Libertarians, help me understand your case for small government.

I would describe myself as a liberal who subscribes to the philosophies of social democracy. I have never understood the case for small government. One of the biggest things I can't wrap my mind around is that in a free market, the businesses (and boards of directors and CEO's) determine how things are done. If that market is regulated by an elected government, it seems to me that I would rather have the power to elect someone to keep things in check rather than leave it to businesses to determine whats right for the market.