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Definition of Producer Surplus
For the definition of producer surplus, we must first understand that producers will only sell a good if the sale makes them better off. This captures the concept of the producer surplus, as it is how much better off producers are when they sell goods. Producers incur costs to make the products they sell. And producers are willing to sell their products for the cost of making the product at least. Therefore, for producers to make a surplus, they must sell their products for a price that is higher than their cost. This tells us that the difference between how much producers are willing to sell their products for and how much they actually sell it for is their producer surplus. Based on this, there are two ways we can define the producer surplus.
The producer surplus is the benefit a producer gains from selling a product in the market.
The producer surplus is the difference between how much a producer is willing to sell a product for and how much the producer actually sells the product for.
The producer surplus is a simple concept - a producer wants to benefit.
The producer surplus depends on cost or willingness to sell. In the context of the producer surplus, the willingness to sell is the cost of making the product. Why? Because the cost of making the product is the value of everything the producer has to give up to make the product, and the producer is willing to sell the product for as low as the cost.
Cost is the value of everything the producer has to give up to produce a given product.
Costs mentioned here include opportunity costs.Read our article on Opportunity Cost to learn more!
Producer Surplus Graph
At the mention of producer, we know we're talking about supply. Therefore, the producer surplus graph is illustrated by drawing the supply curve. We will do this by plotting the price on the vertical axis and the quantity supplied on the horizontal axis. We show a simple producer surplus graph in Figure 1 below.
Fig. 1 - Producer surplus graph
The producer surplus is the shaded area labeled as such. The supply curve shows the price of a good at each quantity, and the producer surplus is the area below the price but above the supply curve. In Figure 1, the producer surplus is triangle BAC. This is in line with the definition of producer surplus, as it is the difference between the actual price and what the producer is willing to sell the product for.
The producer surplus graph is the graphical illustration of the difference between the actual price of a product and how much producers are willing to sell the product for.
- The producer surplus is the area below the price but above the supply curve.
What if the market price of the product increased? Let's show what happens in Figure 2.
Fig. 2 - Producer surplus graph with a price increase
In Figure 2, the price increases from P1 to P2. Before the increase, the producer surplus was triangle BAC. However, when the price went up to P2, the producer surplus of all producers who sold at the initial price became a larger triangle - DAF. Triangle DAF is triangle BAC plus the area of DBCF, which is the added surplus after the price increase. For all new producers who entered the market and only sold after the price increased, their producer surplus is triangle ECF.
Read our article on the Supply Curve to learn more!
Producer Surplus Formula
Since the producer surplus typically has a triangular shape on the producer surplus graph, the producer surplus formula is derived by finding the area of that triangle. Mathematically, it is written as follows:
\(Producer\ surplus=\frac{1}{2}\times\ Q\times\ \Delta\ P\)
Where Q represents the quantity and ΔP represents the change in price, found by subtracting the cost, or how much producers are willing to sell for, from the actual price.
Let's solve a question that will help us apply the producer surplus formula.
In a market, firms produce a bucket for $20, which sells at an equilibrium price of $30 at an equilibrium quantity of 5. What is the producer surplus in that market?
Solution: The producer surplus formula is: \(Producer\ surplus=\frac{1}{2}\times\ Q\times\ \Delta\ P\)
Using this formula, we have:
\(Producer\ surplus=\frac{1}{2}\times\ 5\times\ ($30-$20)\)
\(Producer\ surplus=\frac{1}{2}\times\ $50\)
\(Producer\ surplus=$25\)
Let's solve another example.
A market has 4 producers of shoes. The first producer is willing to sell a shoe for $90 or higher. The second producer is willing to sell a shoe for anywhere between $80 and $90. The third producer is willing to sell a shoe for anywhere between $60 and $80, and the last producer is willing to sell a shoe for anywhere between $50 and $60. What is the producer surplus if a shoe actually sells for $80?
We will solve the above question by showing the supply schedule in Table 1, which will help us illustrate the producer surplus graph in Figure 3.
| Producerswilling to supply | Price | Quantitysupplied |
| 1, 2, 3, 4 | $90 or above | 4 |
| 2, 3, 4 | $80 to $90 | 3 |
| 3, 4 | $60 to $80 | 2 |
| 4 | $50 to $60 | 1 |
| None | $50 or below | 0 |
Table 1. Market Supply Schedule Example
Using Table 1, we can draw the producer surplus graph in Figure 3.
