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Calculating the Elasticity of Demand

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    ♪ [music] ♪
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    - [Alex] In our first lecture
    on the elasticity of demand,
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    we explain the intuitive meaning
    of elasticity.
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    It measures the responsiveness
    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
    to show how to create
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    a numeric measure of elasticity.
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    How to calculate with some data
    on prices and quantities,
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    what the elasticity is over a range
    of the demand curve.
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    So here's a more precise definition
    of elasticity.
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    The elasticity of demand
    is the percentage change
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    in quantity demanded divided
    by the percentage change in price.
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    So let's write it like this.
    We have some notation here.
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    The elasticity of demand is equal
    to the percentage "change in".
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    Delta is the symbol for change in,
    so this is the percentage change
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    in the quantity demanded
    divided by the percentage change
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    in the price.
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    That's the elasticity of demand.
    Let's give an example or two.
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    So, if the price of oil increases
    by 10% and over a period
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    of several years the quantity
    demanded falls by 5%,
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    then the long run elasticity
    of demand for oil is what?
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    Well, elasticity
    is the percentage change
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    and the quantity demanded.
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    That's -5% divided
    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
    are always negative
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    because when price goes up,
    the quantity demanded goes down.
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    When price goes down,
    the quantity demanded goes up.
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    So we often drop the negative sign
    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
    of the elasticity of demand
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    is less than one,
    just like the example
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    we just gave for oil, we say
    that the demand curve is inelastic.
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    Elasticity of demand less than one,
    the demand curve is inelastic.
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    If the elasticity of demand
    is greater than one,
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    we say the demand curve is elastic.
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    And if elasticity of demand
    is equal to one,
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    that is the knife point case,
    then the demand curve
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    is unit elastic.
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    These terms are going to come back,
    so just keep them in mind.
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    Inelastic: less than one.
    Elastic: greater than one.
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    So we know that elasticity
    is the percentage change
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    in quantity divided
    by the percentage change in price,
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    how do we calculate
    the percentage change in something?
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    This is not so hard,
    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
    the highway at 100 miles per hour.
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    I don't recommend this,
    but let's just imagine
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    that you are.
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    You're going 100 miles per hour,
    and now you increase speed by 50%.
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    How fast are you going?
    150 miles per hour, right?
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    Okay, so now you're going
    150 miles per hour.
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    Suppose you decrease speed by 50%.
    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
    increase speed by 50%
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    and then decrease by 50%
    and not be back
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    to where you started?
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    Well the answer is,
    is that intuitively,
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    we have changed the base
    by which we are calculating
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    the percentage change.
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    And we don't want to have
    this inconsistency
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    when we calculate elasticity.
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    We want people to get
    the same elasticity
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    whether they're calculating
    from the lower base
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    or from the higher base.
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    So, because of that, we're going
    to use the Midpoint Formula.
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    So, the elasticity of demand,
    percentage change in quantity
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    divided by the percentage
    change in price,
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    that's the change in quantity
    divided by the average quantity
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    times 100.
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    That will give us the percentage
    change divided by
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    the change in price
    divided by the average price.
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    Again, that times 100.
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    Notice, since we've actually got
    100 on top and 100 on the bottom,
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    those 100s we can actually
    cancel out.
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    Let's expand this
    just a little bit more.
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    The change in quantity.
    What is the change in quantity?
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    Well, let's suppose
    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
    we call after or which one before.
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    So, we're going to then expand this
    to the change in quantity.
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    That's Q after minus Q before
    divided by the average,
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    Q after plus Q before,
    divided by two,
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    divided by the change in price,
    P after minus P before,
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    divided by the average price,
    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,
    but everything, I think,
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    is fairly simple.
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    Just remember change in quantity
    divided by the average quantity
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    and you should always be able
    to calculate this.
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    Let's give an example.
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    Okay, here's an example
    of a type of problem
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    you might see on a quiz
    or a mid term.
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    At the initial price of $10,
    the quantity demanded is 100.
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    When the price rises to $20,
    the quantity demanded
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    falls to 90.
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    What is the elasticity is,
    what is the elasticity over
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    this range of the demand curve?
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    Well, we always want
    to begin by writing down
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    what we know -- our formula.
