Economic surplus

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:

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

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):

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

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

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.[6]

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.

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 ${\displaystyle P=P_{\mathrm {mkt} }}$ 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,

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

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.

Producer surplus is usually expressed by the area below the market price line and above the supply curve. In Figure 1, the shaded areas below the price line and above the supply curve between production zero and maximum output Q₁ indicate producer surplus. Among them, OP₁EQ₁ below the price line. This indicates that the total revenue is the minimum total payment actually accepted by the manufacturer. The area OP_MEQ₁ below the S curve is the minimum total revenue that the manufacturer is willing to accept. In Figure 1, the area enclosed by the market price line, the manufacturer's supply line, and the coordinate axis is the producer surplus. Because the rectangle OP₁EQ₁ is the total revenue actually obtained by the manufacturer, that is, A + B, and the trapezoid OP_MEQ. The minimum total profit that the manufacturer is willing to accept, that is, B, so A is the producer surplus.

Producer surplus

Obviously, the manufacturer produces and sells a certain quantity of Q₁ goods at the market price P₁. The manufacturer has reduced the quantity of goods for Q₁, which means that the manufacturer has increased the production factors or production costs equivalent to the amount of AVC·Q₁. However, at the same time, the manufacturer actually obtains a total income equivalent to the total market price P₁·Q₁. Since AVC is always smaller than P₁, from the production and sales of goods in Q₁, manufacturers not only get sales revenue equivalent to variable costs, but also get additional revenue. This part of the excess income reflects the increase in the benefits obtained by the manufacturers through market exchange. Therefore, in economics, producer surplus is usually used to measure producer welfare and is an important part of social welfare.

Producer surplus is usually used to measure the economic welfare obtained by the manufacturer in the market supply. When the supply price is constant, the producer welfare depends on the market price. If the manufacturer can sell the product at the highest price, the welfare is the greatest. As part of social welfare, the size of the producer surplus depends on many factors. Generally speaking, when other factors remain constant, an increase in market price will increase producer surplus, and a decrease in supply price or marginal cost will also increase producer surplus. If there is a surplus of goods, that is, people can only sell part of the goods at market prices, and producer surplus will decrease.

Obviously, the sum of the producer surplus of all manufacturers in the market constitutes the producer surplus of the entire market. Graphically, it should be expressed as the area enclosed by the market supply curve, the market price line and the coordinate axis.