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 in 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 ban 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, uh, next chapter.

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