Introduction to the economics of slavery and slave owning
Slavery is a system where humans are legally owned, bought and sold. Like objects they have no say in whether they are traded, cannot leave this state, are forced to work and cannot demand compensation. Chattel-slavery, the original form of slavery, which is what most people think of as slavery, gets its name because the slaves are the owner's personal property and are bought and sold as commodities. Taking slaves across national borders is called Human Traffickingespecially when the slaves provide sexual services.
Chattel-slavery has been illegal in most societies for a long time but persists in forms not always regarded as slavery: debt bondage,indentured servitude, serfdom, domestic servantskept in captivity, certain adoptions in which children are forced to work as slaves, child soldiers, forced marriage, and wage slavery.
Wage slavery and the number of slaves
Wage slavery, wage labour where an employee can't change their employer is the elephant in the room here to be discussed elsewhere, for if the similarities between wage labour and slavery are admitted nearly everyone is a quasi-slave free only to change their master, Even if only those who cannot change employer, prisoners or immigrant labour, (for example with restricted work permits or subject to the sponsorship system used in many Middle Eastern countries, where a sponsor is needed to work in the country and the sponsor's permission is needed to leave the country), are included the number of slaves as a proportion of the world population will rise dramatically. I have been told that in the USA employees lose almost all constitutional rights while on the employer's premises, and in the UK employment law is based on a master servant relation which is close to voluntary slavery and employees in these countries should be considered as quasi-slaves.
According to Wikipedia  there are more slaves today than at any point in history. estimates range from 12 million to 27 million, though this almost certainly excludes wage slaves. Most are debt slaves, mainly in South Asia where debt bondage may last for generations. Since the world population is around 7 billion this means around one person in 250 is a slave, worldwide, whereas, again according to Wikipedia, at the start of the 19th century three people out of four were serfs or slaves.
Slaves, Machines and Status
Economists tend to reduce everything to the flow of money, and this is a good starting point though designer clothes and expensive fashionable restaurants with poor food and rude staff suggest that many swap money for status or the appearance of affluence. Certainly in terms of quelling hunger a cheap cafe beats a thousand pounds per head meal at a top restaurant, and diners at the top restaurants must be getting more than just food for their money.
An apparently callous analogy between slaves and a machines is useful, and paralleled by the evolution of the Personnel department (dealing with humans) into Human Resources (dealing with humans resources to be mined, exploited and thrown away). For business owners the difference between slaves, machinery and hired labour must be reduced to total cost and slavery will not survive if machinery or hired labour become cheaper, unless owning slaves brings sufficient added status to over come the differential, just as many buy designer label clothes, identical to cheaper mass produced clothes but far more expensive.
Chattel Slavery: status versus money
In terms of chattel-Slavery, a purely economic analysis must explain why large scale slavery, a situation where most of the workforce were (chattel) slaves arose only in the classical world and on the east coast of America from Virginia to Brazil [Tullock in 3 though I have not found this statement repeated elsewhere online]. Tullock also notes that the Holocaust and the Gulag might be considered slave labour but that the death rate on the camps was higher than any private owner who had to pay for replacements would tolerate. Tullock neglects the fact however that the Nazi camps were designed to destroy prisoners through work, while in the Gulag no one cared if they lived or died and in both cases there were always plenty of replacements the only cost being that of transportation in Germany and Russia and in Russia the cost of an occasional show trial.
Where slavery is legal labor may hired or purchased The business owner may decide to use slaves instead of employees and the initial capital investment must be recovered over the life of the slaveThe slave owner also has running costs and maintenance (food, drink, medical care....), and security costs (ensuring they do not run away or kill the owner), and can only make a profit on the investment if these costs are sufficiently lower than the wages needed to pay free labor to do the same work. Since slave labor can be very inefficient the difference between slave running costs and maintenance and the current wage rate must be substantial.
Tullock's argument is plausible and explains the adoption of machinery if the running costs and capital investment are less than those of either free labour or slaves, but does not allow for the possibility that say tax regimes may skew the balance in either direction. It also ignores the fact that ownership may bring status and the perceived cost of a slave might be lower if the running costs (food) were produced on the plantation rather than being purchased, whereas the cost of hired labour includes running costs. The analogous situation today is the preference employers have for “regular” employees rather than external contractors, who are seen as more expensive because the cost of the employer's contribution to social security, holidays and pensions is included in the rate charged by the external. Permanent workers are also seen as more desirable because they add to a manager's “empire”. I would note that at the same time many employers will baulk at hiring an individual external as expensive, but will happily pay three times the rate to get an employee of a consultancy, just like hiring someone else's slave for a short project like digging a ditch.
Apart form the total cost of ownership a slave might confer status and an owner might be willing to take a loss on slaves, as long as the business is overall profitable, in order to boost their status. If the price of slaves was seen to be rising, the purchase of slaves in the short term and the breeding of slaves in the long term could be seen as a good investment, though I am unaware of any slave price bubbles in the American West. In the classical world aristocrats were, as far as I am aware, expected to keep slaves and so a slave was a social necessity, just as in 19th century Britain an aristocrat was expected to keep a full complement of servants.
