Price elasticity of demand using the midpoint method | Elasticity | Microeconomics | Khan Academy

Summary

This educational video delves into the concept of elasticity of demand, illustrating how changes in price affect the quantity demanded. The script explains the economic measure using percentages to ensure unit consistency and compares it to the stretchiness of a rubber band to clarify the concept. It demonstrates calculations of elasticity at various points on a demand curve, emphasizing the method to achieve consistent results regardless of price change direction, and encourages viewers to apply these concepts to understand market dynamics.

Takeaways

• 📚 Elasticity of demand measures how the quantity demanded changes in response to a change in price.
• 🔍 Demand refers to the entire curve, while quantity demanded is a specific point on that curve.
• 📈 Economists calculate elasticity by dividing the percent change in quantity demanded by the percent change in price, ensuring a unitless measure.
• 🌐 The use of percentages in elasticity calculations eliminates the dependency on specific time frames or units of measurement.
• 💡 The term 'elasticity' is likened to an elastic band, where the stretchiness of demand is analogous to the band's ability to stretch.
• 📊 Elasticity is categorized as 'very elastic' if a given price change results in a large percentage change in demand, and 'very inelastic' if the change is small.
• 📐 The script demonstrates how to calculate elasticity at different points along a demand curve, emphasizing the importance of using averages to find consistent results.
• 📝 The calculation method involves dividing the change in quantity by the average of initial and final quantities, and similarly for price, to find the elasticity.
• 🔢 The elasticity values can vary along the demand curve, even if the price and quantity changes are the same, due to different starting and ending points.
• 🤔 The script invites viewers to verify the calculations themselves to understand the concept of elasticity better.
• 🚀 The video concludes with an invitation to explore the implications of the calculated elasticity values in a subsequent video.

Q & A

What is the primary focus of the video script?

The video script focuses on explaining the concept of elasticity of demand, how it is measured, and its significance in economics.

How is elasticity of demand defined in the script?

Elasticity of demand is defined as a measure of how the quantity demanded changes given a change in price, or how a change in price impacts the quantity demanded.

What is the difference between 'demand' and 'quantity demanded' as mentioned in the script?

In the script, 'demand' refers to the entire demand curve, while 'quantity demanded' refers to a specific quantity on that curve.

Why do economists use percentages to measure elasticity of demand?

Economists use percentages to measure elasticity of demand because it provides a unitless number, making the measure independent of the specific units or time frame used.

What analogy is used in the script to explain the concept of elasticity?

The script uses the analogy of an elastic band or rubber band to explain elasticity, where the ability to stretch represents the responsiveness of quantity demanded to a change in price.

What is the formula for calculating elasticity of demand as described in the script?

The formula for calculating elasticity of demand is the percent change in quantity demanded over the percent change in price.

Why is the average of starting and ending points used in the calculation of elasticity of demand in the script?

The average of starting and ending points is used to ensure consistency in the elasticity measure, regardless of whether the price change is positive or negative.

What does the script suggest about the elasticity of demand at different points along a demand curve?

The script suggests that elasticity of demand can vary at different points along a demand curve, depending on the starting and ending points of price and quantity.

How does the script differentiate between 'very elastic' and 'very inelastic' demand?

The script differentiates by stating that 'very elastic' demand has a large percentage change in quantity for a given percentage change in price, while 'very inelastic' demand has a small percentage change in quantity for the same price change.

What is the significance of calculating elasticity of demand at multiple points along a demand curve as mentioned in the script?

Calculating elasticity at multiple points helps to understand how responsive quantity demanded is to price changes across different ranges of the demand curve, providing a more nuanced view of consumer behavior.

Outlines

00:00

📊 Introduction to Elasticity of Demand

This paragraph introduces the concept of elasticity of demand, which is a measure of how the quantity demanded of a good changes in response to a change in its price. The speaker clarifies the difference between 'demand' as a whole and 'quantity demanded' as a specific point on the demand curve. The measurement of elasticity is explained as a percentage change in quantity demanded over the percentage change in price, emphasizing the use of percentages to achieve a unitless measure that is consistent regardless of the time frame or units used. The analogy of an elastic band is used to illustrate the concept, with elasticity being high when a small change in price results in a large change in quantity demanded, and low when the change is minimal.

