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♪ [music] ♪

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- [Alex] In our first lecture[br]on the elasticity of demand,

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we explain the intuitive meaning[br]of elasticity.

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It measures the responsiveness[br]of the quantity demanded

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to a change in price.

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More responsive means more elastic.

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In this lecture, we're going[br]to show how to create

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a numeric measure of elasticity.

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How to calculate with some data[br]on prices and quantities,

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what the elasticity is over a range[br]of the demand curve.

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So here's a more precise definition[br]of elasticity.

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The elasticity of demand[br]is the percentage change

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in quantity demanded divided[br]by the percentage change in price.

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So let's write it like this.[br]We have some notation here.

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The elasticity of demand is equal[br]to the percentage "change in".

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Delta is the symbol for change in,[br]so this is the percentage change

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in the quantity demanded[br]divided by the percentage change

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in the price.

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That's the elasticity of demand.[br]Let's give an example or two.

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So, if the price of oil increases[br]by 10% and over a period

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of several years the quantity[br]demanded falls by 5%,

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then the long run elasticity[br]of demand for oil is what?

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Well, elasticity[br]is the percentage change

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and the quantity demanded.

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That's -5% divided[br]by the percentage change

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in the price.

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That's 10%.

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So the elasticity of demand

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is -5% divided by 10%, or -0.5.

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Elasticities of demand[br]are always negative

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because when price goes up,[br]the quantity demanded goes down.

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When price goes down,[br]the quantity demanded goes up.

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So we often drop the negative sign[br]and write that the elasticity

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of demand is 0.5.

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Here's some more important notation.

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If the absolute value[br]of the elasticity of demand

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is less than one,[br]just like the example

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we just gave for oil, we say[br]that the demand curve is inelastic.

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Elasticity of demand less than one,[br]the demand curve is inelastic.

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If the elasticity of demand[br]is greater than one,

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we say the demand curve is elastic.

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And if elasticity of demand[br]is equal to one,

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that is the knife point case,[br]then the demand curve

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is unit elastic.

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These terms are going to come back,[br]so just keep them in mind.

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Inelastic: less than one.[br]Elastic: greater than one.

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So we know that elasticity[br]is the percentage change

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in quantity divided[br]by the percentage change in price,

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how do we calculate[br]the percentage change in something?

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This is not so hard,[br]but it could be a little bit tricky

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for the following reason.

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Let's suppose you're driving down[br]the highway at 100 miles per hour.

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I don't recommend this,[br]but let's just imagine

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that you are.

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You're going 100 miles per hour,[br]and now you increase speed by 50%.

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How fast are you going?[br]150 miles per hour, right?

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Okay, so now you're going[br]150 miles per hour.

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Suppose you decrease speed by 50%.[br]Now, how fast are you going?

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75 miles per hour, right?

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So how is it that you can[br]increase speed by 50%

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and then decrease by 50%[br]and not be back

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to where you started?

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Well the answer is,[br]is that intuitively,

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we have changed the base[br]by which we are calculating

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the percentage change.

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And we don't want to have[br]this inconsistency

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when we calculate elasticity.

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We want people to get[br]the same elasticity

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whether they're calculating[br]from the lower base

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or from the higher base.

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So, because of that, we're going[br]to use the Midpoint Formula.

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So, the elasticity of demand,[br]percentage change in quantity

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divided by the percentage[br]change in price,

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that's the change in quantity[br]divided by the average quantity

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times 100.

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That will give us the percentage[br]change divided by

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the change in price[br]divided by the average price.

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Again, that times 100.

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Notice, since we've actually got[br]100 on top and 100 on the bottom,

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those 100s we can actually[br]cancel out.

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Let's expand this[br]just a little bit more.

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The change in quantity.[br]What is the change in quantity?

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Well, let's suppose[br]we have two quantities.

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Let's call them after and before.

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It doesn't matter which one[br]we call after or which one before.

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So, we're going to then expand this[br]to the change in quantity.

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That's Q after minus Q before[br]divided by the average,

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Q after plus Q before,[br]divided by two,

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divided by the change in price,[br]P after minus P before,

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divided by the average price,[br]b after plus b before,

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divide by two.

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So that's a little bit of a mouthful,[br]but everything, I think,

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is fairly simple.

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Just remember change in quantity[br]divided by the average quantity

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and you should always be able[br]to calculate this.

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Let's give an example.

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Okay, here's an example[br]of a type of problem

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you might see on a quiz[br]or a mid term.

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At the initial price of $10,[br]the quantity demanded is 100.

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When the price rises to $20,[br]the quantity demanded

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falls to 90.

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What is the elasticity is, [br]what is the elasticity over

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this range of the demand curve?

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Well, we always want[br]to begin by writing down

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what we know -- our formula.

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The elasticity of demand[br]is the percentage change

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in quantity divided[br]by the percentage change in price.

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Now, let's remember[br]to just expand that.

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That's Delta Q over the average Q[br]all divided by Delta P

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over the average P.

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Now, we just start[br]to fill things in.

