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.

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, ok 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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