"No firm is completely sheltered from rivals; all firms compete for consumer dollars." This does not address what a monopoly in reality is. A firm has a monopolistic position if there are no rivals to present any competition to the firm. It could then increase the price of its products till doing so reduces the net revenue inflow due to the decrease in volume caused by the increase in price.
A monopoly would do the least damage if the product being manufactured by it is one that all consumers can avoid using and this in no way negatively affects the consumers. A monopoly firm producing something that is a necessity can harm consumers immensely as consumers have to buy from the firm no matter how high the prices are set.
In a Free Market, monopolies cannot exist. It does not preclude, however, a company from capturing a majority of the particular business that it's in, but that can only be accomplished by producing the best quality goods and services at the cheapest cost, which will drive demand up. Capitalism requires a Free Market, which implies competition. Whenever a monopoly exists, there's some form of coercion, either businesses colluding together to fix prices, or the tacit encouragement and acceptance by government.
Responding to your post #2, I would argue that there is less of an incentive for a monopoly to innovate. Sure, it may have the economic profit that would allow it to innovate, but there is no reason for them to want to innovate. Therefore, the monopoly's ability to innovate is not all that important.
It is difficult to attain a pure monopoly through ethical business practices, but, as the age of Robber Barons illustrated, unethical practices make it easier to create monopolies. The recent federal approval for Whole Foods Markets to buy out competitors illustrates how government can encourage creation of monopoly, even while ostensibly expressing disapproval of monopoly, as organic food goods become ever harder to find and more expensive at both Whole Foods and other markets.
I would agree that a pure monopoly cannot exist under these circumstances. As stated by vangoghfan, it would take governmental intervention for a "pure" monopoly to be able to exist (based upon their illegality). As mentioned above, there are many different ways a company can become a monopoly (by raising or lowering costs), a pure monopoly would have a corner on a very specific market which all consumers need (problems would arise given the company could charge anything they desired based upon consumer need).
I would agree that it is difficult to establish a pure monopoly unless the government somehow intervenes in the economy and enforces a pure monopoly. Under conditions of relative market freedom, it seems likely that few monopolies can sustain their monopoly statuses for very long. If the monopoly for some reason decided to provide goods at extremely cheap costs, there might be no incentive for a potential competitor to found a competing company. Many monopolies, however, are tempted to exploit their positions by charging more than many people want to pay.
No firm is completely sheltered from rivals; all firms compete for consumer dollars. If that is so, then pure monopoly does not exist. Do you agree? Explain.
The costs monopolist and competitive producers face may not be the same. On the one hand, economics of scale may make lower unit cots available to monopolist but no to competitors. Also, pure monopoly may by more likely than pure competition to reduce cost via technological advance because of the monopolist’s ability to realize economic profit, which can be used to finance to produce with the least costly combination of inputs is more common among monopolists than among competitive firms. Also, monopolists may make costly expenditures to maintain monopoly privilege than are conferred by government. Finally, the blocked entry of rival firms weakens the monopolist’s incentive to be technologically progressive.