decreased the individual's welfare.

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 they may buy more and receive even more consumer surplus; and additional consumers who were unwilling to buy at the initial price will buy at the new price and also receive some consumer surplus.

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 consumers who buy more, and 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 bounded on the left by the line extending vertically upwards from Q₀, on the right and top 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 consumer surplus for small changes in supply with a constant demand curve. Note that in the special case where the consumer demand curve is linear, consumer surplus is the area of the triangle bounded by the vertical line Q=0, the horizontal line $P=P_{mkt}$ and the linear demand curve. Hence, the change in consumer surplus is the area of the trapezoid with i) height equal to the change in price and ii) mid-segment length equal to the average of the ex-post and ex-ante equilibrium quantities. Following the figure above,

$\Delta CS={\frac {1}{2}}\left({Q_{1}+Q_{0}}\right)\left({P_{0}-P_{1}}\right),$

where:

• CS = consumers' surplus;
• Q₀ and Q₁ are, respectively, the quantity demanded before and after a change in supply;
• P₀ and P₁ are, respectively, the prices before and after a change in supply.

See also

• Deadweight loss
• Gross operating surplus
• Induced demand
• Price discrimination
• Price support
• Shortage
• Surplus product
• Surplus value
• Utility
• Value added
• Welfare economics
• Economic rent

Further reading

• Henry George, Progress and Poverty
• Modern Microeconomics, A.Koutsyiannis.
• Microeconomic Theory, A Mathematical Approach, James M.Henderson and Richard E.Quandt.