Producer Surplus Formula

Producer Surplus Formula Graph

Let's go over the producer surplus formula with a graph. To begin, we must understand that producer surplus is the benefit that the producers gain when they sell a product in the market.

While this definition makes sense, it can be difficult to visualize it on a graph. Considering that most producer surplus questions will require some visual indicator, let's take a look and see how producer surplus may appear on the supply and demand graph.

Fig. 1 - Producer Surplus.

The graph above shows a simplistic example of how producer surplus may be presented on a diagram. As we can see, producer surplus is the area below the equilibrium point and above the supply curve. Therefore, to calculate the producer surplus, we must calculate the area of this region highlighted in blue.

The formula to calculate the producer surplus is the following:

\(Producer \ Surplus= 1/2 \times Q_d \times \Delta P\)

Let's break this formula down. \(\ Q_d\) is the point where quantity supplied and demand intersect on the supply and demand curve. \(\Delta P\) is the difference between the market price and the minimum price that a producer is willing to sell their good for.

Now that we understand the producer surplus formula, let's apply it to the graph above.

\({Producer \ Surplus}= 1/2 \times Q_d \times \Delta P\)

Plug in the values:

\({Producer \ Surplus}= 1/2 \times 5 \times 5\)

Multiply:

\({Producer \ Surplus}= 12.5\)

Therefore, the producer surplus for the graph above is 12.5!

Producer Surplus Formula Calculation

What is a producer surplus formula calculation? Let's start out by viewing the producer surplus formula:

\({Producer \ Surplus}= 1/2 \times Q_d \times \Delta P\)

Let's now look at a question where we might utilize the producer surplus formula:

The first step is to recognize that the question above calls for us to utilize the producer surplus formula. We know that the quantity demanded is an integral part of the formula, and we know that we will need to use a change in price for our formula as well. With this information, we can begin plugging in what we know:

\({Producer \ Surplus}= 1/2 \times 200 \times \Delta P\)

What is \(\Delta P\)? Recall that the price change we are looking for is the marketplace minus the minimum price that producers are willing to sell their goods at. If you prefer visual indicators to remember what values to subtract, recall that producer surplus is the area below the equilibrium price point and above the supply curve.

Let's plug in what we know once more:

\({Producer \ Surplus}= 1/2 \times 200 \times (300-250)\)

Next, follow the order of operations by subtracting:

\({Producer \ Surplus}= 1/2 \times 200 \times 50\)

Next, multiply:

\({Producer \ Surplus}= 5000\)

We have successfully calculated for producer surplus! To briefly review, we must recognize when it's appropriate to utilize the producer surplus formula, plug in the proper values, follow the order of operations, and calculate accordingly.

Producer Surplus Example

Let's go over a producer surplus example. We will take a look at an example of producer surplus at the individual and at the macro level.

First, let's take a look at producer surplus at the individual level:

Knowing that producer surplus is the benefit that producers gain when they sell a good, we can simply subtract the market price for laptops (300) by the minimum price Sarah will sell her laptops (200). This will get us the following answer:

\({Producer \ Surplus}= 100\)

As you can see, solving for producer surplus at the individual level is quite simple! Now, let's solve for producer surplus at the macro-level

Fig. 2 - Producer Surplus Example.

Viewing the graph above, we can use the producer surplus formula to start plugging in the correct values.

\({Producer \ Surplus}= 1/2 \times Q_d \times \Delta P\)

Let's now plug in the appropriate values:

\({Producer \ Surplus}= 1/2 \times 30 \times 50\)

Multiply:

\({Producer \ Surplus}= 750\)

Therefore, the producer surplus is 750 based on the graph above!

Change in Producer Surplus Formula

What causes a change in the producer surplus formula? Let's view the producer formula to further our understanding:

\({Producer \ Surplus}= 1/2 \times Q_d \times \Delta P\)

In addition, let's look at producer surplus on the supply and demand graph:

Fig. 3 - Producer and Consumer Surplus.

Currently, producer surplus and consumer surplus are both 12.5. Now, what would happen if the United States implemented a price floor for the agricultural industry to assist them with their sales? Let's see it implemented in the following graph:

Fig. 4 - Producer Surplus Price Increase.

What do you notice about the producer and consumer surplus after the price increase? Producer surplus has a new area of 18; consumer surplus has a new area of 3. Since the producer surplus is a new area, we will need to calculate it a bit differently:

First, calculate the blue shaded rectangle above the "PS."

\(3 \times 4 = 12\)

Now, let's find the area for the shaded triangle labeled "PS."

\(1/2 \times 3 \times 4 = 6\)

Now, let's add the two together to find the producer surplus:

\({Producer \ Surplus}= 12 + 6\)

\({Producer \ Surplus}= 18 \)

Therefore, we can say that a price increase will result in producer surplus increasing and consumer surplus decreasing. Intuitively, this makes sense. Producers would benefit from a price increase since the higher the price, the more revenue they can generate with every sale. In contrast, consumers would be harmed by a price increase since they have to pay more for a good or service. It's important to note that a price decrease has the opposite effect. A price decrease will harm producers and benefit consumers.