Externalising the cost of Slavery
Tullock says that had the total costs of slavery, including security to prevent them running away, fallen exclusively on the slave holders of Ancient Rome or the American South, the system would probably not have survived Instead, these costs were largely imposed upon the free population by some form of conscription, like compulsory service in the legions (Rome) or the county patrol (USA) and cites George Fitzhugh as saying, "The poor constitute our militia and our police. They protect men in possession of property, as in other countries; and do much more, they secure men in possession of a kind of property which they could not hold a day but for the supervision and protection of the poor." Thus the rich use the poor to keep the poorest of the poor in check.
In brief some of the costs of slave owning were externalised and this cost was more or less happily paid by the community, or more precisely by the poorer members of society protecting the interests of the rich. Today the costs of pollution and outsourcing work to developing countries are also externalised and paid, largely uncomplainingly, by society.
The slave as investment: capture versus breeding
Breeding slaves is a slow expensive process, while capture is cheap. According to  the African kings supplied most of the slaves, something I have not yet found corroborated elsewhere, obtained either as captives of war or as tribute from their subjects. This meant that the kings, the slave traders and the end clients did not have to bear the cost of breeding slaves.
Since what is obtained cheaply is not valued captured slaves were treated badly. Before the abolition of the slave trade (but not slavery), in 1806 in the USA and 1870 in Brazil a slave had an average life expectancy of five years. In the UK in the last few decades government encouragement of importation by big business of cheap labour from developing countries similarly led to exploitation of these desperate wage slaves on the grounds that they could easily be replaced. After the slave trade was abolished, and in the ancient world when there were no wars to supply slaves, the slave became a valuable commodity and could even be regarded as an investment, like shares in a company. Tullock states that since the only two major cases of significant economic use of slaves began during the worst Roman wars, and when slaves could be freely captured in Africa, suggests that slavery is only viable if captured slaves are available. This ignores the possibility of treating the slave like a share in a company to be traded as the price rises and falls.
Manumission and the Prisoners Dilemma
Owners could get more work from their slaves by promising to free them eventually by “paying” them a fraction of the value of the extra work, and the price of their freedom would be more than their free market sale price. This benefited both master and slave but while the individual owner would have been better off with such a deal, widespread grants of freedom to slaves would have endangered the "property rights" of slaveholders in those that were still fully or partially owned. Thus the slaveholders had a motive collectively to favour laws against freeing slaves, and for social pressure against it, even though each one would have benefited from permission to free his own slaves if they were the only one given such permission. This is a classical prisoner's dilemma situation, and may have helped perpetuate the system.
Adam Smith, Slavery and Racism
Brown  looks at capitalism, free enterprise and slavery taking a critical view that covers some of the points made above about slave owning bringing status. One of the first points he makes is that Smith, who he later reminds us was opposed to slavery (illegal in Britain but legal in the colonies, perhaps a case of “out of sight out of mind”), made no mention of it in The Wealth of Nations, preferring to concentrate on what might nowadays be considered microeconomics, in considering how the butcher, the brewer and the baker bettered all by furthering their own self interest, something diametrically opposed to the Prisoner Dilemma mentioned above, where slave owners benefited all by suppressing their best interests. Commerce in Smith's day was the Atlantic Ocean, not the weekly market, trafficking of Tobacco, Sugar and Slaves, not Bread, Butter and Beer over a Glasgow market stall. He also notes that the Atlantic slave trade differed from that of antiquity in that Slavery became part of the global economy. In antiquity many Roman slaves were sold because they had been captured in war, while in the Atlantic Trade Africans were captured in order to make them slaves. He also notes that slavery arose because of the cheapness of the labour, and Negroes were the cheapest labour available. Slavery gave rise to racism once whites began to fear slave rebellions and then began to consider slaves as racially inferior. I note a similar tactic in the Third Reich where Jews were progressively cast as less than human, finally justifying the horrors of the Holocaust.
Brown cites a passage from The Wealth of Nations in which Smith encapsulates non-financial reasons for slavery and by generalisation, for the generally poor treatment of low paid employees (wage slaves).
The pride of man makes him love to domineer, and nothing mortifies him so much as to be obliged to condescend to persuade his inferiors. Wherever the law allows it, and the nature of the work can afford it, therefore, he will generally prefer the service of slaves to that of freemen
Brown states that the absence of treatment of Slavery in The Wealth of Nations, other than the brief mention above allowed the fiction that an unfettered market economy promotes human freedom. It seems to me that Smith turned his back on the slavery that endowed his friends the tobacco lords with wealth and, according to Brown, let Smith live in luxury, concentrating on areas that would not upset his friends or make him confront the darker origins of his comfortable lifestyle. Smith also failed to discuss women in his economic models. The privileges of the rich after the abolition of Slavery continued and continue to be that of ignoring those less fortunate who sweat and burn themselves out to provide food, clothing, shelter and luxuries. The elite have changed from the tobacco lords of Glasgow and the Aristocracy of London to investment bankers and Media moguls and luxuries have grown to include computer games, but the attitude of the elite to their serfs is to use them, burn them out and replace them.
This essay adds no more than a drop to the ocean of ink expended writing about slavery. It has shown how microeconomic forces drive the decision to use slaves rather than free labour or machinery. Adam Smith omitted slavery from his seminal work allowing the fiction to arise that an unfettered free market promotes freedom, a fiction because the freedom he promoted was on the back of slaves. While in the 17th and 18th centuries wealth was built on chattel-Slavery, after the Industrial Revolution wealth was built on wage slavery. At the same time the rich continued, and continue to enjoy the ability to ignore the poor who they exploited in order to enjoy their wealth.