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Voiceover: In this video[br]I want to clarify a little

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bit about why we calculate[br]the percent changes

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when we're thinking about elasticity

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the way that we do.

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So just to remind ourselves,

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a little focus on price[br]elasticity of demand,

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although we've been exposed to other

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types of elasticities already.

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Just as a review, price[br]elasticity of demand,

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so the elasticity of demand,

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is defined as the percent[br]change in quantity

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demanded over the percent change in price.

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So first I'll calculate[br]it the conventional way,

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the way you would do it in a traditional

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microeconomics class.

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Then I'll calculate it the way

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that you would just based on how you would

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traditionally calculate percentages

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and we'll see why microeconomists

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like to do it the way that they do.

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First we'll talk about the "correct" way.

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I'll put it in quotes because correct

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is by definition really[br]just by convention.

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But when we first think about[br]the percent change in quantity,

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percent change in quantity[br]and we're going to assume,

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we're going to calculate the elasticity

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of demand between point A over here,

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point A and point B over here.

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So what is our percent change in quantity?

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Well, our absolute change in quantity

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going from A to B we have increased by 2.

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So we have increased by 2.

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I'll write it down here.

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This is going to be 2 over and then this

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is kind of the slightly strange thing

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that we do when we[br]calculate our percentages.

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We don't say 2 over 4.

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We say 2 over the average of 4 and 6.

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It's 2 over the average of our starting

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point and our ending point.

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The average of 4 and 6 is 5.

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So this is going to be ...

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We have a 40% change based on how

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we calculated the percentages

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in our quantity demanded,

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and then let's do our[br]percent change in price.

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So this is all going to be over

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our percent change in price.

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Our absolute change in[br]price is negative 1 dollar.

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Negative 1 dollar and[br]then instead of doing it

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over our starting point over 2,

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we do it over the average[br]of the 2, over 150.

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Negative 1 over 150 is[br]negative two-thirds,

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or right about negative[br]66.7% if we say roughly.

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So this right over here ...

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so based on how we calculated percentages,

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and I want to make it clear,

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this is kind of a strange way,

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when we do it over the midpoint

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of the starting and ending points,

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but we're saying that our percent change

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from A to B in quantity,

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so our percent change in quantity,

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this right over here we[br]are saying it is 40%,

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and then we are saying that this percent

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change in price right over[br]here is negative 66.7%.

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Now, the reason why this is valuable,

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and then obviously if you[br]do the math right here,

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40% over negative 66.7% percent,

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you're going to get some

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let's see you're going to get something.

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I think it's going to be in the 6s.

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Point 6 something but let's actually get a

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calculator out to calculate it.

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It would be 40 divided by 66.7 gives you,

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it's almost 60 so it's roughly point 60

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if we were to round.

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This is approximately 0.60.

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It was 597 something.

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Actually I'll just leave[br]it that way at point 60.

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Now, what's cool about this

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or what's useful about this,

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and this is the reason why[br]we kind of mis-do it is,

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you would get the same answer

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whether you're going from A to B

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or whether you're going from B to A.

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This is the situation where[br]we're going from A to B,

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but if we were to go from B to A,

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if we were to go from B to[br]A it's the exact same thing.

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If we go from B to A what[br]is our change in quantity?

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Our change in quantity is negative 2.

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It would be negative 2 over,

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now you wouldn't do it[br]over your starting point.

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You do it over the average.

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This is why we will get the same value

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regardless of what direction we go in.

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We get the average of 4[br]and 6 is going to be 5.

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That's going to be over.

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Now going from B to A what[br]is our change in price?

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Our change in price is now plus 1.

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It is plus 1 over the[br]average of our starting

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point and our ending point, over 150.

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Now these are the exact same quantities.

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Both are going to be a negative number.

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Here the negative is on the bottom.

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Here the negative is on top.

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Either way and actually[br]this was a negative

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point 60 because you have a positive

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divided by a negative.

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This too when you evaluate it,

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is going to turn out to[br]be the exact same thing.

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It's going to be negative 0.60.

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Now if you calculated percentages[br]in the traditional way,

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you would not get the same value for the

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price elasticity of demand,

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whether you go from A to B and B to A.

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Just to show that to you,

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I will put this in quotation marks.

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It's not the "wrong"[br]way to do it in general.

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In fact, this is how you would calculate

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price changes traditionally,

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but it's not how you do it in kind of a

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microeconomic sense.

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If you did the wrong way[br]... If you said from A to B

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your absolute change in quantity[br]is plus 2 and your base ...

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Remember this is the way[br]that it's done outside

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of microeconomics.

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Your base is 4 and then[br]your change in price,

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you went down 1 and your base,

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you started at A,

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so your base is 2.

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This is the way you do it[br]outside of economics class.

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This would be equal to

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50% plus 50% over negative 50%,

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over negative 50%.

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You essentially get negative 1.

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Going from A to B using a traditional way

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of calculating percent change.

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What happens if you go from B to A?

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What happens if you go from B to A?

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Now, all of the sudden, your[br]change in quantity is negative 2.

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Your base is now ...[br]the starting point is 6.

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Your starting point is 6.

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Then your change in price,

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once again you're increasing in price by 1

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going from B to A,

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so this is plus 1.

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Your base is now 1.

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You will get,

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this is negative 33% roughly,

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that's negative a third, so 33.333,

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it keeps repeating over 100%.

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This will be equal to negative point 33.

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Notice when you calculate percentages

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in the traditional way,

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you get a different answer[br]whether you're going from

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A to B or whether you're[br]going from B to A.

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The whole reason why when[br]we take the percentages,

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we take it over the average of our

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starting and our ending points,

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over the average of our[br]starting and ending points.

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is so we get the same[br]value for the elasticity

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of demand along this portion of the curve.

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You can really view it as the average

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elasticity of demand over[br]this portion of the curve

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and if you calculate it this way,

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it doesn't matter whether you're going

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from A to B or B to A.