Those three premises are still insuficient to warant desalination.
"Shortage" means little, what we have is a restricted supply curve, that can still meet demand at a higher price. And if that price is insuficient to pay for desalination then it won't happen: when you build your desalination plant and try to sell water at production costs, you won't find any takers. They'll tell you yes, we have a shortage, water prices have exploded by 100%, 2 cents instead of 1 cent, but they certainly won't pay you 10c for desalination.
"Shortage" means little, what we have is a restricted supply curve, that can still meet demand at a higher price. And if that price is insuficient to pay for desalination then it won't happen: when you build your desalination plant and try to sell water at production costs, you won't find any takers. They'll tell you yes, we have a shortage, water prices have exploded by 100%, 2 cents instead of 1 cent, but they certainly won't pay you 10c for desalination.