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    The elasticity of demand
    is the percentage change
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    in quantity divided
    by the percentage change in price.
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    Now, let's remember
    to just expand that.
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    That's Delta Q over the average Q
    all divided by Delta P
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    over the average P.
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    Now, we just start
    to fill things in.
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    So our quantity after, okay,
    after the change is 90.
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    Our quantity before that was 100.
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    So on the top,
    the percentage change
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    in quantity is 90 minus 100
    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,
    and the only trick here
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    is always write it
    in the same order,
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    so if you put the 90 here,
    then make sure you put the 20,
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    the number the price
    which is associated
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    with that quantity started off
    the same way.
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    So, always just keep it
    in the same order.
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    So on the bottom, then,
    we have the quantity --
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    the price after -- which is 20
    minus the price before,
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    which is 10, divided
    by the average price.
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    And now, just, it's numerics.
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    You plug in the numbers
    and what you get is the elasticity
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    of demand is equal to -0.158,
    approximately.
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    We can always drop
    the negative sign
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    because these things,
    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
    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
    we've just calculated
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    is less than one,
    so that makes this one inelastic.
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    There you go.
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    We need to cover one more
    important point
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    about the elasticity of demand,
    and that is its relationship
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    to total revenue.
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    So a firm's revenues
    are very simply equal
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    to price times quantity sold.
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    Revenue is equal
    to price times quantity.
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    Now, elasticity, it's all about
    the relationship
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    between price and quantity,
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    and so it's also going
    to have implications for revenue.
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    Let's give some intuition
    for the relationship
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    between the elasticity
    and total revenue.
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    So revenue is price times quantity.
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    Now suppose the price goes up
    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
    the response of revenue?
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    Well, if price is going up
    by a lot and quantity
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    is going down just by a little bit,
    then revenue
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    is also going to be going up.
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    Now, what kind of demand curve
    do we call that, when price goes up
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    by a lot and quantity falls
    by just a little bit?
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    We call that
    an inelastic demand curve.
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    So, what this little thought
    experiment tells us
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    is that when you have
    an inelastic demand curve,
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    when price goes up
    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
    at this with a graph.
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    So here's our initial demand curve,
    a very inelastic demand curve,
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    at a price of $10, the quantity
    demanded is 100 units,
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    so revenue is 1,000.
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    Notice that we can show revenue
    in the graph
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    by price times quantity.
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    Now, just looking at the graph,
    look at what happens
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    when the price goes up to 20.
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    Well, the quantity demanded
    goes down by just a little bit,
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    in this case to 90,
    but revenues go up to 1,800.
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    So you can just see,
    by sketching the little graph,
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    what happens to revenues
    when price goes up
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    when you have
    an inelastic demand curve.
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    And again, vice versa.
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    Let's take a look
    about what happens
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    when you have
    an elastic demand curve.
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    So let's do the same kind
    of little thought experiment,
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    revenue is price times quantity.
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    Suppose price goes up
    by a modest amount
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    and quantity goes down
    by a lot.
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    Well, if price is going up
    by a little bit and quantity
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    is going down by a lot,
    then revenue must also be falling.
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    And what type of demand curve
    is it when price goes up
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    by a little bit,
    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
    with an elastic demand curve.
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    And again, let's show that.
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    If you're ever confused
    and you can't quite remember,
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    just draw the graph.
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    I can never remember, myself,
    but I always draw
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    these little graphs.
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    So, draw a really flatter,
    elastic demand curve.
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    In this case, at a price of $10,
    the quantity demanded is 250 units.
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    So revenues is 2,500.
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    And see what happens,
    when price goes up,
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    price goes up to $20,
    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
    revenue rectangles
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    to see which way
    the relationship goes.
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    And of course, this also implies,
    going from $20, the price of $20
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    to a price of $10,
    revenues increase.
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    So with an elastic demand curve,
    when price goes down,
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    revenues go up.
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    So here's a summary
    of these relationships.
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    When the elasticity of demand
    is less than one,
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    that's an inelastic demand curve
    and price and revenue
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    move together.
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    When one goes up,
    the other goes up.
