No, capitalism is a system wherein the means of production are privately owned and can be bought and sold. Capitalists can pursue anything they wish and still be capitalists, including monopolies, but usually they try to maximize their profits rather than their market share.
In a market with perfect competition there are no profits.
I hope you can see that that claim doesn't fit the observed evidence. Gas stations somehow generate enough profits to stay in business despite the fact that they're competing to sell something that's an indistinguishable commodity.
Now, in the special case where the marginal cost of production is very low and you're selling a commodity it is true that competition destroys profits. Like if there are two people selling txt files of The Prince neither is going to make much money (that's why we have copyright). But we're talking about rare earth minerals here and those have a substantial cost of production with a corresponding upward slowing supply curve and I assure you that the people mining minerals are making a profit without having a monopoly.
"a substantial cost of production" is often a barrier of entry exploited via a monopoly, whether in the form of superior patetended technology, exclusive production agreements, government subsidy, a distribution cartel, etc, etc.
Are gas stations making profit off the gas or is that often a lost leader for high margin snack sales? I've heard that stations make nothing off gas sales.
Copyright is a government supported distribution monopoly.
"Perfect competition" can only exist in the long term. In the short term, there are start up costs and new improvements. With perfect competition, if you are making a profit someone will come along and undercut you, but that takes time, capital, skill, and luck.
Exactly. In the short term you have some kind of monopoly. Maybe you have the only ice cream shop with a licence to sell booze, or a new supply restricted piece of equipment, or exclusive supply of a rare ingredient, famous partner, etc. product differentiation is at its best, a monopoly. All lasting businesses are built on monopolies.
