Since the article 'The Economics of Slavery in the Ante Bellum South' by Conrad & Meyer and especially the book 'Time on the Cross: The Economics of American Negro Slavery.' by Fogel & Engerman,
I'm not going to attempt to summarize the extremely long debate that has been running since Conrad and Meyer published in 1958 and Fogel and Engermen in 1974. Suffice it to say that there have been numerous closely argued and carefully documented articles demonstrating that both cherry-picked atypical circumstances and made errors in their interpretation of the data.
As for there being conditions under which slavery is economically efficient, as I said there are 'certain very limited exceptions'. These involve the absence of non-slave labor and the absence of any way to induce or acquire non-slave labor. The simplicity of work has not been found to be a significant factor in increasing the efficiency of production through slave, rather than free, labor. The degree to which work shortens life-span has been found to be a factor, in that it ties in to the ability of employers to attract non-slave labor (in the Caribbean, for example, production of tobacco was mostly done by free labor, but when the economies of that area converted to largely sugar production, the intolerable working conditions and high death rates meant free workers would not undertake it. Sugar thus could not have been produced in these areas without slave labor, making slavery an 'economically efficient' choice).
This was the situation in the very early years of the colonization of what is now the USA, for example, and it made slavery a rational economic decision for a short period. Ironically, the agricultural fertility of the southern states enabled land owners there to outbid their northern neighbors for slaves, which is why slavery was geographically concentrated in the USA. After a decade or so, when immigration and then natural population increase caught up with labor demand, slavery ceased to be an efficient mode of production, leaving the southern landowners stuck with the sunk costs of a less efficient labor force they could not fire, lay off seasonally, or even free (it was illegal to free slaves in many slave states). Also ironically, the expansion of publicly expressed anti-slavery sentiments in non-slave-economies such as the northern parts of the USA and England post-dates the demographic and economic shifts that made slavery obsolete as an economically rational choice. Tracking public (and private, through correspondence) comments about slavery in places such as New Hampshire, for example, shows a transition over several decades from "I would use slaves if those damn southerns didn't buy them all at prices I can't afford" to "I would use slaves if it made sense but free labor means I make more money" to "Slavery is bad".
The kindest interpretation is to suggest that the alleviation of urgent economic pressures freed people to more broadly consider the social and humanitarian implications of slavery; less kind, one could suggest that opposition to slavery was an opportunistic, 'making a virtue of economic reality' matter. I also wonder, although I am not aware of any study that explores it, how much northern antipathy to southern slavery had roots in the early colonial resentment at being deprived of access to what was at the time a scarce labor source.
I also note that there is little good data on the economic efficiency/ inefficiency of slavery in Classical times, in part because it is very difficult to find comparative economies in which one utilized slave labor and the other free. One might hypothesize that expansionist states such as the Romans found themselves, at least in early decades, comparatively short of labor, and the use of slaves freed up Roman citizens to undertake military and political service, thus enabling the continued expansion of Rome and, in that sense at least, 'efficient', regardless of the questions of whether or not actual production would have yielded greater output or economic growth would have been quicker using free labor.
This of course raises the question of how different societies see 'the economy' and 'efficiency'. We have not, in this discussion, really touched on the idea that 'the economy' is not a purely factual descriptive term but a value-laden one that includes or excludes different kinds of production and value creation depending on social values - for example, house work, child rearing, and other caring work has only recently been included by some countries in their assessment. A society's
own view of the efficiency of its economy would be affected by, not only its view on what the economy is
for, but also what the economy
is.