A charge occasionally levied against libertarianism is that a vital natural resource, such as a water supply, could be monopolized by an astute businessman, who could then hold society hostage with the threat of cutting off its ability of replenishing its bodily fluids. This is a most curious attack upon capitalism, because it touches upon a fundamental aspect of the system – property rights. Property rights exist for the very purpose of resolving the problem of scarcity. The “water-monopolizer” attack, then, attempts to suggest that scarcity discredits private property – when scarcity is the very problem property rights exist to resolve! 
Let’s unpack the water-monopolizer situation (WM henceforth) and analyze it from two different sides.
From a property rights perspective, if a person has legally  obtained the title to a water supply, then in accordance with property rights he cannot be coercively compelled to relinquish it either partially or wholly. In this respect, the body of water is his property just as his refrigerator is. For someone who accepts the right to property, the conclusion to this scenario is straightforward and the discussion ends here.
Stopping there, however, is unsatisfactory to some people. In all honesty, if this were the sole response to the WM, I too would be a little unsettled, even if I accepted the conclusion. What can be said to a “bleeding heart” who fears for the well-being of the members of the community with the WM? Plenty, as it turns out. 
The main mistake that people make is to forget that the market is not static, but a process. Not only that, but it’s a complex web of inter-dependencies, incentives, and opportunity costs. Let’s see how this plays out.
You ask “what if one person owns the water supply?”
Well, how did he just happen to come to own the water supply? Was he the first person to homestead the entire thing? This is odd, because it likely means that there was no one else in the area before he got there. This means that it’s the fault of whoever decided to come into the area afterwards that he didn’t consider water supply before moving in. That is, if person A is the first person in an area and takes over resource X through legitimate homesteading, I don’t see there being any justice in another person B coming into the area later and whining about not having water. Why would he settle there?
What if, then, there was a group of people in the area for some time, and one of them suddenly decides to homestead the water supply? My question is then “how did that population exist for so long before the homesteading of the water? Did they not drink any water?” The only logical progression of events is that they must have made use of the water supply before the monopolization. As such, they very well could have claim to an easement over part of the water supply, which resolves the issue. 
Consider another option: at some point, there were numerous owners of the water supply, but after a bunch of buyouts the water supply consolidated in the hands of one man. This is likely unfeasible, because as the supply decreases, prices tend to increase. That means that as the supposed monopolist buys more and more water, the remaining owners are more and more likely to hold out their share because they can extract a higher price from him. Imagine, too, if word got out that one person was trying to monopolize the water supply. Consumer groups would then also have an avid interest in buying the water supply to guarantee that people won’t be denied water.
Even in the worst case scenario, if one person does manage to get all the water, remember that water is not the only vital resource. There are resources that the monopolist himself would need. If other people own these other resources, they can withhold these resources from him until he breaks. In fact, since roads would be privately owned, road owners could refuse him passage across their land.
Also, notice a slight omission in the original question: “an astute businessman, who could then hold society hostage.” Catch this mistake whenever possible! Which society? The answer is this specific society. If word gets out about this evil monopolist beyond the local area, then other communities could very well boycott the man’s goods and deal him a financial blow. Furthermore, firms which bottle water in other areas would have an interest in driving in water to the monopolized town because of high profits. This would drive prices down and break the monopoly.
For some economic jargon, if a person decides to withhold resources past the point of unit elasticity of demand, he begins to lose money . This means that the monopolist would be losing money in the present that could have been invested, and the investment could have gained value in the future. And lastly, and oft-forgotten fact about actors in an economy and society – they are humans! They have a memory! What is the monopolist’s long-term strategy? Since a society hard-pressed enough will find substitute sources of water (digging wells, harvesting rain ), what does he plan to do after his water monopoly (inevitably) breaks down? It’s absurd to think that a businessman who was able to amass enough wealth to buy out a water supply would act in such a foolish manner. 
The market is remarkably good at preventing evil monopolies . And in the unlikely event that one such attempt does somehow slip through, once it has been thwarted I expect a web of contracts to spring up that guarantee that such a scenario could not possibly happen in the future. Properly constructed around property rights, such contracts would be enforceable, and then the law would morally be able to directly stop such attempts. 
 One of the motivations for this criticism of the free markets is a belief that evil monopolies would be rampant on the free market. This claim has been repeatedly refuted both in theory and in the historical record by libertarian scholars. Look up “robber baron” or “Gilded Age” on the Mises.org website if interested. On the topic of utilities being natural monopolies, see “The Myth of Natural Monopoly“
 The note here is that the acquisition of property rights must be legitimate – either homesteading of previously-unowned land or transfer of title from another previous rightful owner.
 In most libertarian discussion (at least at a lower-level), there is an apparent divide between the rights-based approach and the utilitarian approach. It is interesting to consider, however, the possibility of morality being just another mean to an end – that is, the utilitarian basis for the existence of a code of rights. For an introduction to these ideas, see “The Utilitarian Foundation of Morality“
 It is outside the scope of this article to describe the precise process of establishing easements – it suffices to say that easements are rights to use (as opposed to ownership) of a natural resource acquired while the resource was unowned.
 A quick explanation of price elasticity of demand: the demand curve for a given curve slopes downwards (in accordance with the law of diminishing marginal utility). The graph has price of the good on the y-axis and quantity on the x-axis. If the seller were able to price the good at any desired point along the demand curve (providing, of course, the appropriate quantity demanded), he or she could receive varying amounts of revenue in their sales equal to the product PQ (the price of the good sold times the number of goods sold). There is a point on the curve called the unit elastic point at which revenue is maximized for a given demand curve. Decreasing the price from there will result in a decrease in revenue – more units will be sold, but the lower price for each unit more than offsets the increase in units sold (this is called inelastic demand). The opposite happens if the price is instead increased past the unit-elastic point – each unit is sold at a higher price, but the decrease in units sold more than compensates for the higher price (this is called elastic demand). Hence, there is a point beyond which a monopolist would find it foolish to increase the price of a good. Remember, once again, that while the neoclassical theory of monopoly claims that monopolists can exist on the free market and can decrease production to the unit-elastic point to increase revenue, evidence for this is scanty if at all present. See pg. 16, Government Failure versus Market Failure by Clifford Winston - indeed, the evidence shows that government fails to decrease consumer prices by busting large businesses.
 I wonder where the members of the society previously got water to irrigate their crops or feed their cattle.
 A strong theoretical case against both monopoly pricing and predatory pricing has been made in the literature by Thomas DiLorenzo. See “The Myth of Predatory Pricing“
 Not only is the market remarkably good, but there is no reason to believe that the government or any other institution would be any better than the market.
 A word of caution, however, to those who held their breaths until the mention of “law” and then breathed a sigh of relief. We have been conditioned to see the swinging weapon of the “law” (usually, as we’re taught, by government) as a tool that can achieve any positive social outcome. The government action model is intriguingly elegant – if there is a problem, all that is needed is to identify it and dispatch the necessary bureaucrats to solve it. Do not think that just because the law can now (after the contracts mentioned in the article) take morally permissible action against monopolizers that it will suddenly do a “better” job than the “mere” free market. Free market checks and balances as explained throughout the article are remarkably resilient, even if present only as incentives to individual actors and not as laws or contracts carved in stone.