05:03

🔢 Calculating Elasticity of Demand with Examples

The speaker proceeds to explain how to calculate the elasticity of demand using a step-by-step mathematical approach. An example is given where the price drops from point A to point B, resulting in a change in quantity demanded. The calculation involves using the average of the starting and ending points for both price and quantity to find the percentage change, which is then used to determine the elasticity. The method ensures that the elasticity measure is consistent whether the price increases or decreases. The paragraph concludes with the calculation of elasticity for the transition from point A to B, resulting in an elasticity value of approximately -5.67, indicating a highly elastic demand.

10:04

📉 Comparing Elasticity at Different Points on the Demand Curve

This paragraph delves into calculating the elasticity of demand at different points along the demand curve, specifically from points C to D and further along the curve. Despite the same numerical changes in price and quantity, the speaker notes that the elasticity will differ due to the varying starting and ending points. The calculations for these sections yield different elasticity values, demonstrating how elasticity can vary along the demand curve. The speaker calculates the elasticity for the transition from C to D, resulting in a unitary elasticity (-1 or 1 in absolute terms), indicating a proportional change in quantity demanded relative to price. The final calculation for another section of the curve results in an elasticity of 0.18, indicating a relatively inelastic demand in that area.

Keywords

💡Elasticity of Demand

Elasticity of demand is a measure in economics that describes the responsiveness of the quantity demanded of a good to a change in its price. It is a crucial concept because it helps to understand how consumers will react to price changes. In the video, the concept is central to the discussion, with the script explaining that elasticity is calculated as the percentage change in quantity demanded over the percentage change in price. The video uses the analogy of a rubber band to illustrate the concept, where a 'very elastic' demand would mean a large change in quantity for a given price change, similar to how a rubber band stretches a lot with a small pull.

💡Quantity Demanded

Quantity demanded refers to the specific amount of a product that consumers are willing and able to purchase at a given price. It is distinct from 'demand,' which refers to the entire relationship between price and quantity. In the script, the distinction is emphasized to clarify that elasticity calculations are based on changes in specific quantities, not the demand curve as a whole. The video script uses the term to explain how a change in price impacts the specific quantity that consumers are willing to buy.

💡Percent Change

Percent change is a way to express the change in a variable as a percentage of its initial value. It is used to compare changes across different scales or units. In the video, percent change is used to calculate elasticity of demand, ensuring that the calculation is unitless and can be compared across different time frames or quantities. The script explains that economists prefer to use percent change over simple change because it provides a standardized measure that is not dependent on the units of measurement.

💡Inelastic

Inelastic demand describes a situation where the quantity demanded of a good does not change significantly in response to a change in price. This term is used in the video to contrast with elastic demand. The video script uses the analogy of a stiff rubber band that does not stretch much when pulled, illustrating that inelastic goods are less sensitive to price changes, suggesting that consumers' demand for these goods is relatively stable regardless of price fluctuations.

💡Elastic

Elastic demand indicates that the quantity demanded of a good is highly responsive to changes in its price. In the video, this is likened to a rubber band that stretches significantly with a small amount of force. The script explains that for elastic goods, a small change in price can lead to a large change in the quantity demanded, which is an important consideration for businesses setting prices and for policymakers.

💡Price Change

Price change refers to an increase or decrease in the cost of a good or service. In the context of the video, price changes are used to explore how they affect the quantity demanded and, by extension, the elasticity of demand. The script discusses how different price changes can lead to different elasticities, depending on the initial and final prices and quantities.

💡Average

The average, in this context, is calculated as the mean of two quantities. The video script explains that when calculating elasticity, the change in quantity demanded is divided by the average of the initial and final quantities, and similarly for price. This method ensures that the elasticity measure is consistent whether the price is increasing or decreasing. The script uses the average to demonstrate how to calculate the elasticity at different points along a demand curve.

