Definitions

# Economic surplus

The term surplus is used in economics for several related quantities. The consumer surplus (sometimes named consumer's surplus or consumers' surplus) is the amount that consumers benefit by being able to purchase a product for a price that is less than they would be willing to pay. The producer surplus is the amount that producers benefit by selling at a market price that is higher than they would be willing to sell for. Note that producer surplus flows through to the owners of the factors of production, unlike economic profit which is zero under perfect competition. If the markets for factors are perfectly competitive as well, producer surplus ultimately ends up as economic rent to the owners of scarce inputs such as land.

## Overview

On a standard supply and demand (S&D) diagram, consumer surplus (CS) is the triangular area above the price level and below the demand curve, since intramarginal consumers are paying less for the item than the maximum that they would pay. In contrary, producer surplus (PS) is the triangular area below the price level and above the supply curve, since that is the minimum quantity a producer can produce.

If the government intervenes by implementing, for example, a tax or a subsidy, then the graph of supply and demand becomes more complicated and will also include an area that represents government surplus.

Combined, the consumer surplus, the producer surplus, and the government surplus (if present) make up the social surplus or the total surplus. Total surplus is the primary measure used in welfare economics to evaluate the efficiency of a proposed policy.

A basic technique of bargaining for both parties is to pretend that their surplus is less than it really is: sellers may argue that the price they ask hardly leaves them any profit, while customers may play down how eager they are to have the article.

In national accounts, operating surplus is roughly equal to distributed and undistributed pre-tax profit income, net of depreciation.

In heterodox economics, the economic surplus denotes the total income which the ruling class derives from its ownership of scarce factors of production, which is either reinvested or spent on consumption.

In Marxian economics, the term surplus may also refer to surplus value and surplus labour.

## Consumer surplus

The individual consumer surplus is the difference between the maximum total price a consumer would be willing to pay (or reservation price) for the amount he buys and the actual total price. For example, suppose you are in Wal-Mart and you see a DVD of Spider-Man 3 on the rack. No price is indicated on the package, so you bring it over to the register to check the price. As you walk to the register, you think to yourself that \$20 is the highest price you would be willing to pay. At the register, you find out that the price is actually \$12, so you buy the DVD. Your consumer surplus in this example is \$8: the difference between the \$20 you were willing to pay and the \$12 you actually paid. 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.

The maximum price a consumer would be willing to pay for a given amount is the sum of the maximum price he would be willing to pay for the first unit, the maximum additional price he would be willing to pay for the second unit, etc. Typically these prices are decreasing; in that case they are given by the individual demand curve. If these prices are first increasing and then decreasing there may be a non-zero amount with zero consumer surplus. The consumer would not buy an amount larger than zero and smaller than this amount because the consumer surplus would be negative. The maximum additional price a consumer would be willing to pay for each additional unit may also alternatingly be high and low, e.g. if he wants an even number of units, such as in the case of tickets he uses in pairs on dates. The lower values do not show up in the demand curve because they correspond to amounts the consumer does not buy, regardless of the price. For a given price the consumer buys the amount for which the consumer surplus is highest.

One bargaining tactic is to pretend a lower consumer surplus.

The aggregate consumers' surplus is the sum of the consumer's surplus for each individual consumer. This can be represented on the figure of the aggregate demand curve.

### 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:

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

Where Pmkt is the equilibrium price (where supply equals demand), Qmkt is the total quantity purchased at the equilibrium price and Pmax 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, minus the definite integral of the constant function D(P)=Qmkt (i.e. PmktQmkt), from the market price to the maximum reservation price (i.e. the price-intercept of the demand function):

$CS = int_\left\{P_\left\{mkt\right\}\right\}^\left\{P_\left\{max\right\}\right\} D\left(P\right), dP;-;P_\left\{mkt\right\}Q_\left\{mkt\right\},$ where $D\left(P_\left\{max\right\}\right) = 0.,$

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; also they may buy more and receive even more consumer surplus, 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.

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 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 surplus for small changes in supply with a constant demand curve. Following the figure above,

$Delta CS = frac\left\{1\right\}\left\{2\right\} left\left(\left\{Q_1 + Q_0 \right\} right\right)left\left(\left\{P_0 - P_1 \right\} right\right)$

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