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So our quantity after, okay,[br]after the change is 90.

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Our quantity before that was 100.

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So on the top,[br]the percentage change

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in quantity is 90 minus 100[br]divided by 90 plus 100, over two.

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That is the average quantity.

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And then on the bottom,[br]and the only trick here

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is always write it[br]in the same order,

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so if you put the 90 here,[br]then make sure you put the 20,

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the number the price[br]which is associated

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with that quantity started off[br]the same way.

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So, always just keep it[br]in the same order.

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So on the bottom, then,[br]we have the quantity --

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the price after -- which is 20[br]minus the price before,

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which is 10, divided[br]by the average price.

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And now, just, it's numerics.

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You plug in the numbers[br]and what you get is the elasticity

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of demand is equal to -0.158,[br]approximately.

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We can always drop[br]the negative sign

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because these things,[br]elasticity of demands,

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are always negative.

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So it's equal to 0.158.

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So does this make the elasticity[br]of demand over this range

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elastic or inelastic?

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Inelastic, right?

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The elasticity of demand[br]we've just calculated

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is less than one,[br]so that makes this one inelastic.

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There you go.

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We need to cover one more[br]important point

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about the elasticity of demand,[br]and that is its relationship

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to total revenue.

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So a firm's revenues[br]are very simply equal

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to price times quantity sold.

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Revenue is equal[br]to price times quantity.

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Now, elasticity, it's all about[br]the relationship

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between price and quantity,

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and so it's also going[br]to have implications for revenue.

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Let's give some intuition[br]for the relationship

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between the elasticity[br]and total revenue.

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So revenue is price times quantity.

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Now suppose the price goes up[br]by a lot and then quantity demanded

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goes down, just by a little bit.

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What then is going to be[br]the response of revenue?

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Well, if price is going up[br]by a lot and quantity

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is going down just by a little bit,[br]then revenue

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is also going to be going up.

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Now, what kind of demand curve[br]do we call that, when price goes up

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by a lot and quantity falls [br]by just a little bit?

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We call that[br]an inelastic demand curve.

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So, what this little thought[br]experiment tells us

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is that when you have[br]an inelastic demand curve,

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when price goes up[br]revenue is also going to go up,

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and of course, vice versa.

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Let's take a look[br]at this with a graph.

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So here's our initial demand curve,[br]a very inelastic demand curve,

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at a price of $10, the quantity[br]demanded is 100 units,

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so revenue is 1,000.

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Notice that we can show revenue[br]in the graph

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by price times quantity.

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Now, just looking at the graph,[br]look at what happens

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when the price goes up to 20.

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Well, the quantity demanded[br]goes down by just a little bit,

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in this case to 90,[br]but revenues go up to 1,800.

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So you can just see,[br]by sketching the little graph,

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what happens to revenues[br]when price goes up

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when you have[br]an inelastic demand curve.

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And again, vice versa.

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Let's take a look[br]about what happens

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when you have[br]an elastic demand curve.

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So let's do the same kind[br]of little thought experiment,

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revenue is price times quantity.

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Suppose price goes up[br]by a modest amount

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and quantity goes down[br]by a lot.

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Well, if price is going up[br]by a little bit and quantity

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is going down by a lot,[br]then revenue must also be falling.

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And what type of demand curve[br]is it when price goes up

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by a little bit,[br]quantity falls by a lot?

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What type of demand curve is that?

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That's an elastic demand curve.

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So, revenues fall as price rises[br]with an elastic demand curve.

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And again, let's show that.

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If you're ever confused[br]and you can't quite remember,

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just draw the graph.

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I can never remember, myself,[br]but I always draw

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these little graphs.

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So, draw a really flatter,[br]elastic demand curve.

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In this case, at a price of $10,[br]the quantity demanded is 250 units.

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So revenues is 2,500.

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And see what happens,[br]when price goes up,

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price goes up to $20,[br]quantity demanded falls to 50,

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so revenue falls to 1,000.

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And again, you can just compare

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the sizes of these[br]revenue rectangles

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to see which way[br]the relationship goes.

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And of course, this also implies,[br]going from $20, the price of $20

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to a price of $10,[br]revenues increase.

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So with an elastic demand curve,[br]when price goes down,

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revenues go up.

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So here's a summary[br]of these relationships.

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When the elasticity of demand[br]is less than one,

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that's an inelastic demand curve[br]and price and revenue

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move together.

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When one goes up,[br]the other goes up.

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When one goes down,[br]the other goes down.

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If the elasticity of demand [br]is greater than one,

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that's an elastic demand curve[br]and price and revenue move

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in opposite directions.

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And could you guess what happens[br]if the elasticity of demand

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is equal to one --[br]if you have a unit elastic curve?

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Well then, when the price changes,[br]revenue stays the same.

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Now, if you have to, again,[br]memorize these,

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but it's really much better[br]to just sketch some graphs.