💡Unitless Number

A unitless number is a numerical value that does not have an associated unit of measurement. In the video, the script mentions that using percentages (unitless numbers) for elasticity calculations allows for a comparison that is not dependent on the specific units of the quantities involved. This is important for making economic analyses that are universally applicable, regardless of the units used to measure quantity or price.

💡Base Quantity

Base quantity refers to the initial quantity used as a reference point when calculating percentage changes. In the video, the script explains that instead of using the starting quantity alone, the average of the starting and ending quantities is used as the base for calculating the percentage change in quantity demanded. This approach is used to ensure that the elasticity measure is the same whether the price is rising or falling.

💡Positive and Negative Changes

Positive and negative changes in the video refer to increases and decreases in price and quantity, respectively. The script discusses how elasticity of demand is calculated for both types of changes, emphasizing that the method of calculation should yield the same elasticity value regardless of whether the price is rising or falling. This consistency is important for a comprehensive understanding of how demand responds to price fluctuations.

Highlights

Introduction to the concept of elasticity of demand and its significance in economics.

Explanation of how elasticity of demand measures the change in quantity demanded in response to a change in price.

Clarification between the terms 'demand' and 'quantity demanded' and their relevance in economic analysis.

The method economists use to measure elasticity of demand as a percentage change.

The importance of using percentages to obtain a unitless number for elasticity, making it independent of specific units.

An analogy comparing elasticity to a rubber band to explain the concept of elasticity in demand.

Definition of very elastic demand based on a large percentage change in quantity for a given percentage change in price.

Definition of very inelastic demand where a small percentage change in quantity occurs for a given percentage change in price.

The calculation of elasticity of demand at multiple points along a demand curve to understand its variability.

The mathematical approach to calculating elasticity of demand using the average of starting and ending points.

The rationale behind using the average for calculating elasticity to ensure consistency in results regardless of the direction of price change.

An example calculation of elasticity of demand between two points on a demand curve.

The significance of the elasticity value in determining the responsiveness of quantity demanded to price changes.

The calculation of elasticity of demand at different points to observe the impact of starting and ending points on elasticity values.

The observation that elasticity values can vary significantly even with the same change in quantity and price due to different starting points.

The final calculation of elasticity of demand and its interpretation in the context of the demand curve.

Transcripts

What we're going to think about in this video

is elasticity of demand-- tis-sit-tity,

elasticity of demand.

And what this is, is a measure of how

does the quantity demanded change given a change in price?

Or how does a change in price impact the quantity demanded?

So change in price-- impact quantity--

want to be careful here-- quantity demanded.

When you talk about demand, you're

talking about the whole curve.

Quantity demanded is a specific quantity-- quantity demanded.

And the way that we, as economist-- I'm not really

an economist, but since we're doing economics,

we could pretend to be economists.

The way that economists measure this

is they measure it as a percent change in quantity

over a percent-- over the percent change in price.

And the reason why they do this, as opposed to just,

say, change in quantity over change in price,

is because if you did change in quantity over change in price

you would have a number that's specific to the units you're

using.

So it would depend on whether you're doing quantity

in terms of per hour, or per week, or per year.

And so you would have different numbers based on the time

frame, or the units, that you might use.

But when you use a percentage it is a unitless number.

Because the percentage-- you're taking a change

in some quantity, divided by that quantity.

So the units themselves actually cancel out.

And the reason why it's called elasticity--

this might make some sense to you-- or the reason

why I like to think it's called elasticity,

is I imagine something that's the elastic.

Like a elastic band or a rubber band.

And in the rubber band, if you pull it,

depending if something-- so let's say this one

is inelastic.

So if you pull, you're not going to able to pull it much.

It's going to be fairly stiff.

It's not going to stretch a lot.

While something is elastic-- if something

is elastic for a given amount of force--

so this is for a given amount of force--

you're not able to pull it much.

