There is a vast literature on the economics of slavery. I would suggest you take a look at Gordon Tullock’s short article. It’s not definitive, but it raises essential points of economics. For example, slaves had capital value which had to be included in any accounting of the profitability of slavery. The dynamic of the market tends to direct investment into different lines of production so that there is a tendency toward the same rate of return in every line of production. In other words, slavery is no more profitable than any other line. Another example: Tullock points out that southern slave owners received a huge subsidy in the form of government mandated slave patrols. He also discuses the economics of manumission.