Your example does not apply. You don't get monopoly rent. Without price control, your local utilities could extract monopoly rent. Pay up, or you can't take a

Your example does not apply. You don't get monopoly rent. Without price control, your local utilities could extract monopoly rent. Pay up, or you can't take a shower. Shortages happen only when the price control is extreme enough to push the price below the cost of supplying/rationing the product. If water costs $x per acre-foot to supply, and demand will cause the lake/river/well to run dry when the price drops below $y per acre-foot, but the monopoly makes the most profit selling at some much greater price $z, then the monopoly rent is $z-max($x,$y) and there will be no shortage if a cap greater than max($x,$y) is set.