Epictetus, a Greek and a slave to a secretary to Nero is applying Stoic ethics to the problem and ethics of slavery. He says, essentially treat them kindly; and you will benefit too. I find this extract fascinating as the slight knowledge I have of Greek Philosophy suggests that the relations between master & servant weren't subject to ethics. Later in life, he was crippled, with one tradition stating this was done by his master, and another saying he was lame from childhood.
To run through this in detail:
If you intend to improve, throw away such thoughts as these:
He intends to offer advice
if I neglect my affairs, I shall not have the means of living
The world is a large place, the ways of making a living are varied; one need not press on continually with ambition; rest is possible - indeed recommended; but also the world offers more to the sensability than that of affairs - politics or trade.
unless I chastise my slave, he will be bad.
The slave is a some-one; who also has his ethical being; one need not assume from the outset that he must be bad; this does not mean that one should assume that he is wholly good; most men are imperfect; one should use observation & judgement.
For it is better to die of hunger and so be released from grief and fear than to live in abundance with perturbation;
Rhetorical statement. He doesn't literally mean this. He is high-lighting the disabling nature of constant anxiety (perturbation). In Buddhism this is another form of dukkho - suffering.
and it is better for your slave to be bad than for you to be unhappy.
One cannot watch him all of the time. If he is bad, then a little badness is liveable with. It is hard to make paragons of men. By releasing yourself from the task of turning your slaves into paragons of servitude - you yourself can attain a more equable frame of mind.
Begin then from little things. Is the oil spilled? Is a little wine stolen?
He's setting a scene - a little drama. Has the slave been careless whilst waiting on you at the table? Has wine gone missing from storage? It seems obvious we should blame those who are foreign to us - our slaves. We may allow
ourselves to feel a degree of righteous anger.
Say on the occasion, at such price is sold freedom from perturbation; at such price is sold tranquillity,
But if a little oil is spilled, or a little wine is stolen - do not start raging. Perhaps laugh: this slave is always a little clumsy. But she sings well. Or he plays with the children well. Through this your estate and yourself are tranquil.
but nothing is got for nothing. And when you call your slave, consider that it is possible that he does not hear; and if he does hear, that he will do nothing which you wish. But matters are not so well with him, but altogether well with you, that it should be in his power for you to be not disturbed."
Recall the asymmetry of power here: you are the master & he is the slave. You have power over him; be mindful of him - if not charitable; the equivalent in Kantian terms is when you treat a man as an end (slave, servant or other hired help) then do not treat them as a mere end; but recall that they too, are men, with souls (psyche) as your own.
edit
Some additional context supporting the above interpretation follows the quoted text; for Epictetus goes on to write:
'How then shall a man endure such a person as this slave?'
Slave yourself, will you not bear with your own brother, who has Zeus as his progenitor, and is like a son from the same seeds and of the same descent from above? But if you have been put in any such higher place, will you immediately make yourself as a tyrant? Will you not remember who you are, and whom you rule?
That they are kinsmen, that they are brethren by nature, that they are the offspring of Zeus.