Hi folks, in our last recording we
learned about price elasticity of demand
and we were using it as an exemplar to
talk about some basic kinds of things
with elasticity. We're going to continue
to do a little more work with the price
elasticity of demand here and we'll call
this chapter six part two-- and I'm going
to highlight for you how elasticity is
actually not a slope, I'm going to try to
teach you a little bit about elasticity
and its relationship with total revenue,
and I'm going to get into a little bit
more of the details about how to
calculate it using a specific convention
called the midpoint convention....so there's a
little overview of what we're going to
do.  Okay
let's start out with the actual
calculations and try to explain this
goofy midpoint convention that your
textbook has already introduced.  The
midpoint convention is really about
making sure that direction doesn't
matter when we're talking about
percentage change.... and that's going to
seem strange, because traditionally it
does matter.  So normally when you're
thinking about percentage change you're
going to use X 2 minus X 1 over X 1
times 100... and this would give you
percentage change,  traditionally.   We do NOT
want to use this, okay?  This is not going
to work,  and the reason that it's not
going to work is because economists
would like to talk about a range and
render the direction meaningless... and you
can't do that using this traditional
formula.  So as an example-- you're going to
see that-- if you were to do this you're
going to get
a 33% increase for our first one... and in
the case of our second one we would have
6 minus 8 over 8... or negative 2 over 8...
and of course this would be a 25% change. 
So you get 33 in one direction and 25
in the other.  Economists just find this
annoying.  They want to talk about 6 to 8
as if it's a range and they want the
answer to come out the same no matter
what.  Well what's really changing between
these two equations the way that we've
set them up??  The overall value on the top
is 2, in absolute value, what's changing
is the denominators.   So if we don't want
the overall percentages to change, then we
need to make sure that the denominators
remain the same.  So for the midpoint
convention what we're going to do is... we
are going to do x2 minus x1 over the
midpoint of those two.  So you can add the
two of them together and divide them by
2 or multiply them by 1/2.   So in our case
you're going to be able to take 6 to 8
or 8 to 6 either one and we're going to
divide by 6 plus 8 times 1/2, so we'll
end up with 2 over 7... and it doesn't
matter which direction we're going there
we are going to end up with the same
exact number.. in this case that's going
to be 28.56
percent..doesn't matter if you're going
from six to eight or eight to six
because we're dividing by the midpoint
of the two of them in either case.  So, the
reason we call this a convention is
because people just decided this is how
they were going to do things, and I'm
trying to give you a sense of why, and that
has to do with them wanting to talk
about it as a range.... but whenever you're
actually calculating the percentage
changes that showed up in our
elasticities I need you to use the
midpoint.  If the question just gives you
the percentages already, then  you don't need
to worry about it,  but if you have raw
data I'm going to expect that you use
this midpoint convention in your
calculations.
Okay let's tackle an other oddity of
elasticity.  Elasticity is absolutely not
a slope.  It's not an expression of rise
over run.  It is going to vary across a
straight line demand curve; unless it's
perfectly vertical, which would be
perfectly inelastic,  or if it's perfectly
horizontal it would be perfectly elastic....
but for any sort of quote-unquote normal
downward sloping demand curve you're
actually going to end up with a unitary
spot or range.   You will end up up here
with the top ...it will have an elastic
range..... and down here towards the bottom
you will end up with an inelastic
range.   The easiest way to start thinking
about why this is the case and why
elasticity won't be constant along a
straight-line demand curve is that when
you are up here in the elastic range any
change in prices are actually going to
be related to changes in quantities;
however,  the changes in quantities
percentage-wise
are quite large, whereas, the changes in
price are relatively small.   If you'll
remember our general formula is
percentage change in quantity demanded
over percentage change in price.  Well in
this elastic range here you've got a
very very big percentage change going on
down here with quantity, but you have a
relatively small percentage change going
on here with price.  Of course if you've
got a big numerator and a small denominator
that number is going to be larger than
one... you're going to get an elastic
response.   Now alternatively if you end up
lowering the price to 1 you're going to
end up with a very large change in price
but you're going to end up with a very
small percentage change in quantity. I hope
that's obvious to see now.  That's going
to produce an inelastic number,  of course
somewhere in the middle you're going to
end up with a tipping point,  so you'd
have a unit elastic or unitary.... but
elasticity is not a slope... keep that
straight in your mind.  And that's going
to also have implications for firms,
because if they decide they're going to
start to change prices (if they're in a
position to do so) it's going to have
consequences.   There will be a range where
they can raise prices and actually
generate more money for themselves,  and
then there is going to be a range where
as they continue to raise prices they're
actually gonna start losing money.  We'll look
at that coming up.  Okay, so let's continue
with that train of thought from the last
slide.  As a firm raises prices sometimes
they're going to make a little more
money,  sometimes they're actually going
to lose money.  You'd like to have some
sort of way to figure out what you
should do if you were a firm who
actually has control over their prices,
or some amount of price making power. 
