> mutually exclusive
Governments often set floors for wages. In fact, this is called the minimum wage.
> This system is the same as shopping at a store that sells you the same goods at a lower price than another store.
That's how it works in a perfect world, but not how it works in reality. In a perfect world monopolies wouldn't be an issue. The reason they are an issue is that with a monopoly it is very easy to manipulate the market that you control. The reason we generally break up monopolies is because they are actively manipulating said market and stiffing innovation. We tend to not go after monopolies that aren't doing this.
> I do not see what this has to do with a “plutocrat”.
A plutocrat is someone who's power is derived from wealth. A plutocracy is a form of government where that power, derived from wealth, is instrumental to political power. You may think that this is universal to all governmental systems, but it isn't. Often we see the reverse (wealth derived from political power vs political power derived from wealth).
Anti-trust laws, IP laws, the SEC, etc are all designed to prevent this from happening. I think the problem you're running into is that you're taking perfect models (spherical cow in a vacuum) and assuming that they work identically in the real world. This is naive just as it is naive to assume a spherical cow in a vacuum falls out of a plane at the same rate as a living cow. There's an approximation and you can get some useful planning from the simple model, but it is going to have significant errors in the real world experiment.
What it comes down to is a lack of sufficient complexity and nuance in the model you're using. An econ 101 course or even a B.A. in economics will not be enough to sufficiently understand the economy in high detail. It is really easy to overestimate the utility of our knowledge and mental models because we tend to not measure likelihood of events based on random samples but instead have a large selection bias (getting random samples is also quite difficult).