Elasticity and the Economics of Slave Redemption

Should economists shy away from teaching hard topics for fear of offending someone’s moral sensibilities? Should we restrict ourselves to the market for ice cream? The tagline of our textbook, Modern Principles, is See the Invisible Hand: Understand Your World. We take understand your world seriously and we teach topics that other textbooks do not such as the economics of network goods like Facebook or the economics of tying and bundling which students see regularly when they purchase cell phones and minutes and Cable TV.

The world, however, is not always a pleasant place and so we also discuss modern slavery and how the concept of the elasticity of supply can help us to evaluate programs like slave redemption. It’s important to teach this material with seriousness, it’s not an idle exercise in “freakonomics,” and it’s possible to misstep but we think students need to see economics as a vital discipline that can be used to make the world a better place, even if only one small step at a time.

Here is Tyler on elasticity and the economics of slave redemption. This is from the elasticity section of our course at MRUniversity, released today along with taxes and subsidies. You can also find a lengthier treatment with more details in Modern Principles.


By all means teach it, but only to an audience already sufficiently knowledgeable in economics. Otherwise before you know it you'll be accused of being a neoliberal slavery-apologist. It's the same if you're trying to teach e.g. the economics of sex trafficking.

This is one of my favorite parts of the micro sections in the book (I only touch on it in principles of macro): it demonstrates the versatility of the economic way of thinking and shows us that while economics can help us with a lot of fun and irreverent topics ("should I finish watching 'Anchorman 2' even though I hate it after 30 minutes?"), it also helps us understand some of the most serious moral crises people face. Economics also guides us toward ethical maturity by showing us how good intentions can lead to bad results.

The "dismal" implication is that slave redemption can make things worse, but economics also gives us reasons to be hopeful. By framing the problem correctly, we can start to identify what might work.

This lesson is nominally about the elasticity of supply, but I will suggest that it's intended to impress upon the student that government programs intended to do good often do bad. Cowen and Tabarrok could have used the subject of slavery to teach a different principle, namely that slavery, while it may appear profitable to the slave owner to pay nothing for labor, was actually unprofitable because, for example, slaves had no incentive to become better at their jobs.

"while it may appear profitable to the slave owner to pay nothing for labor, was actually unprofitable because, for example, slaves had no incentive to become better at their jobs."

There were plantations using slave labor around for over a century. So I don't believe the argument that slavery was "unprofitable".

There is another argument that says technological changes were on the cusp or had just crossed over to the point of making slavery unprofitable. That seems possible, but not really provable.


Slaves weren't the only ones picking the cotton, there were plenty of free blacks and poor whites doing it as well.

This lesson is nominally about the elasticity of supply, but I will suggest that it’s intended to impress upon the student that government programs intended to do good often do bad.

This seems very ideological and judgement loaded IMO. I think economics has two underlying assumptions:

1. There are constraints on resources used for inputs and as a result for outputs.
1.1 AS a result there are a huge array of possible choices or outcomes.

2. Attempts to maximize the outcome acts as a potent attractor that allows us to explain a sizeable portion of behavior and predict outcomes.

These two statements, I think, are general enough that you could apply economic theory to a lot of things other than money, commerce, and even human behavior (for example, you could analyze how ant colonies utilize resources). The intellectual enterprise of economics then is to see how far we can get with #2. What are the boundaries, if any, of economic explanations as the causes of behavior and outcomes?

So take your statement that gov't programs often do more bad than good. Then why are they around? #1 and #2 would say they are around because they are benefitting someone or something and that benefit means they will use more power to defend the program than those harmed will use to end the program.

Since when are ants humans?

Of course, this is an ideological web site, so I expect ideological posts. But sending an ideological message in the guise of teaching an economic principle is more like indoctrination than instruction. Doing Bad by Doing Good, I get it. It reminds me of the Upside of Down: Why Failing Well is the Key to Success and the dialogue between the author (McArdle) and Cowen hosted by, I believe, someone from AEI, who tried, valiantly, to get the two to address the greatest failure of the past 50 years and what those responsible learned from it but, alas, the host got nothing other than a wave of the hand. Seeing the world through an ideological prism is fine for a zealot, but not an academic.

