Total consumer surplus as area | Microeconomics | Khan Academy

Summary

The script explains the concept of consumer surplus using an orange stand example. It highlights how consumer surplus is the difference between what consumers are willing to pay and what they actually pay. The marginal benefit curve, or demand curve, reflects this. For each pound of oranges, if the willingness to pay is higher than the set price, the surplus is the area between the demand curve and the price. In this case, with a price of $2 and 300 pounds sold, the total consumer surplus is calculated as the area of a triangle, yielding $300.

Takeaways

• 🍊 The demand curve represents the willingness to pay for oranges, with each additional pound having a slightly lower value.
• 💲 Setting a price of $2 allows the sale of 300 oranges, which is a strategic decision to maximize consumer surplus.
• 📊 Consumer surplus is calculated as the difference between what consumers are willing to pay and what they actually pay.
• 🔍 The consumer surplus for the 100th pound is $1.30, as they paid $2 but were willing to pay $3.30.
• 📐 The total consumer surplus is the area between the demand curve and the price line at $2.
• 📈 For a linear demand curve, the total consumer surplus can be calculated as the area of a triangle.
• 📖 Calculating consumer surplus involves integrating under the demand curve, which can be approximated with smaller rectangles for non-linear curves.
• 📉 The base of the triangle representing total consumer surplus is the quantity sold (300 pounds), and the height is the difference between the maximum willingness to pay and the price ($1.00).
• 🧮 The formula for the area of a triangle is used to calculate the total consumer surplus: 1/2 * base * height.
• 💵 The total consumer surplus in this scenario is $300, which is the area between the demand curve and the price line at $2.

Q & A

What is the concept of consumer surplus explained in the script?

Consumer surplus is the difference between how much a consumer is willing to pay for a good and how much they actually pay for it. It represents the extra benefit or value that consumers receive beyond what they paid.

How is the willingness to pay represented in the script?

The willingness to pay is represented by the demand curve or marginal benefit curve, where the price a consumer is willing to pay for each additional pound of oranges decreases as more pounds are considered.

What is the significance of the 100th pound of oranges in the script?

The 100th pound of oranges is used as an example to illustrate how consumer surplus is calculated for an individual pound. The consumer paid $2 but was willing to pay $3.30, resulting in a consumer surplus of $1.30 for that pound.

Why did the price for oranges get set at $2 in the script?

The price was set at $2 as an example to demonstrate how consumer surplus is calculated when the market price is lower than the willingness to pay for some consumers.

How many oranges were sold at the price of $2 according to the script?

At the price of $2, 300 oranges were sold.

What is the formula for calculating the area of a triangle as it relates to consumer surplus in the script?

The formula used to calculate the area of a triangle, and thus the total consumer surplus, is 1/2 times the base times the height. In the context of the script, the base is the quantity of oranges sold (300 pounds), and the height is the difference between the willingness to pay and the price ($3.30 - $2 = $1.30).

How does calculus play a role in calculating consumer surplus in the script?

Calculus is mentioned as a method to improve the approximation of the consumer surplus by using thinner and thinner rectangles to approximate the area under the demand curve, especially when the demand curve is non-linear.

What is the total consumer surplus calculated in the script?

The total consumer surplus is calculated to be $300, which is the area of the triangle formed by the demand curve and the price line at $2.

Why is it important to understand consumer surplus from the perspective of each pound of oranges in the script?

Understanding consumer surplus per pound helps to visualize the additional value each consumer receives relative to what they paid, which when summed up gives the total consumer surplus.

How does the script suggest improving the estimation of consumer surplus?

The script suggests using smaller rectangles to approximate the area under the demand curve, which would provide a better estimation of consumer surplus, especially for non-linear demand curves.

What is the practical implication of understanding consumer surplus for a business like an orange stand?

Understanding consumer surplus can help a business like an orange stand to set prices that maximize consumer benefit while also ensuring profitability, as it shows the value consumers receive beyond what they pay.

Outlines

00:00

🍊 Understanding Consumer Surplus

This paragraph explains the concept of consumer surplus in the context of an orange stand. It uses a demand curve to illustrate how the value or willingness to pay for oranges decreases with each additional pound. The example focuses on the 100th pound of oranges, where the consumer is willing to pay $3.30 but only pays $2, resulting in a consumer surplus of $1.30 for that pound. The paragraph then extends this concept to calculate the total consumer surplus by considering the area between the demand curve and the price line set at $2 for all sold oranges.