Elasticity provides us a relationship
between elasticities and total revenue. 
So the general rules here are if you are
in the elastic region of the demand
curve,  then you are going to be able to
increase your total revenue by dropping
your price.  If you are in the inelastic
region,  then you're going to want to
increase your price in order to raise
your total revenue... and the tipping point
where you're at your maximum is where
total revenue, total revenue is maxed I
should say at the unitary spot.  The
easiest way to start to understand this
is to look at it graphically,  If in fact
you are in the elastic region of the
curve and you lower your prices,  you are
going to go ahead and drop price and as
you drop price you are going to grab
some more quantity.  Now total revenue is
nothing more than P times Q, so the area
of that blue box compared to the old
black box that was there shows you
what's happening with revenue. It's going
to be obvious that you lost this area
since--at least I hope it's obvious to you--that
parts no longer in the new revenue box
so this is a loss in revenue, but the
nice thing about it is that you are
going to actually pick up an area here, 
right?... that's new addition and of course
this is a gain to total revenue.  That
blue rectangle is larger than the black
one, so by lowering prices in the elastic
region you actually were able to gain
total revenue.  Now the exact opposite is
true when you are over here in the
inelastic region.  If you were to go ahead
and
decrease your prices here... you would
essentially
grab on to this extra area, but you would
lose this area.  Of course the losses here
are going to be bigger than the gains,  so
by lowering your price in the inelastic
region you actually hurt your total
revenue. Here in the inelastic region you
want to go ahead and raise that price. 
Okay hopefully this helps you to keep it
all straight, uh, the best spot that you can
be at is when your elasticity is equal
to one.  If your elasticity is equal to one
then this will naturally maximize your
total revenue,  this is useful for firms
to know particularly if they're like a
monopoly and they essentially are going
to choose where they want to be on a
demand curve.   All right so we're going to
do something a little different in this
little lecture series... I want you to take
a look at this problem and after we get
it set up I want you to go ahead and
pause the video and work it out....so if I
were to give you a scenario and told you
that the price of gasoline was going to
go from 189 to 217, and the quantity
demand was going to decrease from 20,000
to 18,000 gallons...uh,  I want to know what
the elasticity of demand is, the price
elasticity of demand.... and I want to know
what the changes in total revenue and
does this make sense?  So calculate the
elasticity, then calculate the change in
total revenue and relate it back to
those rules that we were just thinking
about in the previous slides.   Go ahead
and hit pause now and work this out.
Okay, hopefully you got that worked out. 
Let's see if you got the right answer.
I've organized the information from the
last slide in a little demand table
here.  We need to go ahead and stick these
values into our general formula for
elasticity.  We're also going to
eventually take the absolute value of
this, so that matches up with the ranges
that we learned.  Wo our new Q is 18, our
old Q is 20,000.  I'm just dropping
the zeros, because they will go away anyways,
and we're going to add the two of those
together and multiply them by a half,  so
the same thing as dividing by two.   This
is the top part of our equation here.  The
hundreds are going to cancel out,  so I'm
going to ignore those for the moment.  p2
minus p1, we've got to get this
information from our price. Our 18 and 20
came from our QD.   So let's go ahead and
do our price stuff... new price is 217,  old
price was 189,  we're of course going to go
ahead and add those together and then
multiply them by 1/2.   Once you've got all
this plugged in all you've got to do now
is calculate the final answer.  Oftentimes
if you're working by hand, or on a
calculator, it's useful to calculate the
number in the numerator write it down.
Calculate the number in the denominator and 
write it down..... and then divide the two of
them.   That'll help you keep things
straight,  otherwise students have a
tendency to make calculator errors.
Once you plugged all these in you're
going to find out that this comes out to
a negative 0.76,  and if you take the
absolute value of that we're going to
find out that Ed is equal to 0.76 ...and
this is inelastic.  Hopefully that's the
answer that you got. The other piece of
this question is was what's going on with
total revenue? Now total revenue you'll
recall is just equal to P times Q, so
you've got 20,000 times 189 in our
scenario number one,  and then we've got
18,000 times 2 17 in scenario 2.
This is going to work out to be thirty
seven thousand eight hundred and this
bottom one is going to work out to be
thirty nine thousand sixty,  so total
revenue actually has gone up,  which makes
perfect sense... because if we're in the
inelastic region of the curve increasing
the price is supposed to increase total
revenue and that's exactly what we see
happening here.   Total revenue went up by
twelve hundred and sixty dollars. 
Hopefully that helps in terms of setting
stuff up.  All you really need for elasticity is
practice.
