Applications Using Elasticity

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 -- 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.