Fig. 3 - Market producer surplus graph
Note that even though Figure 3 shows steps, an actual market has so many producers that the supply curve has a smooth slope since small changes in the number of producers cannot be seen that clearly.
Since the fourth producer is willing to sell for $50, but the shoe sells for $80, they have a producer surplus of $30. The third producer was willing to sell for $60 but sold for $80 and got a producer surplus of $20. The second producer is willing to sell for $80, but the shoe sells for $80; hence no producer surplus here. The first producer does not sell at all since the price is below their cost.
As a result, we have a market producer surplus as follows:
\(\hbox{Market producer surplus}=\$30+\$20=\$50\)
Producer Surplus with a Price Floor
Sometimes, the government places a price floor on a good in the market, and this changes the producer surplus. Before we show you the producer surplus with a price floor, let's quickly define a price floor. A price floor or price minimum is a lower boundary placed on the price of a good by the government.
A price floor is a lower boundary placed on the price of a good by the government.
So, what happens to the producer surplus when there is a price floor? Let's have a look at Figure 4.
Fig. 4 - Producer surplus with a price floor
As Figure 4 shows, the producer surplus increases by the rectangular area marked as A since they can sell at a higher price now. But, producers may see the opportunity to sell more products at a higher price and produce at Q2.
However, the higher price means consumers reduce their quantity demanded and want to buy at Q3. In this case, The area marked as D represents the cost of products made by producers that have gone to waste since nobody bought them. The lack of sales causes the producers to lose their producer surplus in the area marked as C. If the producers correctly produce at Q3, which matches the demand of the consumers, then the producer surplus will be the area marked as A.
In summary, a price floor can cause the producers to be better off or worse off, or they may feel no change at all.
Read our article on Price floor and its effect on equilibrium or Price Controls to learn more on this topic!
Producer Surplus Examples
Shall we solve some examples of producer surplus?
Here's the first example.
In a market, each of the three producers makes a shirt at a cost of $15.
However, three shirts are sold in the market for $30 a shirt.
What is the total producer surplus in the market?
Solution:
The producer surplus formula is: \(Producer\ surplus=\frac{1}{2}\times\ Q\times\ \Delta\ P\)
Using this formula, we have:
\(Producer\ surplus=\frac{1}{2}\times\ 3\times\ ($30-$15)\)
\(Producer\ surplus=\frac{1}{2}\times\ $45\)
\(Producer\ surplus=$22.5\)
Note that there are two other producers, so the quantity becomes 3.
Shall we look at another example?
In a market, each firm produces a cup at a cost of $25.
However, a cup actually sells for $30, and a total of two cups are sold in the market.
What is the total producer surplus in the market?
Solution:
The producer surplus formula is: \(Producer\ surplus=\frac{1}{2}\times\ Q\times\ \Delta\ P\)
Using this formula, we have:
\(Producer\ surplus=\frac{1}{2}\times\ 2\times\ ($30-$25)\)
\(Producer\ surplus=\frac{1}{2}\times\ $10\)
\(Producer\ surplus=$5\)
There is another producer, making the quantity 2.
Read our article on Market Efficiency to learn more about the background of producer surplus!
Producer Surplus - Key takeaways
- The producer surplus is the difference between how much a producer is willing to sell a product for and how much the producer actually sells for.
- Cost is the value of everything the producer has to give up to produce a given product.
- The producer surplus graph is the graphical illustration of the difference between the actual price of a product and how much producers are willing to sell the product for.
- The producer surplus formula is: \(Producer\ surplus=\frac{1}{2}\times\ Q\times\ \Delta\ P\)
- A price floor is a lower boundary placed on the price of a good by the government, and it can cause producers to be better off, worse off, or they may feel no change at all.
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Frequently Asked Questions about Producer Surplus
What is the formula for calculating producer surplus?
The formula for calculating producer surplus is:
Producer surplus=1/2*Q*ΔP
How do you calculate a change in producer surplus?
The change in producer surplus is the new producer surplus minus the initial producer surplus.
How does tax affect consumer and producer surplus?
Tax affects the consumer and producer surplus by causing reductions in both.
What happens to consumer and producer surplus when supply increases?
Both the consumer surplus and the producer surplus increase when supply increases.
What is an example of producer surplus?
Jack makes shoes for sale. It costs Jack $25 to make a shoe, which he then sells for $35. Using the formula:
Producer surplus=1/2*Q*ΔP
Producer surplus=1/2*1*10=$5 per shoe.
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