Hang on a minute. Government programs are backed with the force of armed police, funded by taxes taken if necessary by the same force. And implemented by people with no stake in the outcome other than its perpetuation. And you are insulted that the question of their effectiveness is even raised?

The 20 the century was defined by the utter evil of government programs implemented at the cost of millions of lives. Those were the worst cases. The working countries ended the century by reforming, scaling back or optimizing the government programs from earlier years as the full effects of their implementation became apparent.

It was definitely profitable for the slave owner. And surely there were efficiency gains to be had. Study (formal and informal) of optimal working conditions would and likely did improve efficiency.

What I think you've meant to say but horribly misconstrued, is that slavery is less efficient than non slavery as a social policy, because it reduces the incentive on the worker to increase productivity and invest in their human capital.

Nonetheless, I'm not sure I buy even your revised theory, slaves could/would have some incentive to be more profitable to their owners. Less beatings, more rations, more sleep etc. etc.

Decent Econ 101 video especially on deducing elasticity from price. To complete the video there should be a discussion of what happens to the supply curve (it shifts up) if slavery is outlawed.

Yes you should restrict yourself. The weird way you guys push stuff like this makes the otherwise excellent book hard to adopt. I am not a teacher that shies away from controversy, but there's just no pedagogic reason to go there. I steer very clear of those parts of your book and really wish they weren't there.

Move on up to the 6th graders then, they're not so removed from the world.

No, you should not restrict yourself. If students cannot be taught that economics can be used to analyze important questions like this, they might as well not be taught economics at all.

I don't know if it's just my impression, but the video makes it seem like the number of enslaved people could actually increase if supply is sufficiently elastic. But even if supply were perfectly elastic, the number of people actually enslaved wouldn't increase, it would be exactly the same as before, with each "redeemed" slave set free, and all the originally enslaved people still enslaved.

The point of the video still stands, that the charitable practice of redeeming slaves is offset by the fact that it increases the demand for slaves and thus increases the quantity of people captured as slaves, but I think it bears clarification that the reduction in enslaved people will be somewhere between 0 and 1 per redeemed slave.

On further reflection, it also bears clarification that since the actual process of being captured for enslavement is surely terrible, even if you are later released, then the program of slave redemption could do more harm than good. And if some people are killed in the process of trying to bring them to market, that's even more terrible. So these points certainly weaken my original critique of the video.

William, both of your points are correct and are discussed in the textbook and in more detail in a second video in the elasticity section that can be found here:


...and while the number of enslaved people would decrease in the scenario described, some free people would become enslaved, which is also terrible.

The road to Hell is paved with good intentions.

Is it also possible that redemption does damage beyond what the supply-demand curve predicts? That is, by turning slave trading into a bigger business, they increase the capacity of the slavers and thus cause more than one new slave to be taken for each one bought? Or does that argument somehow double-count something.

Fair point. It's possible. See the graph on "Long Run Supply in a Decreasing Cost Industry" (find "downward sloping supply curve"):


I think there are two answers (at least) to your question. I would say the Econ 101 answer is that there will be fewer slaves in the sense of fewer slaves actually being consumed. Why, clearly the redemers are going to out bid the marginal slave buyer who wants to consumer the capial good services the slave represents. Those marginal buyers are prices out of the market ultimately. Since the total demand for really has not changed -- and that's masked in the story told about the supply side. So we probably end up with a more inelastic demand curve but pretty much the same equalibrium positoin in terms of quantity of slaves sold per day (or whatever time frame the graphs are representing). So there really isn't an incentive to invest in new slave producing technology that would result in a downward shift in the supply curve making the increase in quantity supplied at a givern price possible.

That, however, ignores some importand things your comment raises -- such as what are the holding costs of slave inventory or are they treated as parishable goods any that didn't clear the market are summarly killed. In that scinaro the initial supply response to the new bidders and preceived shift in demand would result in a lot of people getting killed that otherwise would not have.

