Consumer Surplus Formula

Do you ever feel good or bad about the products that you buy? Do you ever wonder why you might feel good or bad about certain purchases? Maybe that new cell phone felt good for you to buy, but the new pair of shoes just didn't feel right to purchase. Generally, a pair of shoes will be cheaper than a new phone, so why would you feel better about buying a cell phone than a new pair of shoes? Well, there is an answer to this phenomenon, and economists call this consumer surplus. Want to learn more about this? Continue reading to learn more!

Consumer Surplus Graph

What does consumer surplus look like on a graph? Figure 1 below shows a familiar graph with supply and demand curves.

Fig. 1 - Consumer Surplus.

Based on Figure 1, we can use the following consumer surplus formula:

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

As you can see, the supply-demand curve gives us everything we need to apply the consumer surplus formula to it. \(Q_d\) is the quantity at which supply and demand intersect. We can see that this point is 50. The difference of \( \Delta P\) is the point where the maximum willingness to pay, 200, is subtracted by the equilibrium price, 50, which will give us 150.

Now that we have our values, we can now apply them to the formula.

\(\hbox{Consumer Surplus}=1/2 \times 50\times 150\)

\(\hbox{Consumer Surplus}=3,750\)

Not only were we able to use the supply-demand curve to solve for consumer surplus, but we can also visually see the consumer surplus on the graph! It is the area that is shaded underneath the demand curve and above the equilibrium price. As we can see, the supply-demand curve provides great insight into solving consumer surplus problems!

Consumer Surplus Formula Economics

Let’s go over the consumer surplus formula in economics. Before we do so, we must define consumer surplus and how to measure it. Consumer surplus is the benefit that the consumer receives when purchasing goods in the market.

To measure consumer surplus, we subtract the amount that a buyer is willing to pay for a good from the amount they pay for the good.

Now that we understand how to find the consumer surplus for the individual, we can look at the consumer surplus formula for the supply and demand market:

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

Let's look at a brief example to see the consumer surplus formula in the supply and demand market.

Let's utilize the formula once more:

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

Plug in the necessary values:

\(\hbox{Consumer Surplus}=1/2 \times 200\times 100\)

\(\hbox{Consumer Surplus}=10,000\)

We have now solved for consumer surplus on the supply and demand market!

Calculating Consumer Surplus

Let’s see how we can calculate consumer surplus with the following example:

Using the formula, how will we set up this equation?

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

Plug in the numbers:

\(\hbox{Consumer Surplus}=1/2 \times 50\times (30-25)\)

\(\hbox{Consumer Surplus}=1/2 \times 50\times 5\)

\(\hbox{Consumer Surplus}=1/2 \times 250\)

\(\hbox{Consumer Surplus}=125\)

Therefore, the consumer surplus for this market is 125.

Total Consumer Surplus Formula

The total consumer surplus formula is just the same formula as the consumer surplus formula:

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

Let's do some calculations with another example.

Let's start with our formula:

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

Plug in the necessary values:

\(\hbox{Consumer Surplus} =1/2 \times 200\times (300-150) \)

\(\hbox{Consumer Surplus} =1/2 \times 200\times 150\)

\(\hbox{Consumer Surplus} =1/2 \times 200\times 150\)

\(\hbox{Consumer Surplus} =15,000\)

We have now calculated for total consumer surplus!

Consumer Surplus as a Measure of Economic Welfare

What is consumer surplus as a measure of economic welfare? Let's first define what welfare effects are before discussing their application to consumer surplus. Welfare effects are the gains and losses to consumers and producers. We know that the gains of consumer surplus are the maximum that a consumer is willing to pay subtracted by the amount that they end up paying.

Fig. 2 - Consumer Surplus and Producer Surplus.

As we can see from the example above, the consumer surplus and producer surplus are currently 12.5. However, how might a price ceiling alter the consumer surplus?

Fig. 3 - Consumer and Producer Surplus Price Ceiling.

In Figure 3, the government imposes a price ceiling of $4. With the price ceiling, the consumer and producer surplus both change in value. After calculating the consumer surplus (the area shaded in green), the value is $15. After calculating the producer surplus (the area shaded in blue), the value is $6. Therefore, a price ceiling would result in a gain for consumers and a loss for producers.

Intuitively, this makes sense! A price decrease will end up better for the consumer since the product will cost less; a price decrease will end up worse for the producer since they are generating less revenue from the price decrease. This intuition works for a price floor as well — producers will gain and consumers will lose. Notice that interventions like price floors and price ceilings create market distortions and lead to deadweight losses.

Consumer vs Producer Surplus Measures

What is the difference between consumer vs producer surplus measures? First, let's define producer surplus. Producer surplus is the benefit the producer receives when they sell a product to consumers.

Fig. 4 - Producer Surplus.

As we can see from Figure 4, the producer surplus is the area above the supply curve and below the equilibrium price. We will assume that the supply and demand curves are straight lines for the following examples.

As we can see, the first difference is that producers obtain the benefit in producer surplus, not consumers. In addition, the formula is slightly different for producer surplus. Let's take a look at the formula for producer surplus.

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

Let's break down the equation. \(Q_d\) is the quantity where supply and demand meet. \(\Delta\ P\) is the difference between the equilibrium price and the minimum price producers are willing to sell at.

At first glance, this may seem like the same equation as consumer surplus. However, the difference comes from the difference in P. Here, we start with the price of the good and subtract it from the minimum price that the producer is willing to sell at. For consumer surplus, the difference in price started with the maximum price that consumers are willing to pay and the equilibrium price of the good. Let's take a look at a brief example of a producer surplus question to further our understanding.

Fig. 5 - A Numerical Example of Producer Surplus.

Using the formula, how will we set up this equation?

Plug in numbers:

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

\(\hbox{Producer Surplus}=1/2 \times 1000\times (200-100)\)

\(\hbox{Producer Surplus}=1/2 \times 1000\times 100\)

\(\hbox{Producer Surplus}=1/2 \times 100,000\)

\(\hbox{Producer Surplus}=50,000\)

Therefore, the producer surplus is 50,000.