05:04

📏 Calculating Total Consumer Surplus

The second paragraph delves into the calculation of total consumer surplus by treating it as the area between the demand curve and the price line at $2 per pound. It simplifies the calculation by considering the linear nature of the demand curve, which allows for the use of the triangle area formula (1/2 * base * height). The base is the quantity of oranges sold (300 pounds), and the height is the difference between the maximum willingness to pay and the actual price ($3.30 - $2). The calculation results in a total consumer surplus of $300, emphasizing the value that consumers receive beyond what they paid.

Keywords

💡Demand Curve

The demand curve represents the relationship between the price of a good and the quantity consumers are willing to purchase at different price points. In the video, it is shown as a downward-sloping line, indicating that as the price decreases, the quantity demanded increases. The orange stand owner uses this curve to understand the willingness of customers to pay for oranges at various price levels.

💡Marginal Benefit

Marginal benefit refers to the additional satisfaction or utility a consumer gains from consuming one more unit of a good. In the video, the marginal benefit is tied to how much consumers value each incremental pound of oranges, with the first few pounds having a higher marginal benefit than later ones as they purchase more.

💡Willingness to Pay

Willingness to pay is the maximum price a consumer is prepared to pay for a good or service. It is closely related to the demand curve, where consumers’ willingness to pay decreases as they buy more of the good. The video illustrates this with the example of consumers being willing to pay $3 for the first 100 pounds of oranges, but less for subsequent pounds.

💡Price

Price refers to the amount of money a consumer must spend to purchase a good or service. In the video, the orange stand sets the price of oranges at $2 per pound. This price is key in determining how many pounds of oranges the customers buy, and it also helps calculate the consumer surplus.

💡Consumer Surplus

Consumer surplus is the difference between what consumers are willing to pay for a good and what they actually pay. In the video, it is calculated by finding the area between the demand curve and the price level, showing how much benefit consumers receive beyond the cost they pay for oranges. For example, for the 100th pound of oranges, the consumer surplus is $1.30.

💡Marginal Benefit Curve

The marginal benefit curve is similar to the demand curve and shows how the additional benefit decreases as more of a good is consumed. In the video, this curve is used to represent how much benefit consumers receive from each additional pound of oranges, with the first pounds providing more benefit than later ones.

💡Total Consumer Surplus

Total consumer surplus is the sum of the consumer surplus across all units of the good sold. In the video, it is calculated as the area under the demand curve and above the price line for all 300 pounds of oranges sold. The total consumer surplus in this case is $300.

💡Area of a Triangle

The area of a triangle is used to calculate the total consumer surplus in the video. Since the demand curve is linear, the surplus can be calculated as the area of a triangle, with the base representing the quantity sold (300 pounds) and the height representing the difference between the highest willingness to pay and the price ($2).

💡Linear Demand Curve

A linear demand curve shows a constant rate of change between price and quantity demanded, depicted as a straight line. In the video, the demand for oranges is represented by a linear curve, simplifying the calculation of consumer surplus as the area of a triangle. The curve slopes downward, indicating that consumers will buy more oranges as the price decreases.

💡Non-linear Demand Curve

A non-linear demand curve shows a variable rate of change between price and quantity demanded, typically curving instead of being straight. In the video, the presenter mentions that if the demand curve were non-linear, calculating consumer surplus would require more precise tools like calculus to account for varying changes in price and quantity.

Highlights

The demand curve represents how much consumers are willing to pay for each pound of oranges, or the marginal benefit of each additional pound.

At the 100th pound, a consumer is willing to pay $3 per pound, but you set the price at $2 per pound.

Consumer surplus is defined as the benefit consumers get above and beyond what they paid.

For the 100th pound, the consumer surplus is $1.30 ($3.30 benefit - $2 paid).

To find the total consumer surplus, you need to calculate it for every pound sold.

Consumer surplus is visually represented as the area between the demand curve and the price line on a graph.

For linear demand curves, the total consumer surplus is the area of the triangle between the demand curve and the price line.

If the demand curve were non-linear, you would need to use calculus to approximate the area and find the consumer surplus.

The total consumer surplus is the sum of all individual surpluses across every pound sold.

For the 100th pound, the consumer surplus is represented by the area of a small rectangle with a height of $1.30 (difference between benefit and price).

As the price per pound is set at $2, the demand curve slopes downwards as willingness to pay decreases with each additional pound.

