Applications Using Elasticity

In this video, we take a look at real-world applications of elasticity, using the examples of slave redemption in Sudan and and the effects of gun buyback programs in the U.S.

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- [Alex] In the last video,
Tyler introduced the topic

of slave redemption

and how elasticity can help us
to understand its consequences.

In this video,
we'll dive deeper into this problem

and show how to analyze it using
supply, demand, and elasticity.

We'll also look
at some other real world

applications of elasticity.

Let's get started.

- [Tyler] Okay, let's begin our analysis.

We'll put the price of slaves
on the vertical axis,

the quantity on the horizontal axis.

And this is the demand for slaves
from potential slave owners.

So, this is the demand --
if you like -- from the bad guys.

It often helps in these situations
to begin with a polar case.

So let's assume to start
with that the supply of slaves

is perfectly inelastic --
that is, it doesn't respond at all --

quantity supplied of slaves
does not respond to the price.

Given these assumptions,
the equilibrium is found at point A

with a price of slaves
of $15 per slave

and with 1,000 people being enslaved --

being put into captivity

every period --
every year, in this case.

Now...

what does the redemption program do?

Well, what the redemption
program does is it increases

the demand for slaves.

So the demand for slaves

now shifts out --
twists out -- to this red curve.

And this is the demand
from the potential slave owners

plus the demand from the redeemers.

So, this is the total
demand for slaves.

And with that new
increased total demand,

what we see
is the equilibrium is at point B

with a price of slaves
of $50 per slave.

Now -- that increased price
of slaves is a good thing

from the point of view
of the program

because it's precisely
that higher price

which is going to discourage
the potential slave owners

from buying slaves.

It's that higher price
which prices them out of the market.

What the redeemers are really doing

is they're making
slaves too expensive

for potential slave owners to buy.

So the potential slave owners

start off at a price of $15
buying 1,000 slaves.

At the higher price of $50,

the potential slave owners
only buy 200 slaves.

So, 200 slaves end up
being held in captivity

after the redemption
program -- per year --

compared to 1,000
before the redemption program.

So, what the redemption program does
is it ends up freeing 800 slaves.

And in this situation

where the supply curve
is perfectly inelastic,

the program works quite well --

in the sense that every freed slave

would have been a slave

had it not been
for the redemption program.

That is --
of these 800 freed slaves --

all of them
would have been held in captivity

were it not
for the redemption program.

And what we're going
to see in a minute,

is that when the supply curve
is more elastic, that's not the case.

When the supply curve is more elastic,

the redemption program itself
can increase the number of people

who are enslaved
at least for a period of time.

So let's take a look now

at the case where the supply
curve is more elastic.

So now, we're basically
going to repeat the analysis

but with a more elastic supply curve.

So here's our demand curve --
just the same as we had it before.

Here's our more
elastic supply curve.

Notice that I've drawn the curves

so that the equilibrium is exactly
the same as it was before --

that is, at point A.

The price of slaves
is $15 per slave

and there are 1,000 people

who are enslaved
in our initial equilibrium --

again -- exactly as we had before.

Now, what does
the redemption program do?

It increases the demand for slaves.

At the new higher demand --
okay, we’re at point B --

is our new equilibrium.

At point B,

notice that the price
of slaves is $30 per slave.

Not $50 per slave --

the price has not gone
up as much as it did before.

Why not?

Well, the price hasn't gone
up as much as it did before

because now the higher price
induces a greater quantity supplied.

So now,
what the redeemers have done

by increasing
the demand for slaves,

they've increased
the incentive of the slave traders

to go out and capture more slaves.

And indeed, before,

the slave traders were capturing
1,000 people per period --

now they're capturing
2,200 people per period.

So there's been
an increase of people

who are enslaved --
who are put into slavery -- of 1,200.

The program still works
in the following sense.

The quantity of slaves

demanded by the potential
slave owners does fall,

not as much as before

because the price
isn't driven up as high.