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    When one goes down,
    the other goes down.
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    If the elasticity of demand
    is greater than one,
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    that's an elastic demand curve
    and price and revenue move
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    in opposite directions.
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    And could you guess what happens
    if the elasticity of demand
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    is equal to one --
    if you have a unit elastic curve?
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    Well then, when the price changes,
    revenue stays the same.
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    Now, if you have to, again,
    memorize these,
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    but it's really much better
    to just sketch some graphs.
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    I never remember them,
    as I've said myself,
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    I never remember
    these relationships,
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    but I can always sketch
    an inelastic graph
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    and then with a few changes
    in price, I can see
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    whether the revenue rectangles
    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
    pretty easily.
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    Here's a quick practice question.
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    The elasticity of demand for eggs
    has been estimated to be 0.1.
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    If egg producers raise their prices
    by 10%, what will happen
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    to their total revenues? Increase?
    Decrease? Or it won't change?
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    Okay, how should we
    approach this problem?
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    If the elasticity of demand is 0.1,
    what type of demand curve?
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    Inelastic demand.
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    Now, what's the relationship
    between an inelastic demand curve?
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    When price goes up,
    what happens to revenue?
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    If you're not sure,
    if you don't remember,
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    draw some graphs.
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    Draw an inelastic,
    draw an elastic, figure it out.
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    Okay, let's see. What happens?
    Revenue increases, right?
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    If you have an inelastic
    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
    so hard to win?
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    Well, drugs are typically
    going to have
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    a fairly inelastic demand curve.
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    What that means
    is that when enforcement actions
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    raise the price of drugs,
    make it more costly to get drugs,
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    raising the price,
    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
    with no prohibition,
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    here's our demand curve,
    our inelastic demand curve.
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    What prohibition does,
    is it raises the cost
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    of supplying the good.
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    But that raises the price,
    which is what it's supposed to do,
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    and that does reduce
    the quantity demanded of the drug.
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    But it also has the effect
    of increasing seller revenues.
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    And seller revenues may be
    where many of the problems
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    of drug prohibition come from.
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    It's the seller revenues
    which drive the violence,
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    which drive the guns,
    which make it look good
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    to be a drug dealer,
    which encourage people
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    to become drug dealers,
    and so forth.
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    So there's a real difficulty
    with prohibition,
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    with prohibiting a good,
    especially when it has
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    an inelastic demand.
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    Here's another application
    of elasticity of demand
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    and how it can be used
    to understand our world.
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    This is a quotation from 2012
    from NPRs food blog "The Salt."
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    "You've all heard a lot
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    about this year's devastating
    drought in the Midwest, right?
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    US Department of Agriculture
    announced last Friday
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    that the average US cornfield
    this year will yield less per acre
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    than it has since 1995.
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    Soybean yields are down, too.
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    So you think that farmers
    who grow these crops
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    must be really hurting.
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    And that's certainly the impression
    you get from media reports.
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    But how's this,
    for a surprising fact?
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    On average, corn growers
    actually will rake in
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    a record amount of cash
    from their harvest this year."
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    So can you explain this secret side
    of the drought?
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    I'm not going to answer
    this question.
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    This is exactly the type
    of question you might receive
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    on an exam.
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    But you should be able
    to answer it by now,
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    with a few sketches
    on a piece of paper.
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    And in particular, what I want you
    to answer is,
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    what type of demand curve,
    for corn, would make exactly
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    this type of outcome
    perfectly understandable?
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    Not a secret or surprise,
    but perfectly understandable.
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    Okay, that's the elasticity
    of demand.
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    Next time we'll be taking up
    the elasticity of supply,
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    and we'll be able to move
    through that material much quicker
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    because it covers
    many similar concepts.
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    Thanks.
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    - [Narrator] If you want
    to test yourself,
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    click Practice Questions,
    or if you're ready to move on,
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    just click Next Video.
  • 15:47 - 15:51
    ♪ [music] ♪
Title:
Calculating the Elasticity of Demand
Description:

Elasticity of demand is equal to the percentage change of quantity demanded divided by percentage change in price. In this video, we go over specific terminology and notation, including how to use the midpoint formula. We apply elasticity of demand to the war on drugs, and more broadly to the prohibition of a good when it has an elastic demand.

Microeconomics Course: http://mruniversity.com/courses/principles-economics-microeconomics

Ask a question about the video: http://mruniversity.com/courses/principles-economics-microeconomics/calculate-elasticity-demand-formula#QandA

Next video: http://mruniversity.com/courses/principles-economics-microeconomics/elasticity-supply-midpoint-formula

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Video Language:
English
Team:
Marginal Revolution University
Project:
Micro
Duration:
15:52

English subtitles

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