(The reality of this is that the whole discussion assumes that the market actually works like the pictures which is probably not the case. In reality the slavers will probably sell some surplus at "below market" as they walk down the demand curve as the cost of getting the slave is sunk, there is a holding cost and there is clearly an opportunity cost of not selling the extra slaves cheap as long as it's not unmining the "normal market" prices that the lecutre was suggesting are pressent. In other words there will be a lot of noise in the data and the economic theory cannot conclusively tell us the answer. The answer to whether the redemption program resulted in more or less people actually being slaves would require a fairly significant empirical research effort of direct observation and sampling -- after which we can then calculate all those economic elements but wouldn't really need to because we could simply to some simple math to get the answer.

Now, this should not be taken as bashing economics, merely pointing out a limitation of the field.)

Before I watch the video it is my impression from history that African slavery was the norm in both North and South America (but not in Europe). The importation of new slaves was outlawed in the US soon after the Constitution was ratified but the US was the last American country to have slavery.

While the South fought for slavery up until the end of the Civil War, the ban on importing slaves was one anti-slavery policy that was allowed to be enacted. Southern slavery therefore had to renew itself by slave owners also enslaving the children of existing slaves.

Was the ban on importing new slaves actually a pro-slavery policy since it gave existing slave owners a monopoly on the sale of slaves (if you wanted to buy one, your only choice was from someone who already owned one)? Did this actually make the incentive for supporting slavery stronger in the US by giving slave owners exceptionally strong property rights/incentives not only in the current stock of slaves but also future slaves and the institution as a whole?

Well the practice of capturing slaves was brutal and the transportation to the New World had a high casualty rate. Furthermore, the children of female slaves were considered slaves long before the Atlantic slave trade came to a halt.

So, I think on net stopping the Atlantic slave trade was a positive.

"...the US was the last American country to have slavery."

Not clear what you mean by "American country", but if we are talking about the Americas, Cuba abolished slavery in 1886 and Brazil (which imported more slaves than anyone else) abolished it in only in 1888.

"While the South fought for slavery up until the end of the Civil War .." Kind of. They wanted a Constitution that placed more emphasis on the rights of the states, and when they decided they weren't going to get it, they left the union. Slavery was just on thing but there were other things. They did not like the Congress passing trade tariffs, for example. In 1828 Congress protected northern manufacturers but hurt the economies of the southern states by passing a tariff on manufactured goods from Europe. Various states declared the tariff unconstitutional within the boundaries of their states, and the Feds sent the Navy to enforce the tariffs.

"They wanted a Constitution that placed more emphasis on the rights of the states": not while they controlled the Federal government, they didn't.

"not while they controlled the Federal government, they didn’t. "

Yes actually they did.


Not sure I buy that. If they wanted more emphasis on states' rights would they have accepted a compromise that consisted of banning slavery in exchange for numerous states' rights provisions? I doubt it. Slavery was integral to their economy and the economic growth of the North implied that sooner or later they would be outnumbered. 'States rights' was an ideological speed bump to try to slow down the work of democracy undermining slavery.

Have you read the South Carolina Articles of Secession? All it talks about in regard to states rights is slavery.

The South Carolina Articles of Secession were 30 years after the Nullification Crisis.

Slavery in the ante-bellum US, a topic that never goes away. Let's always remember the horror of slavery but forget the murder of the native Americans and the theft of their property. Would there have been a difference in the economic development of the country if the European invaders would have to pay a fair price for the land, if the natives had effectively refused to give up their property or the European invaders would have had to conform to the existing forms of property ownership?

We would have done just fine under those conditions, and the American Indians and Indian-governed lands would be a major force in the affairs of the United States.

This context, presumably, is this criticism from Joseph Heath.