But the price rises from $15 to $30

and that reduces
the quantity of slaves

demanded by the potential
slave owners to 600.

So the program
is still successful

in the sense
that before the program begins,

1,000 people are held in captivity.

After the program,
only 600 people are held in captivity,

so 400 people are freed.

However, those 400 net freed

come at a high price

because now...

...1,200 additional people

are put into slavery --
at least, for some period of time.

A bunch of them
are then bought up

but 1,200 of the 1,600 people

who are redeemed
would not have been slaves

had it not been
for the redemption program.

So the redemption program ends up

in a sense, freeing more people --

the number of people
freed on the books is 1,600.

But 1,200 of those

wouldn't have been slaves

had it not been
for the redemption program itself

driving up the price of slaves

and the incentive
to capture more slaves.

So, on net, only 400 people
are actually freed.

So the program is less successful

when the supply curve
is more elastic,

really, for two reasons.

First,

the number of people
who are freed on net goes down --

we don't get as big a drop
in the quantity of slaves demanded

because the price
doesn't go up as much.

The second reason, however,

is that in order
to get that net freed,

we've actually created more slaves,

we've actually created
more people who are captured.

So, at the end of the day,

400 people are still freed.

On net, fewer people end up
being slaves at the end of the day,

but to get there,
at the beginning of the day,

we've got a lot more
people who are enslaved --

who were taken
by the slave traders.

So, this makes it very difficult.

The more elastic
the supply curve is,

the less successful
the program can be

and the more of these terrible,
terrible trade-offs that there are.

And if we remember
some of the facts about elasticity --

in particular, remember...

supply curves get more
elastic in the long run --

well that's exactly what we saw
in the case in the Sudan.

At the beginning,

the redemption program
increased the price of slaves a lot,

but as the supply curve
became more elastic over time,

the price of slaves began
to fall back down again --

it was not increased by as much.

And thus, this redemption program

became less successful over time.

So, this is a very tricky issue.

It's a very controversial issue.

Did the groups like Christian
Solidarity International --

were they on net helpful?

There are these terrible trade-offs.

Economics can't answer this question,

but it can at least point
to the supply response

and what that means in moral terms.

Let's look at another application.

Let's look at another
important question

which we can analyze
using demand and supply.

What is the effect of gun buybacks?

Now these buybacks

are often sponsored
by local governments,

the local police,
the local mayor and so forth.

In this buyback --
which was held in Oakland --

the officials offered $250 cash

for each working gun,
no questions asked.

They then collected the guns
and they melted them down.

The idea was to get
guns off the street.

They ended up collecting
about 500 guns in this buyback.

These buybacks are often held.

There's been one
in Washington, D.C.

and Rochester, New York,
and throughout the United States.

They're fairly common,
again, at the local level.

The question is:
can these buybacks be effective?

And to answer that we need
to make some assumptions

or we need to know something
about demand and supply.

In particular,

what assumptions would make sense

about the elasticity of supply?

Is the supply curve of guns
to a city like Washington, D.C.

or Oakland, California --

is that supply curve going
to be inelastic or elastic?

Bear in mind what that means.

So we're looking

at the elasticity of supply

of guns in a city

like Washington, D.C. or a town.

Also bear in mind

that the United States as a whole --

there are hundreds
of millions of guns --

and that guns continue
to be produced, manufactured,

bought and sold, every day.

So what assumptions would you make

about the local supply curve

of guns in a city
like Washington, D.C.?

Think about that.

I'll give you an answer
on the next slide.

The supply of guns
to a local region

is going to be very elastic.

Remember our earlier example

of suppose that we have an increase

in demand for gasoline
in Washington, D.C. --

is that going to increase the price
of gasoline in Washington, D.C.?

The answer is no --

because just a tiny
increase in price

and lots of gasoline
will come in from Virginia,

from Maryland,
from other states in the country.

