We've aready talked about linear demand functions
that actually have changing price elasticity
As we go down the curve
and we've shown the extremes
we've shown things that are perfectly inelastic
and things that are perfectly elastic
What I want to do with this video
and it will be a quick little video
is think about, can we construct a demand curve
-or at least understand what it looks like-
that has a constant elasticity across the curve
and just for fun let's make it a constant elasticity of 1
so it has constant unit elasticity of demand
So let's think about how we can create that
and hopefully it will give us a little more intuition
on how this elasticity business even works
so let's draw our axes
that is price, and that right there is quantity
Now let's put some numbers there, that will just help us
draw this demand curve that has unit elasticity at every point, every price, and every quantity
I'm just going to put some numbers here, that over there is 10, so that's $10 or whatever we're doing,
and that this is 10 units per time period, 10 units per week, 10 units per month, or whatever else.
Now, we want the absolute value of the elasticity of the demand to be equal to 1 at all points.
We're going to assume that this curve meeets the law of demand
which means that as price goes down, quantity demanded goes up.
So let's think, this is going to be a downward slope, and really, we're going to say
so the elasticity of demand is going to be equal to -1
If we have a 1% decrease in price,
we're going to have a 1% increase in quantity and vice versa
so let's think about it. If we're up here,
where the price is nearly $10, and where maybe
the quantity is closer to 1,
let's think about what a 10% movement in price would look like,
a 10% movement down.
It would be about roughly about this size
A 10% movement would be roughly there.
I'm just trying to get the general shape of this curve,
I'm not going into the deeper mathematics behind it
or the calculus of it.
So that is a 10% price movement down
and we also want a 10% in quantity movement up
but remember, our quantity is only 1
so 10% quantity movement up, would only be 10% of 1
so if we're moving 10% in price downwards,
this is a 10% move upwards in quantity
so our curve up here, would look something like this,
which would have to be quite steep.
Now, let's think about what the curve would look like over here.
Now, once again, we want 10% for both of them.
Because we want the price elasticity of demand
to be 1 throughout the curve.
So, if we go over here for a 10% movement in price,
so let's say we're down here where price is close to 1.
A 10% movement in price is going to be very small.
A 10% movement in price is going to be like that,
It's going to be roughly a tenth of a unit
so that's a 10% movement in price,
but a 10% movement in quantity demanded is going to be
much larger, it's going to look like that
because the quantity is approaching 10, so 10%
of that is about 1 unit, just like that, so at this point in the graph
it would look something like this
it would flatten out a good bit, just like that, and when
the price and quantity are the same
so let's say that this is 2, and this is 3,
right over here, your percent movements are going
to be the same, but since the price and quantity are the same
the absolute movements are also going to be the same
so at that point
our curve should look somthing like that,
it should have a slope of one
so if you connect the dots, you would get the general shape of a demand curve
that has a price elasticity of demand of -1 throughout
the curve, whose absolute value of the price elasticity
of demand is 1, so let's just
do that, so the curve will look something like that
it will keep getting steeper, as we get the quantity closer to zero
and it would keep flattening out as the quantity
grows and grows and grows.