I got that impression too. And Alex really misses Joe's point, which is not that economics should shy away from controversial topics. Rather, he's concerned a lot of economics curricula builds in certain ideological conclusions. In particular he has critiqued the inconsistency among economists who are willing to talk about efficiency about not fairness given that both are equally normative standards. (i.e. efficiency is a moral consideration, not purely scientific.) This lead him to write a mini-textbook on normative economics: http://homes.chass.utoronto.ca/~jheath/text/table.html

"In particular he has critiqued the inconsistency among economists who are willing to talk about efficiency about not fairness given that both are equally normative standards"

I'd highly dispute the "equally normative" phrase. Efficiency is, considered on it's own, nearly universally praised. When it's condemned, it's not generally condemned intrinsically, but instead because it may lead to a change to the status quo.

Fairness on the other hand is often in the eye of the beholder and in contentious matters what one person considers fair another considers unjust.

*But it doesn't matter that fairness is in the eye of the beholder*

All that matters is that there is a preference for it, and folk will take that to the polls on election day. Social disputes are resolved by the legislature and the courts. If the citizenry wants to fuck themselves over with inefficient laws, let them; it's what they want. To do otherwise is egregious paternalism.

"To do otherwise is egregious paternalism."

Yes, that's a good point.

Are you saying that the distribution of surplus has not bearing on whether or not we should consider the allocative efficiency of the a market system good or not? Keep in mind here that the underlying assumption of my question is that the equilibrium position is the same, it's just who gets how much of the surplus (consumer & producer) that's in question.

"This context, presumably, is this criticism from Joseph Heath."

From the linked article:
"Why people hate economics, in one lesson"
"But Tabarrok and Cowen are unable to restrain themselves, and so instead of trying to make the action theory seem platitudinous, they present it in a way that makes it seem both morally suspect and politically conservative.
shows that they can’t resist getting a little dig in against the left, with its tender-hearted conviction that government can be an effective force for good in the world.
Unfortunately, if students get fed moral skepticism and right-wing ideology – or if not exactly right-wing ideology, then something that sounds an awful lot like right-wing ideology – on the very first day of class, many will conclude that economics as a whole is unworthy of their attention.

How are Alex and Tyler present something in a way that might make it seem politically conservative! That's not how academia works. The author reads like a person "Who Hates Capitalism" is upset because conservatives are contaminating his economics with their ideas.

Get back to me when he starts posting critiques of Paul Krugman's ideological editorials.

It is a really confused critique. Yes, as he points out, most people know that incentives matter, but most people don't apply that remotely universally to situations. Hence the prison ship example. In addition, one of the main moral insights from economics (not exclusively from econ, but certainly reinforced there) is that good intentions are not enough, hence the references to failed ways of improving the treatment of prisoners on the ships. That's not a right-wing ideology at all.

Heath is speaking from experience both a former student and as someone who teaches applied decision theory. His contention is that the standard way econ is presented can be alienating. If you can't see how you're already too deep in the bubble. Health's popular econ book Filthy Lucre was his attempt to do pop-econ without the right-wing subtext by dividing it into left and right wing fallacies. And his other popular book, Rebel Sell, is essentially a critique of the countercultural left. So while I can't speak about his views on Krugman, Heath doesn't pull punches on the left or the right.

Regardless of whether he punches both the right and the left, he clearly objects to Tabarrok and Cowen video/text, not because the points are wrong, but because it's made from a politically conservative perspective.

Before the Civil War, the importation of new slaves into the US was illegal making the supply elasticity near 0. It would be interesting to compare how much it would have cost the North to purchase the freedom of the slaves vs how much the Civil War cost the North and the whole country.

A solid explanation of the concept of elasticity of supply.

However, what I think you are really attempting to do is to teach the law of unintended consequences. However, attempting to teach that law to liberals makes them recoil quite badly. It looks like in response you used one of the harshest examples available. While this may actually be enough to break through to some students, I think it will reduce sales of the book since liberal professors, who will not be swayed by any argument, will reject your book due to this chapter.

Interesting, as I have worked through this, as I would assume you already have, I find that you have foregone profits simply for the hope of teaching an important idea to some percentage of students. That is quite altruistic in some ways.

