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The term surplus is used in economics for several situations. 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 mechanism that is higher than they would be willing to sell for.
Note that producer surplus generally flows through to the owners of  the 

factors of production: in perfect competition, no producer surplus accrues to the individual firm. This is the same as saying that economic profit is driven to zero. Real-world businesses generally own or control  some of their inputs, meaning that they receive the producer's surplus due to them: this is known as normal profit, and is a component of the firm's opportunity costs. 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 some schools of 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, surplus product and surplus labor.

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. 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 alternating 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.

1.  Friedman, David D

 
Price Theory: An Intermediate Text - Chapter 9 and

 2. Further Reading Henry George, Progress and Poverty [1]

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:

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, minus the definite integral of the constant function D(P)=Q_mkt (i.e. P_mktQ_mkt), from the market price to the maximum reservation price (i.e. the price-intercept of the demand function):

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 than at the initial 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 , the 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 surplus for small changes in supply with a constant demand curve. Note that in this special case where the consumer demand curve is linear, consumer surplus is the area of a triangle. Following the figure above,

       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

Editors note: And now back to Quick Notess

 IV. Consumer's and Producer's Surplus
       A) Econ Concepts in 60 Seconds Video on Consumer's and Producer's Surplus  
       B) Allocation efficiency exists at the equilibrium quantity and at other quantities, 
            there are efficiency losses.
            1. Deadweight Loss
            2. Tax Incidence and Deadweight Loss

Unit 4 Review Amount producer receives minus what they are
 willing and able to sell product to customers.

  V. Determine Demand
      A. Video
      B. Readings
          1. Indifference Curve
          2. Budget Constraint
          3. Expansion Path