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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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