When I took an Economic History class as an undergraduate, this topic was brought up. The professor (one Jeremy Atack) crunched the numbers and argued fairly persuasively that the material cost of the Civil War -- ignoring the loss of lives -- exceeded the market value of the U.S. slave population in 1861 by a fair measure. I believe this remained true when looking only at the Union's material costs. I've tried to find this analysis online, but a quick search didn't reveal it.

Of course, I'm not sure that an agreement could have been reached at any price, but if the parties in power were rational, it seems a deal could have been struck.

"... but if the parties in power were rational, it seems a deal could have been struck".

This is why so many people mock economists (the assumption of can openers, ladders, and rationality).

Trigger warning

Would it have a more positive impact if the payment for the slaves was in the form of a high velocity piece of lead? That would appear to reduce the demand.

Apparently every generation of academics has to fight for the right to be academics:


The video was doing real well until the end where it claimed that fluctations in price were evidence that supply was elastic. In a perfect, unregulated, market, that might be true. But this is a far from perfect, far from unregulated market (even if informally by cultural expectations). So this is not good evidence in either way.

Economics: when the theory doesn't match the evidence, discard the evidence.

Seems to work with Climate Science too for that matter.

While I realize the subject was elasticity of Supply the larger discussion -- summarized in the statement good intentions are not sufficient -- seemed a bit misplaced. First, the general idea can be discussed without recourse to the economic element. Second, if one is going to start making such a point then consideration of the demand side in greater detail is required. We don't know if the slave redemers have displaced others demanding slaves who were forced out of the market due to the rise in price, resulting a decline in prices as these marginal slave buyers leave (we need to understand price elasticity of demand).

For this reason I think using such "hard" subjects to present basic, but isolated, elements of economic analysis is misguided -- it lends itself to implying conclusions that are not merited whereas more nuetral topics -- like ice cream will not have that natural tendency towards moral conclusions.

How about another similar dilemma. Does the paying off ransoms to the various political extremists encourage more hostage taking, or is it a display of compassion towards the hostages and their families?

These are hard questions and force us into the very uncomfortable position of recognizing the market for evil.

The question and implications of paying off ransoms to hostage takers is a bit different than the slave trade setting. Moreover I see you're asking the question and suggesting it be discussed without using a partial economic analyst as you setup for the discussion. That fits directly into my first observation.

Yes, I agree these are hard questions and the subject mater rather uncomfortable for trying to keep emotional responses out of the analysis. But that's not why I took issue with the effort. The problem is just using elasticity of supply cannot get us to any conclusion about the end equilibrium and so to any indication as to good or perverse results from that slave redeemer's attempts to manipulate the market outcomes.

As the the question of "market for evil" that's going to raise even more difficulties for the economic analysis as it's not at all clear to me that pecuniary profits are what really drive such a market. Applying that to the issue of slaves, perhaps the slavers would be perfectly happy getting half the price of for the slave because they really only need to cover basic costs or operations and the taking and abusing of other humans until sold at the slave market is really what their compensation is. What's *that* supply curve look like and what's it's elasticity characteristics?

The statement that good intentions is not enough is misplaced? Odd criticism of Alex and Tyler. You should be criticizing the actual slave redeemers.

You miss the point being made. The redeemers are not the ones suggesting that a partial economic analysis can lead to any initial inference about conclusions of the end results. The attempt to get to perverse outcomes due to good intentions, but not thought through, is very premature in that lesson.

Like Marshall (or was it Mill?) said -- you cannot do your cutting with only one of the blades. (Yet oddly enough that's actually how most textile workers will use scissor just that way more often than not. But then economics is not textiles.)

Well this has been a bad week and clearly my brain has not been engaged well as I little of I've posted holds -- too bad my fingers were willing to go along with me.

A good video, but let me suggest that greater elasticity may suggest that at least some of the slaves at the margin aren't really "slaves" to begin with. Some savvy fellow might set up camp in Sudan and spread the word that he'll pay $5 to anyone who is willing to live in a hovel for one day and pretend to work, which happens to be the day he expects their naive rescuers to show up willing to pay $100 per head.

Comments for this post are closed