Government as OS
When the US was founded, people had the curious idea that the government was simply all of us. The founders called it 'democracy', or government by the people. If we still believed this, we might have no problem with things like government support for the old or for poor children. Why shouldn't we all chip in a little so that no one in this prosperous country needs to go hungry or live in shacks?
I won't attempt to revive this antique concept; instead, I'd like to suggest that government plays the same role in an economy as an operating system plays in a computer. It sets up the basic conditions for other agents to do their work, provides the basic services, and prevents resource gridlock and system crashes.
A good operating system makes it easy for programmers to write programs: they can use system services rather than doing everything themselves; they spend their time accomplishing something for the user rather than fighting the computer (or other programs).
Likewise, a good government makes it easy for businesses and individuals to prosper. It provides services that benefit everybody, resolves disputes, and keeps the system running fairly.
Ayn Rand is wrong: individuals don't prosper all by themselves. They owe their success to the other people that help them, and to the government that provides them with opportunities, reduces risks, and provides public goods. Evidently ours does a good enough job that Americans think that these things come free, like the air.