I think, my friend, that if you wish to know, as the long days go, that to live is happy, you must first acquire money enough for a decent life, and power enough to be your own master. (2.247)
After money and weapons, the third in Undershaft's list of the Top 3 Most Important Things in Life is power (take note, BuzzFeed) and is very important in how it functions as part of Undershaft's notion of "good."
The power Barbara wields here—the power that wields Barbara herself—is not Calvinism, not Presbyterianism, not Methodism— (2.266)
Dolly is kind of in awe of the very unique power that Barbara seems to have in her work at the Salvation Army—she's not a mere follower, in his opinion. Dolly goes on to say "Barbara is quite original in her religion" (2.268).
Just as much as it is your duty to submit to your husband. Come, Biddy! these tricks of the governing class are of no use with me. I am one of the governing class myself; and it is waste of time giving tracts to a missionary. I have the power in this matter; and I am not to be humbugged into using it for your purposes. (3.91)
Despite having been successful in bullying her children and their boyfriends for most of the play, Lady B has definitely met her match with her hubby, who understands that, in terms of status, gender, and money, he's got her over a barrel—and he refuses to pretend otherwise. In other words, he's got all the power here.
UNDERSHAFT: From the moment when you become Andrew Undershaft, you will never do as you please again. Don't come here lusting for power, young man. CUSINS: If power were my aim I should not come here for it. You have no power. UNDERSHAFT: None of my own, certainly. CUSINS: I have more power than you, more will. You do not drive this place: it drives you. And what drives the place? UNDERSHAFT [enigmatically]: A will of which I am a part. (3.295-299)
Andrew has been playing up the importance of power and how much he has, but here he kind of contradicts all those statements by suggesting that you don't really have any power of your own once you become Andrew Undershaft—and Dolly concurs, suggesting that the products/production themselves drive everything.
UNDERSHAFT: Not necessarily. Remember the Armorer's Faith. I will take an order from a good man as cheerfully as from a bad one. If you good people prefer preaching and shirking to buying my weapons and fighting the rascals, don't blame me. I can make cannons: I cannot make courage and conviction. Bah! you tire me, Euripides, with your morality mongering. Ask Barbara: she understands. [He suddenly reaches up and takes Barbara's hands, looking powerfully into her eyes]. Tell him, my love, what power really means. BARBARA [hypnotized]: Before I joined the Salvation Army, I was in my own power; and the consequence was that I never knew what to do with myself. When I joined it, I had not time enough for all the things I had to do. (3.302-303)
Andrew is getting tired of Dolly's teeth gnashing about the morality of joining the Undershaft's business. So, he gets Barbara thinking about what she recently learned about power, which he thinks will help convince Dolly.
BARBARA: Yesterday I should have said, because I was in the power of God. [She resumes her self-possession, withdrawing her hands from his with a power equal to his own]. But you came and shewed me that I was in the power of Bodger and Undershaft. Today I feel—oh! how can I put it into words? Sarah: do you remember the earthquake at Cannes, when we were little children?—how little the surprise of the first shock mattered compared to the dread and horror of waiting for the second? That is how I feel in this place today. I stood on the rock I thought eternal; and without a word of warning it reeled and crumbled under me. I was safe with an infinite wisdom watching me, an army marching to Salvation with me; and in a moment, at a stroke of your pen in a cheque book, I stood alone; and the heavens were empty. That was the first shock of the earthquake: I am waiting for the second. (3.305)
At her father's prompting to remember what she's learned about power, Barbara basically recounts her realization that, instead of being "in the power of God" when she was with the Army, she was actually in the power of her father and the whisky distiller Bodger…you know, corporate interests. So, it seems that this is the answer that Andrew was looking for? The idea seems to be that Dolly is (like everyone, really) already in the sway of the Undershaft fortune, so he might as well work for it outright. If you can't beat them, join them.
It is not the sale of my soul that troubles me: I have sold it too often to care about that. I have sold it for a professorship. I have sold it for an income. I have sold it to escape being imprisoned for refusing to pay taxes for hangmen's ropes and unjust wars and things that I abhor. What is all human conduct but the daily and hourly sale of our souls for trifles? What I am now selling it for is neither money nor position nor comfort, but for reality and for power. (3.403)
In addition to wanting to respect "reality," Dolly is open about the fact that he now embraces the opportunity to have a bit more power (it doesn't seem like he felt like he had much in the past). Even though he calls it selling his soul, he feels like he's already done that plenty of times before—and, it seems, got less for it.
I think all power is spiritual: these cannons will not go off by themselves. I have tried to make spiritual power by teaching Greek. But the world can never be really touched by a dead language and a dead civilization. The people must have power; and the people cannot have Greek. Now the power that is made here can be wielded by all men. (3.407)
Dolly continues musing about power…Now he's saying that it's not weapons that make power, but the spiritual might behind them (this is a bit different from what he was saying before, when he suggested that the weapons had more power than the man producing them).
You cannot have power for good without having power for evil too. Even mother's milk nourishes murderers as well as heroes. This power which only tears men's bodies to pieces has never been so horribly abused as the intellectual power, the imaginative power, the poetic, religious power that can enslave men's souls. As a teacher of Greek I gave the intellectual man weapons against the common man. I now want to give the common man weapons against the intellectual man. I love the common people. I want to arm them against the lawyers, the doctors, the priests, the literary men, the professors, the artists, and the politicians, who, once in authority, are more disastrous and tyrannical than all the fools, rascals, and impostors. I want a power simple enough for common men to use, yet strong enough to force the intellectual oligarchy to use its genius for the general good or else perish. (3.408-409)
Now Dolly has come over to the view that resisting violence and arms is kind of bougie; in his opinion, embracing arms production will not only give him power, but actually make power more democratic overall, giving the good the opportunity to fight back against the bad. Um…yeah, sure…whatever you say Dolly.
BARBARA: Is there no higher power than that [pointing to the shell]? CUSINS: Yes: but that power can destroy the higher powers just as a tiger can destroy a man: therefore Man must master that power first. I admitted this when the Turks and Greeks were last at war. My best pupil went out to fight for Hellas. My parting gift to him was not a copy of Plato's Republic, but a revolver and a hundred Undershaft cartridges. The blood of every Turk he shot—if he shot any—is on my head as well as on Undershaft's. That act committed me to this place for ever. Your father's challenge has beaten me. Dare I make war on war? I dare. I must. I will. And now, is it all over between us? (3.410-411)
Dolly is still musing about power, reflecting that his Greek lessons probably weren't as helpful to his former student as the cartridges he gave him as a parting gift when he left to fight. In his view, that gift means that he was already "committed" to the Undershaft cause, and now he's just making it official.