Producer Surplus Equation

Definition

There are two ways to define producer surplus, depending on whether it is being calculated for one unit of a product or for a given quantity of the product.

For One Unit of Product

Producer surplus is the difference between the price producers actually receive and the price producers are willing to receive. 

In other words, it is defined as the difference between the market equilibrium price and the price producers are willing to receive.

Let’s put it in a more simple way. Producer surplus is the difference between two prices:

1. The price producers receive, which is the market equilibrium price.
2. The price producers are willing to receive: This price is shown by any point on the supply curve or by any price shown in the supply schedule.

So, here are the formulas:

Producer Surplus = The price producers receive – The price producers are willing to receive 

Producer Surplus = Market equilibrium price – The price producers are willing to receive

The producer surplus is created by market price beyond the lowest price producers would instead be willing to accept for a product. 

For a Given Quantity of Product

Producer surplus is the difference between the amount producers receive and the amount producers are willing to receive. 

So, here is the producer surplus formula:

Producer Surplus = The amount producers receive – The amount producers are willing to receive 

So, for a given quantity of a product, the producer surplus is the difference between how much producers receive by selling that quantity of the product at the market price as compared to what they are willing to receive, as indicated by the supply curve. This surplus or difference amount is the advantage that producers have in selling the product in the market. 

Calculation Example

Let’s consider the following table:

 The first column contains the quantity that producers supply. The second column contains the price that producers actually receive. This is the market equilibrium price, P0, and is taken as $8. The third column contains the price that producers are willing to receive. This is denoted as P1. You can see that this price is increasing from $2 to $8 with the increase in quantity supplied from 1 unit to 5 units. This is according to the law of supply, where an increase in the price of a product leads to an increase in its quantity supplied. 

Graphs

For one unit of product, producer surplus is the vertical distance between a point on the supply curve and the price line, as shown in the graph below.

In the above graph, price is taken on the vertical axis (y-axis) and quantity on the horizontal axis (x-axis). As shown in the above graph, for unit 2,

The price producers actually receive = AC = $8

The price producers are willing to receive = BC = $4

Producer surplus for Unit # 2 = AC – BC = AB

                                                = $8 - $4 = $4

For a given quantity of product, producer surplus is the area above the supply curve and below the price line, as shown in the diagram below.

 In this graph, the producer surplus is the triangular area above the supply curve and below the price line at the price point P0. This area 0P₀E₀ can also be calculated by using the following formula:. 

Producer Surplus = 1/2 (base × height)

Importance of Producer Surplus

Economists use producer surplus to find the impact of various factors affecting the market on producers. Producer surplus is an important indicator of the welfare of producers when they sell products. An increase in producer surplus is good for producers, while a decrease in its value indicates a negative effect on producers. The magnitude of change in producer surplus indicates how much positive or negative effect is faced by producers due to any economic change. 

Changes in Producer Surplus

The following points explain the changes in producer surplus.

Change in Demand

A rise in the demand for a product increases producer surplus due to an increase in the market price, and vice versa. A decrease in producer surplus due to a fall in the demand for a product is illustrated by the following diagram.

Before the fall in demand, producer surplus = X + Y

After the fall in demand, new producer surplus = Y

The decrease in producer surplus = X

For example, if the income of consumers is decreased, there will be a fall in the demand for the product, leading to a decrease in its price due to the reduced purchasing power of consumers. This means that the producer surplus will decrease. 

Change in Price Elasticity of Supply

Any change in the price elasticity of supply (PES) changes the magnitude of producer surplus. Producer surplus decreases with an increase in the value of price elasticity of supply, and vice versa.

Price Discrimination

Producers can increase their surplus through an increase in the price of the product if they can. One way to do this is through the use of price discrimination, where producers charge different prices to different customers for the same product with an intention to increase producer surplus and hence their revenue. This must be kept in mind that the firm should have control over price in the form of market power (in monopoly and oligopoly), and other conditions of price discrimination must also be met.

Consumer Surplus

The excess of the amount that a consumer is willing to pay for a product over the amount they actually pay when buying it is called a consumer surplus. On the graph, consumer surplus is the area below the demand curve and above the price line.

Total Surplus

The total surplus is also known as total economic surplus, which is simply the combination of consumer and producer surplus, which is mainly created by their interactions in the free market instead in a controlled setting, such as price controls, with quotas, etc. Both consumer surplus and producer surplus are the different areas that can be represented on the demand and supply curves. 

The total surplus can be calculated as:

Total Surplus = Consumer Surplus + Producer Surplus

The total surplus indicates the net benefit to society.

In the above, the area below the demand curve and above the price line is consumer surplus. The area above the supply curve (also called the marginal cost curve) and the price line is producer surplus. The sum of the values of consumer surplus and producer surplus gives us total surplus. 

Difference between Producer Surplus and Consumer Surplus

The following table contains the main points of difference between producer surplus and consumer surplus.

Conclusion

In conclusion, the producer surplus tells us about the welfare of producers. It is the difference between what producers receive and what their willingness to receive is. On the other hand, consumer surplus is the result obtained by finding the difference between what consumers are willing to pay and what they actually pay. Adding consumer surplus and producer surplus gives the total surplus, which indicates the total welfare of society.