# Consumer Surplus Formula

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## 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:

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

Note that we are using a supply-demand graph with straight lines for simplicity. We cannot use this simple formula for graphs with non-straight supply and demand curves.

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!

- Supply and Demand

- Aggregate Supply and Demand

- Supply

- Demand

## 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.

Consumer surplus is the benefit that consumers gain from purchasing products 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.

For example, let’s say Sarah wants to buy a cellphone for a maximum price of $200. The price for the phone she wants is$180. Therefore, her consumer surplus is $20. 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. $$Q_d$$ = 200 and $$\Delta P$$ = 100. Find the consumer surplus. 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: Let’s say that we are looking at the supply and demand market to purchase a new pair of shoes. The supply and demand for a pair of shoes intersect at Q = 50 and P =$25. The maximum that consumers are willing to pay for a pair of shoes is $30. 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. We are looking at the supply and demand market for cell phones. The quantity where supply and demand meet is 200. The maximum price a consumer is willing to pay is 300, and the equilibrium price is 150. Calculate the total consumer surplus. 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! The total consumer surplus formula is the aggregate benefit that consumers receive when purchasing goods in the market. ## 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.

Welfare effects are the gains and losses to consumers and producers.

## 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.

Let’s say that some people are looking to sell laptops for their businesses. The supply and demand for laptops intersect at Q = 1000 and P = $200. The lowest price for which the sellers are willing to sell laptops is$100.

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.

Producer Surplus is the benefit that producers gain from selling their products to consumers.

## Consumer Surplus Formula - Key takeaways

• Consumer surplus is the benefit that consumers gain from purchasing products in the market.
• To find consumer surplus, you find the consumer's willingness to pay and subtract the actual price of the product.
• The formula for the total consumer surplus is the following: $$\hbox{Consumer Surplus}=1/2 \times Q_d \times \Delta P$$.
• Producer surplus is the benefit the producer receives when they sell a product to consumers.
• Welfare benefits are the gains and losses to consumers and producers in the market.

#### Flashcards in Consumer Surplus Formula 13

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What is consumer surplus and its formula?

Consumer surplus is the benefit that consumers gain from purchasing products in the market. The formula is: Consumer surplus = (½) x Qd x ΔP

What does consumer surplus measure and how is it calculated?

Consumer surplus measure is calculated by the following formula: Consumer surplus = (½) x Qd x ΔP

How does consumer surplus measure welfare changes?

Consumer surplus welfare changes based on the willingness to pay and the price of a good in the market.

How to accurately measure consumer surplus?

Accurately measuring consumer surplus requires knowing the maximum willingness to pay for a good and the market price for the good.

How do you calculate consumer surplus from a price ceiling?

A price ceiling alters the formula of the consumer surplus. To do so, you must find disregard the deadweight loss that occurs from the price ceiling and calculate the area underneath the demand curve and above the price ceiling.

## Test your knowledge with multiple choice flashcards

Mike's willingness to pay for shoes is $50, and the market price is$30. What is his consumer surplus?

Sarah's willingness to pay for a computer is $200, and the market price is$170. What is her consumer surplus?

If Lindsey's willingness to pay for a watch is $50, and the market price is$50, then she has no consumer surplus.

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