Can a company be guilty of monopolizing just by being very successful?

I don't know if this is the right place, but in our startup, we were discussing the distant future for us. Suppose a software company just sells superior software a low cost and overall becomes the number one supplier of the products. Its competitors can't keep up because:

• the company releases updates quickly with the updates targeting biggest user complaints
• the company regularly prices its software at a low cost (not reducing them to sweep out competition, but let's say their development is quicker and smoother, so they can afford to charge less)
• the company has tied in a variety of products, such that there is a mutual login system, internal advertisements of other company products, etc. Not tying in the legal sense, since each product works well on its own, but basically making life easier for users if they just end up using all of the company's products
• the company is known for being good to its employees, customers, and even competition (in the sense that they don't undermine other products; their own are just better)

and other similar and to my mind perfectly legal reasons. So for these reasons, there are few if any competitors.

Would this company be guilty of monopolizing? Could this company be sued for anything similar, given the above description?

From Wikipedia :

A monopoly exists when a specific person or enterprise is the only supplier of a particular commodity. Monopolies are thus characterized by a lack of economic competition to produce the good or service and a lack of viable substitute goods. The verb "monopolise" refers to the process by which a company gains much greater market share than what is expected with perfect competition.

Regardless of how "nice" your company is and how "good" your product is -- if there are no competitive goods or services -- you're operating as a monopoly. Plain and simple.

Now, if you are able to secure a monopoly for a particular market, will you necessarily be investigated and prosecuted? Probably not.

Antitrust laws are usually designed to stop anti-competitive behavior such as price fixing -- not to punish companies for being extremely successful. Also, the monopoly has to be pretty egregious for it to make it onto the radar of most state and federal anti-trust agencies.

If you're able to establish yourself as the only viable company in an industry using entirely legal and ethical means, then you'd be operating as a de facto monopoly. But these are unsustainable according to economic theory. The amount of profits you'd be making would attract a significant number of new competitors to the market and you'd lose your monopoly power.