To estimate total consumer surplus, you sum up all these small rectangles, representing the surplus for each pound sold.

The base of the triangle representing consumer surplus is 300 pounds, and the height is the $2 price difference.

The formula for the total consumer surplus (area of the triangle) is 1/2 * base * height.

The total consumer surplus for 300 pounds sold at $2 per pound, with a demand curve starting at $3 per pound, is $300.

Transcripts

Let's say you run an orange stand.

And this right here, you could view this

as either the demand curve for your orange stand

or your marginal benefit curve, or really you

could call it the willingness to pay,

the first 100 pounds of oranges.

Or that very 100th pound, someone

would be willing to pay $3 per pound.

But then the 101st pound would be a little bit less than that.

So that's the willingness to pay,

or the marginal benefit of that incremental pound.

But let's say you decide to set the price at $2,

and you are able to sell 300 oranges in that week.

What I want to think about is, what

is the total consumer surplus that your consumers got?

And the way to think about consumer surplus

is, how much benefit did they get above and beyond what

they paid?

So for example, the person who bought--

let's just think about the exact 100th pound.

The 100th pound, they paid $2.

They paid $2, but their benefit looks like it was,

I don't know, $3.30.

But they only paid $2.

So their benefit on that one pound, their benefit,

or I should say their consumer surplus,

is going to be $3.30 minus a $2.30.

So that person who bought that 100th-- not all the 100 pounds,

just that 100th pound-- got a consumer surplus of $3.30 minus

$2, which is a $1.30 consumer surplus.

So if you wanted to figure out the entire consumer surplus,

well, you just have to do it for all of the pounds.

So that was 100th pound.

So essentially, you could view this

as the area of this little thing right over here.

And let me zoom in, just to make sure you

understand what's going on.

That thing that I just drew, if we zoom in,

will look something like this.

It was one pound wide.

And this right over here was $2.

And then we had our marginal benefit curve, or our demand

curve, sloping down like that.

And this point right over here was $3.30.

And so to figure out the consumer surplus for that pound

we said, OK, for that pound they were willing to pay $3.30.

The benefit to them was $3.30.

But they only had to pay $2.

So the height of this right over here was $1.30.

And so the consumer surplus is $1.30 per pound times one

pound.

And so that's where we got the $1.30 consumer surplus.

Now, we could do that for every one of the pounds.

So we could do that for the 101st pound.

Let me get a different color.

The 101st pound, we would do it like that.

Then the 102nd pound, we would do it like that.

103rd pound like that.

We'd do it for the 99th pound like that.

And so you could imagine if we wanted

to find the total consumer surplus, what are we doing?

Well, we're essentially just finding

the area between our demand curve

and this line where the price is equal to 2.

So we're just going to sum up this area.

And if you're familiar with calculus,

you might know that you can actually

make these things arbitrarily small.

You don't have to take a one pound wide rectangle.

You get a half a pound wide rectangle,

or a quarter pound wide rectangle.

Then you'll just have more rectangles.

It doesn't matter so much if you have a linear demand curve,

but if you had a non-linear demand curve

then it would matter.

You'd want to get smaller and smaller and smaller, or thinner

and thinner and thinner rectangles,

so you could get better and better approximations

for the consumer surplus.

But needless to say, what you're really doing-- especially

if you get unbelievably thin rectangles,

and you have an unbelievably high number of them-- you're

really just estimating the area under the demand curve

and above the price equals $2.

And so if you want to know this consumer surplus--

and I really want you to understand why this was.

I mean, just think about it for each pound.

It was just how much more value that pound,

whoever bought that pound, how much more value do they

get relative to what they paid.

And we're just summing that up across all of the pounds.

So to really figure out the total consumer surplus,

we just have to find this area of this blue area.

And that's just finding the area of a triangle.

So this right over here, you have a base of 300.

This length right over here is 300 pounds.

And then our height over here.

And we can just use this as the area of a triangle,

because this is a simple linear demand curve.

We would actually have to use a little bit of calculus

if this was a non-linear curve.

But the height here is 2.

So our area, the area between the demand curve and our price

equals 2, is equal to 1/2 times base times height.

1/2 times the base, which is 300 pounds, times the height, which

is $2 per pound.

The pounds cancel out.

1/2 times 2 is 1, times 300 is 300.

So we get 300.

And all we're left with is dollars.

So the total consumer surplus in this case is $300.

And it really is just the area between the demand curve

and this price equals 2 line right over there.