Remember,
the more local the supply,

the more elastic the supply curve.

So, an increase in the demand
for gasoline in Washington, D.C. --

that's not going to increase
the world price of gasoline.

And it's not even going to increase

the price of gasoline
in Washington, D.C.,

because if it did,

people would start
to sell gas in Washington, D.C.

instead of next door,
in Virginia or Maryland.

So the price has got
to be about the same

throughout the United States.

The same thing is true for guns.

The supply of guns
to a local region

like Oakland or Washington, D.C.
is going to be very elastic.

That has surprising facts.

It means that local buybacks

won't affect the number
of guns on the street

nor even their price.

Let's take a look
at the diagram.

Here is our demand curve for guns.

Here's our supply curve,

which is drawn very elastic

because it's a local market.

The initial equilibrium is at point A

at a certain price of guns
and a certain quantity of guns

traded each period.

What the buyback
does is it increases

the demand for guns,

shifting the equilibrium to point B.

So the buyback --
they end up buying a lot of guns,

but all of the guns
they end up buying

come from the increase
in the quantity supplied.

Notice that the buyback
doesn't push the price of guns up.

Because it doesn't push
the price of guns up,

no one stops buying a gun.

Remember, a buyback
is going to be effective

only if it makes guns
more expensive --

only if it reduces
the quantity demanded of guns.

Since all of the increase in supply

is being generated
by the buyback itself,

the buyback doesn't increase
the price of guns in Washington, D.C.,

therefore it doesn't reduce
the quantity demanded of guns

in Washington, D.C.,

therefore no effect
on the number of guns held.

Now in particular,
what's going to happen

is that if the mayor
offers $250 for a gun,

people are going
to go into their closet,

they're going to find
an old low-quality gun --

a gun they don't really want.

They're going to turn
that in and maybe a few weeks

or a few months later,
they're going to buy a new gun.

Think about it this way.

Imagine for whatever odd reason

that the government
in Washington, D.C.

wanted to reduce the number
of people wearing sneakers.

So they offered
a sneaker buyback.

For $50, they would buy any pair
of sneakers -- no questions asked.

Well, of course people are going
to go into their closet,

they're going to find
old pairs of sneakers

they don't really want anymore
and they're going to turn those in.

They're going to sell --

they're going to sell
those sneakers to the government.

But -- is anyone in Washington, D.C.

going to end up,
in the long run, going shoeless?

Even going sneaker-less? No.

They may turn their sneakers in,

but a few weeks
a few months later,

they're going to be buying
a new pair of sneakers.

We haven't changed
the price of sneakers,

therefore we haven't changed
the quantity demanded of sneakers,

therefore we're going
to stay at the equilibrium.

Once the buyback is over,

we're going to be
at the same equilibrium at point A.

So local gun buybacks don't work.

They're really --
in my view -- a waste of time.

This doesn't mean
that we can't do anything.

We may want to put
more police on the street,

we may want
to fight crime in other ways,

but a local gun buyback
isn't going to work.

Another point, a few countries,

such as Australia,
that had required buybacks,

mandatory buybacks,

where they banned guns
and then, buy them back.

Well, since that's, A Mandatory,
and B for the country as a whole,

that might get guns off the street,

but here, we're talking
about a local buyback.

And because
of the elasticity of supply,

it's not going to affect
the number of guns

on the local streets
nor even their price

and thus it's going to be,
in my view, completely ineffective.

It's really quite amazing
how a little bit of economics

can go a long way

to understanding
and improving public policy.

Hopefully, you see the argument

about the elasticity
of supply of guns

and yet we see these policies
being passed all the time,

these ineffective policies
are actually often put into place.

A little bit of economics

goes a long way
to improving public policy,

if only we can get the message out.

Okay, thanks very much.
See you next chapter.

- [Narrator] If you want to test
yourself, click “Practice Questions.”

Or, if you're ready to move on,
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