And if something is elastic, maybe

for the same amount of force, you're

going to be able to pull it a lot.

So this right over here is elastic.

And so the analogy, maybe, might make a little bit sense--

relative to applied price and demand.

Something is elastic-- so let me write this down.

So let me write, very elastic.

If a given change in price-- given price change

you have-- and we'll talk about percentages in a little bit.

But a given change in price, you have a large change

in demand-- so large percentage change.

And let me just speak in terms of percentage.

Given a percentage change in P, you

end up having a large percentage change in Q.

That would be very elastic.

So you could imagine the P is like the force,

and the Q, the quantity demanded,

is how far the thing can get stretched apart.

And that's why we would call this very elastic.

Just like a very elastic rubber band.

And if something is very inelastic, if given a percent

change in P, you have a small percent change in Q.

So just like a rubber band-- for a given amount of force,

if you're not able to pull it much at all,

then it's inelastic.

If you're able to pull a lot, it's elastic.

Same thing with price and quantity.

For a given change in price, if the percent quantity demanded

changes a lot-- very elastic.

If it doesn't change a lot-- very inelastic.

Now, with that out of the way, let's

actually calculate the elasticity

for multiple points along this demand curve right over here.

And I think that will give us a bit better grounding.

Especially because there are a little slightly-- I would call

them unusual ways of calculating the percent change in quantity

and the percent change of price--

just so that we get the same number when

we have a positive change in price.

And the same as we get the negative change

in price-- or a negative and a positive-- or a drop in price

and an increase in price.

So let me give myself some real estate over here

because I want to do some actual mathematics.

And actually all of this we will be reviewing in what I'm about

do, and it will give me some real estate to work with.

So let me clear all of that.

And let me clear is that right over here.

And what I'm going to do is I'm going

to calculate the elasticity of demand

at several points along this demand curve right over here.

And so the first one, I will do it at point A

to point B. So let me make another column

right over here-- elasticity of demand.

And actually, we're going to have

one column that's elasticity of demand.

So it's a big E with a little subscript D. And the other one,

I'll just take its absolute value.

Because, depending on-- sometimes

people like to just think of the number,

which will tend to be a negative number.

And sometimes, people like to look

at the absolute value of it.

So we'll look at both and see what it actually means.

So let's say our price drops from point A

to point B. So from point A to point

B we have a $1-- a negative $1 change in price.

And we have a positive-- so this is a negative $1

change in price.

And we have a positive $2-- sorry--

a positive two burger per hour change in quantity demanded.

So what is the elasticity of demand there?

So let's write it over here.

I'll do it in A's color.

So the elasticity of demand, remember,

it's the percent change in quantity.

So percent change in quantity-- I'll rewrite it.

It's the percent change in quantity

over percent change in price.

And so we have-- what's our percent change in quantity?

So it's going to be the change in quantity over some base

quantity.

So our change in quantity is two.

So it's going to be equal to 2 over-- now

in traditional terms-- and this is what I want to, kind of,

clarify-- is a little bit unusual in how we do it.

But we do it, so that we get the same elasticity of demand

whether we go from A to B or B to A.

Or essentially, we get the same elasticity

of demand along this whole part of the curve.

Instead of just dividing the change

in quantity divided by our starting point, what

I want to do is I'm going to divide

the change in quantity divided by the average of our starting

and our ending, points.

So that's going to be 2 over-- and I'll actually

do the math explicitly.

Actually, no, let's just think about it.

What's the average between 2 and 4.

Well, the average is just going to be 3.

That's the average of 2 and 4.

Let me write it down to, just so it's clear.

That right over here is 2 plus 4 over 2.

That's how you get 3.

That's how you would calculate the average.

So that is our proportionate change.

And then you want to multiply by 100-- times 100--

to actually get a percentage.

And then, what is our change in price?

Well we're going to do the same thing, or the percent

change in price.

Our change in price is negative 1.

It is negative 1 over-- and once again, we don't just

do negative 1 divided by 9, we do it

over the average of 8 and 9.

