A fellow on Quora had these observations about slaves and crucifixion, which are certainly plausible:
They usually weren’t. That would have been sort of stupid, since slaves were valuable property who did work for their owners, and crucified slaves can’t, you know, work.
The Romans crucified slaves captured in servile rebellions because that was considered making war on the state, and since slaves were non-citizens of Rome, they received the legal punishment for capital offenses against the state by a non-citizen. That was crucifixion. The Romans could have simply returned them to slavery, but they felt it was more important to make an example out of them by brutally executing them. Furthermore, a slave that has already rebelled once is a danger to do so again.
John Cate's answer: They usually weren’t. That would have been sort of stupid, since slaves were valuable property who did work for their owners, and crucified slaves can’t, you know, work. The Romans crucified slaves captured in servile rebellions because that was considered making war on the s...
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Of course when you look at it pure from a point of view of monetary efficiency this would be right.
Better sell a slave then crucify them.
However crucifixion is one of the things that has a psychological impact as well.
Seeing a fellow slave crucified would be quite a deterrent to any slave bad behaviour.
Running away from your master is rebellion to your master, and indirect rebellion to the roman system.
A lot of other crimes can be seen as rebelious too. stealing, assault, disobidience etc.
As for the value of slaves, They weren't dirt cheap, but most cost was in their maintenance: food, clothing etc.
Value ofc dependend on skills, age/health, attitude, obidience and other factors as well.
Some compare slaves and their maintainance with buying a new car and the taxes/maintenance/fuelcosts for a car.
The car in itself is not cheap, but a lot of cost is in the car's use.
The less value you had for your master the easier it was for a master to take the loss of your value, save on your maintenance cost and get rid of you. Selling to the mines or galleys/other horrible very short lived jobs, or have them crucified.
Some more levelheaded master would probably try to sell the unwanted slaves.
Others more emotional ones would give into rage over a slight and have them crucified.
Honor is Roman society was an other factor.
IF a slave would do something that would diminish the honor of the family to the public,
crucifixion or even having them whipped in public would probably be a better choice then selling that slave.
To only look at the supposed economic value of slaves is quite shortsighted.
It is only one of many factors involved with a masters decision how to punish or get rid of a "rebelious" slave.