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I never remember them,[br]as I've said myself,

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I never remember[br]these relationships,

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but I can always sketch[br]an inelastic graph

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and then with a few changes[br]in price, I can see

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whether the revenue rectangles[br]are getting bigger or smaller

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and so I'll be able to recompute

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all of these relationships[br]pretty easily.

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Here's a quick practice question.

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The elasticity of demand for eggs[br]has been estimated to be 0.1.

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If egg producers raise their prices[br]by 10%, what will happen

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to their total revenues? Increase?[br]Decrease? Or it won't change?

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Okay, how should we[br]approach this problem?

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If the elasticity of demand is 0.1,[br]what type of demand curve?

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Inelastic demand.

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Now, what's the relationship[br]between an inelastic demand curve?

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When price goes up,[br]what happens to revenue?

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If you're not sure, [br]if you don't remember,

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draw some graphs.

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Draw an inelastic,[br]draw an elastic, figure it out.

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Okay, let's see. What happens?[br]Revenue increases, right?

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If you have an inelastic[br]demand curve and price goes up,

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revenue goes up as well.

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Here's an application.

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Why is the war on drugs[br]so hard to win?

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Well, drugs are typically[br]going to have

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a fairly inelastic demand curve.

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What that means[br]is that when enforcement actions

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raise the price of drugs,[br]make it more costly to get drugs,

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raising the price,[br]that means the total revenue

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for the drug dealers goes up.

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So check out this graph.

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Here is the price[br]with no prohibition,

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here's our demand curve,[br]our inelastic demand curve.

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What prohibition does,[br]is it raises the cost

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of supplying the good.

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But that raises the price,[br]which is what it's supposed to do,

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and that does reduce[br]the quantity demanded of the drug.

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But it also has the effect[br]of increasing seller revenues.

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And seller revenues may be[br]where many of the problems

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of drug prohibition come from.

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It's the seller revenues[br]which drive the violence,

0:13:47.642,0:13:52.012
which drive the guns,[br]which make it look good

0:13:52.012,0:13:54.672
to be a drug dealer,[br]which encourage people

0:13:54.672,0:13:57.374
to become drug dealers,[br]and so forth.

0:13:57.799,0:14:01.099
So there's a real difficulty[br]with prohibition,

0:14:01.099,0:14:03.527
with prohibiting a good,[br]especially when it has

0:14:03.527,0:14:05.616
an inelastic demand.

0:14:06.181,0:14:08.858
Here's another application[br]of elasticity of demand

0:14:08.858,0:14:11.436
and how it can be used[br]to understand our world.

0:14:11.858,0:14:16.738
This is a quotation from 2012[br]from NPRs food blog "The Salt."

0:14:17.206,0:14:18.318
"You've all heard a lot

0:14:18.318,0:14:21.502
about this year's devastating[br]drought in the Midwest, right?

0:14:21.856,0:14:24.686
US Department of Agriculture[br]announced last Friday

0:14:24.733,0:14:29.192
that the average US cornfield[br]this year will yield less per acre

0:14:29.192,0:14:31.869
than it has since 1995.

0:14:32.430,0:14:34.191
Soybean yields are down, too.

0:14:34.712,0:14:37.103
So you think that farmers[br]who grow these crops

0:14:37.103,0:14:38.986
must be really hurting.

0:14:38.986,0:14:42.876
And that's certainly the impression[br]you get from media reports.

0:14:44.104,0:14:46.349
But how's this,[br]for a surprising fact?

0:14:46.349,0:14:49.613
On average, corn growers[br]actually will rake in

0:14:49.613,0:14:53.883
a record amount of cash[br]from their harvest this year."

0:14:55.095,0:14:58.776
So can you explain this secret side[br]of the drought?

0:14:59.301,0:15:01.016
I'm not going to answer[br]this question.

0:15:01.016,0:15:03.536
This is exactly the type[br]of question you might receive

0:15:03.536,0:15:05.087
on an exam.

0:15:05.087,0:15:07.602
But you should be able[br]to answer it by now,

0:15:07.602,0:15:09.883
with a few sketches[br]on a piece of paper.

0:15:09.949,0:15:12.370
And in particular, what I want you[br]to answer is,

0:15:12.370,0:15:17.010
what type of demand curve,[br]for corn, would make exactly

0:15:17.010,0:15:20.408
this type of outcome[br]perfectly understandable?

0:15:20.408,0:15:24.462
Not a secret or surprise,[br]but perfectly understandable.

0:15:25.082,0:15:28.086
Okay, that's the elasticity[br]of demand.

0:15:28.086,0:15:31.220
Next time we'll be taking up[br]the elasticity of supply,

0:15:31.220,0:15:33.700
and we'll be able to move[br]through that material much quicker

0:15:33.700,0:15:36.843
because it covers[br]many similar concepts.

0:15:36.843,0:15:38.455
Thanks.

0:15:39.469,0:15:41.296
- [Narrator] If you want[br]to test yourself,

0:15:41.296,0:15:45.287
click Practice Questions,[br]or if you're ready to move on,

0:15:45.287,0:15:47.058
just click Next Video.

0:15:47.088,0:15:50.882
♪ [music] ♪