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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