Low unemployment points is a tight labor market, meaning there is also competition to get workers.
And the economy is hardly dominated by monopolies. Take a moment to tally where all of your money is spent, and see how many of those companies are anywhere near a monopoly. The vast majority of people's expenses is spent in competitive markets: housing, food, energy (no company is a monopoly in any of those markets - largest housing company has < 10% of market share, largest bank has < 20% of market, largest energy company has < 30% of market share).