And the average of 8 and 9 is 8.5.

And then multiply by 100 to get your percentage.

Now, these 100s, obviously, cancel out.

These 100s cancel out.

And so we are going to be left with-- when you divide

by a fraction, it's the same thing

as multiplying by its inverse.

So we're going to get 2/3 times negative 8.5 over 1--

or times negative 8.5.

I'll get out our calculator and it

is-- well, multiply 2 times negative 8.5,

and then divided by 3, which gives us negative 5.6667.

It's really negative 5 2/3.

So I'll just write it negative-- I'll

round it-- it's negative 5.67.

So this is approximately equal to negative 5.67.

So right over here it's negative 5.67.

And this absolute value is, obviously, just 5.67.

And I'll leave it to you to verify, for yourself,

that you'll get the same elasticity of demand

using this technique-- where you use

the average as your base in the percentage.

Going from 9 to 8 as going-- going from 9 to 8

in price as going from 8 to 9 in price.

Which is different than if you used the 9 as the base or the 8

as the base.

So this right here is the elasticity

of demand-- not just at point A. You can, kind of, view

it is the average elasticity of demand

over this little part of the curve, which is really

a line in this example-- over this part of the arc.

So we'll write that part right over here.

I'll write the absolute value.

The absolute value of our elasticity of demand is 5.67.

Now let's do the other two sections right over here.

So let's think about what happens

when we go from C to D. So our elasticity of demand there.

So from C to D we have a change in quantity, once again,

of plus 2.

And our change in price, once again, is negative 1.

But we'll see, even though that the change in the quantity

over-- the change of quantity is the same,

and the change in price is the same,

we're going to have a different elasticity of demand,

because we have different starting points.

Our starting points and our ending points for price

are lower and our starting and ending points for quantity

are higher.

So it will actually change the percentage.

So let's see what we get.

So our percent change in quantity-- we

have a change in quantity of 2.

And then our average quantity is 9

plus 11, which is 20, divided by 2 is 10.

All of that over percent change in price.

So we have-- let me scroll down a little bit-- negative one

divided by the average price.

So negative 1 is the change in price.

And we want to divide that by the average price.

Well, $5.50 plus $4.50 is $10-- divided by 2 is $5.00.

So the average is $5.00.

And we can multiply the numerator

by 100 and the denominator by 100,

but that won't change anything, because we could just

divide both by 100.

And so this is equal to 2 over 10,

times-- dividing by a fraction is the same thing

as multiplying by its inverse-- times negative 5 over 1.

And this is just because 2 over 10 is the same thing as 1/5.

1/5 times negative 5 over 1-- it is negative 1.

So this right over here.

So our elasticity of demand right over here is negative 1.

Or it's absolute value is 1.

So the absolute value of the elasticity of demand,

right over here, is equal to 1.

Now let's just do one more section,

and maybe, the next video we can think a little bit

about what it's telling us.

So let's do this last section over here,

just for some practice.

I encourage you to pause it and try it yourself.

And so we're going to think about this section

right over here.

So once again, our change in quantity is plus 2,

and our change in price is negative 1.

And our elasticity of demand-- change

in quantity-- 2 over average quantity, which is 17.

Change in price is negative 1 over average price--

1 plus 2 divided by 2 is $1.50.

Or $1.50 is right in between these two-- divided by $1.50.

We don't have to multiply the numerator and the denominator

by 100 because those just cancel out.

So we get 2 over 17, times negative-- well,

we could just write this as negative $1.50 over 1.

And this is equal to-- getting our--

getting our calculator back out.

So this is equal to-- I'll just write-- well,

it's really just going to be negative 3 over 17, right?

2 times negative $1.50 is negative 3 over 17.

So negative 3 divided by 17 is equal to, I'll just say,

negative 0.18.

So here it is, negative 0.18, and its absolute value is 0.18.

So the elasticity of demand over here is 0.18.

And I'll leave you there, and in the next video

we'll think about these results a little bit.