Were slave plantations economically superior or inferior to plantations with paid labor?

In this course taught by David Blight, he explains that slavery was extremely profitable.

EDIT Per comments, Blight explains that slavery was profitable enough to warrant, among other things: 1) a free soil political movement in the North and 2) a willingness, in the South, to secede from from the Union and engage in a brutal civil war.

I don’t remember the micro economics of plantations, but slaves were valuable. This value derived from their economic value (as opposed to simply luxury or status).

https://itunes.apple.com/us/course/the-civil-war-and-reconstruction-era-1845-1877/id733019681

The Romans (well, a few stoic philosophers at least) already knew slavery was economically unsound. A slave needs to be housed, cared for, fed, medicated and supervised. Also during the hours the slave doesn't work. (Being sick, sleeping or whatever.) No matter if you manage them poorly or generously. Nobody likes to be a slave, it's quite common to work as little as possible. Hence the myth of lazy and stupid Africans. They weren't lazy or stupid, but appearing that way saved them a few lashes.

Hiring non slaves is initially more expensive, but you don't have to pay for housing, caring, feeding and medicating. You do have to supervise your employees, but no where near the level you need for slaves. You only pay them for the time you use them. How to keep themselves alive is their problem.

I agree that a lot depends on specific circumstances, but compare it with a modern taxi. Per km driven far more expensive than owning a car. If you consider all costs of a car (parking in a garage, insurance, maintenance, etc.) it's cheaper than owning a car. You only pay per km you actually are driven.

“My question is are there any reliable economic data about profitability of slave plantations on one side, and plantations with payed labor on other side, immediately before and after US civil war”

I don’t think there are some direct data to compare, because slave plantations ceased to exist immediately after Civil War, and I am not aware of significant number of plantations with payed labor before Civil War . However, I think that in general antebellum South slave plantations were more profitable - otherwise planters would sell or free majority of their slaves and hire laborers (who could be the same former slaves).

Generally speaking, slave labor could be more profitable comparing with other types of labor within some technology level boundaries. It is not profitable to own slaves if they can not produce significantly more than they consume themselves; it could be more profitable to hire skilled worker to operate complicated machinery than invest in training of the slave. In between, slavery could be more profitable than alternative. By the mid-XIX century technology was high enough to make payed labor more profitable. However, the were some loopholes, and the huge one was raw cotton production in US South after cotton gin introduction.

According to “Time on the Cross: The Economics of American Negro Slavery “ by Robert Fogel (Nobel Laureate in economics) and Stanley Engerman, South plantations were about 20-30% more profitable than free labor farms on both North and South (don’t have this book on hand and can not quote exect pages and numbers).

Antebellum plantation slave labor profitability depended on specific crop, on market demand, and on market competition. It is why american raw cotton dominated world market and constituted huge majority of US exports, while american raw sugar was predominantly consumed on the South, could not compete with better and less expensive caribbean sugar on international market, and was barely profitable only due to protectionists 24% tariffs.

“Federal protection was a lifeline for an industry that could not openly compete with its rivals in the Caribbean. The sugar duty guaranteed reasonably good profits of 6 to 12 percent and offset the notoriously heavy cost of cane sugar production” The Fair Trade Fraud, by James Bovard, NY 1991, ISBN 0-312-06193-5, Page 71

It is due to high cotton profitability planters sometimes preferred to buy other agriculture products from North rather than divert slave labor and soil:

“the chief articles imported are bacon and mules from the Northern States. The only article sold is cotton” North America, its agriculture and climate, by Robert Russell, Edinburgh 1857, p. 289-291

It is because cotton profitability due to huge demand by industrial development, Southern morality turned from labeling slavery as necessary evil to praising it as positive good. It is why three biggest US protestant denominations were split on southern and northern branches between cotton gin introduction and secession. “The prevailing ideas entertained by him (Thomas Jefferson) and most of the leading statesmen at the time of the formation of the old constitution, were that the enslavement of the African was in violation of the laws of nature; that it was wrong in principle, socially, morally, and politically. It was an evil they knew not well how to deal with, but the general opinion of the men of that day was that, somehow or other in the order of Providence, the institution would be evanescent and pass away. This idea, though not incorporated in the constitution, was the prevailing idea at that time... Those ideas, however, were fundamentally wrong” Alexander H. Stephens, “Cornerсtone Speech", March 21, 1861

“Finally, even today socialists and left-leaning authors then to hold US civil war as a conflict between ruling classes primarily concerned about profit, not ethics: From a Marxist perspective, here is the true cause of the main stage of the American Civil War. The Union, or the North, had developed an economy based on wage slavery; whereas, the Confederacy, or the South, had retained chattel slavery. These two economic system were both subdivisions of Capitalist economics, or the private ownership of the means of production. Theoretically, it is impossible for these two subsystems to coexist peacefully in any economy; so, an ultimate conflict to determine the future of capitalist production was inevitable”

I don't think this is correct. Conflict was not about profit: slave South and manufacturing North were mutually profitable, and could still profitable until demand on cotton was high and cotton harvesting was not mechanized (both middle of XX century)**. So from economics point of view, they could coexist peacefully for a long time. The problem was political: most ambitious southerners wanted to control not just their plantations, but whole country, and it did not work anymore.

** Table 3, pages 6-8, of following source http://www2.census.gov/prod2/decennial/documents/17862820-1969ch01.pdf https://livinghistoryfarm.org/farminginthe50s/machines_15.html

UPDATE After reading comments, I would like to clarify the last point of my answer, that the immediate problem planters were going to solve by trying to expand slavery and by subsequent secession was not economical but mostly political. In 1787, they did not want to join the Union until 2/3 clause granted them preferential treatment in House and presidential elections. By 1860 all this was lost, so they did not want to stay in the same Union being hopeless minority in all branches of government. It is why they insisted on slavery expantion to territories, hoping that new slave states would give them if not majority, but at least parity in Senate.