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# Price elasticity of demand using the midpoint method

Introduction to price elasticity of demand. Created by Sal Khan.

## Want to join the conversation?

• He may have covered this, but I didn't catch it. He gives the absolute value of elasticity; is there any value in knowing if the elasticity is negative or positive?
• Since the Law of Demand is true, a change in price means a change in quantity in the opposite directs. This means price elasticity of demand will always be a negative number.
Because it's always negative, we drop the minus sign (by convention) and use the unsigned number (the absolute value) instead.
• Why did Sal do 2/3 / -1/8.5 at around ? Wouldn't it be the change in both? I just don't get why you divide the difference by the average price.
• Price elasticity of demand on certain interval of graph = percentage of change of quantity demanded over interval / percentage of change of price over interval

Note: price elasticity is not the same as slope. Slope remains the same on a straight line graph but elasticity changes.

In the formula for finding percent change (which is derived by rearranging what it means to have a new value after a certain percent change is added) is:
[(New value – old value) / old value] *100

Going from (example)
4 to 5 = 25% increase
5 to 4 = 20% decrease

On a demand graph, we would be working with the same prices: 4 and 5, but the answer for the elasticity over that interval is different just because the percent change is different.

**The formula for elasticity of demand is actually in absolute value, since the negative does not tell us anything about the elasticity. It is assumed that the elasticity will be the same regardless if we measure going up in price or going down in price relative the same prices.

Going 4 to 5, the percent change = | (5-4)/4 | *100

Going 5 to 4, the percent change = | (4-5)/5 | *100

The percent change is different because in one case we divide by 4 and in the other by 5

What we do to avoid this error: divide by the average price.
Average of 4 and 5 = (4+5)/2 = 4.5

That way, in both cases we divide by 4.5 and get the same answer regardless if going from 4 to 5 or 5 to 4.

Sources:
“Sometimes you will see the absolute value of the price elasticity measure reported. In essence, the minus sign is ignored because it is expected that there will be a negative (inverse) relationship between quantity demanded and price”
https://2012books.lardbucket.org/books/microeconomics-principles-v2.0/s08-01-the-price-elasticity-of-demand.html
• in the last video sal was just calculating the ped as (2/2)/(-1/9) for the first change, how come here he did it as (2/3)/(-1/8.5)? I understand that it was because he was taking an average, but why did he take the average?
• Why has a new definition of percentage change been invented for this video? Percentage change is defined as the change divided by the original value, hence the "change" part. It's asking what the percentage change is from the original value not what the percentage change is from the average, because there wasn't an average until it changed.
• Is there any good textbook or ebook if one wants to get deeper understanding?
• I'm studying with : Principles of Economics by N. Gregory Mankiw
• At the beginning of the video ( at i think), Sal said that elasticity of demand is how much the quantity demanded changes for a change in price. For the math-minded around here, is that not just the slope (dQ/dp)?
• Elasticity of demand is not the slope of the curve. The percentage part of the equation is crucial. Use the formula Sal gives and test it by yourself. On a straight line, elasticity will be highest near the vertical axis and get more and more inelastic as you move toward the horizontal axis.
• Normally we take the independent variable ( in this case ) price on the X axis and dependent variable on the Y axis. Why this divergent in economics?
• Hello, Nadeem! There are had been cases when economists plotted price on horizontal axis and quantity on vertical. It was a mess, some did this and some did that. But, after Alfred Marshall economists conventionally mark vertical axis as price.

Alfred Marshall wrote a very authoritative book in 1890 called Principles of Economics, apparently, he decided that it is easier to explain the law of supply and demand and all that comes with it with price as being independent variable and quantity as the one that changes with price.

I believe that tradition started with him.
• When the slope is essentially the same throughout this graph, why is the elasticity different?
(1 vote)
• Because elasticity is not slope! It's a comparison of percentage changes. That's not what slope is.

Make a demand curve and Try some sample calculations for yourself. You will see, For example, that a change of 1 is a bigger percentage when the price is 10 than it is when the price is 100.
• at why didn't you multiply each fraction by hundred?