> You haven't explained how a shortage can lead to paying less on the part of companies.
There is no shortage. They promote the story of the shortage to pressure government to let in more indentured foreigners, with the slower goal of encouraging more locals to pursue those careers.
You'll notice that "paying more" (the classical/rational economic solution) doesn't seem to be an option.
But “don’t wanna pay” (when companies and 1%ers are hoarding like never before) doesn’t equal a shortage.