How do libertarians deal with issues of inelastic demand?

Finally have some time to post this over here. So my question is, what do you think about inelastic demand? What happens when the water supply is privately owned? There is no way for the market to find the "right price" for water, considering anyone will pay anything they can as it is completely necessary, right?

So then if one company controls the local water supply, it's going to end in tyranny, correct?