That's not how it works :). If the productivity doubles, the product will still cost $10, but the company will happily pocket that $5 improvement - and no, they won't raise the salaries of their workers, because why would they? There's zero reason to. Also note that "efficiency improvement from the manufacturing plant" usually means a) automating a part of the production process, and b) firing the workers who are no longer needed.
So now you have a product that's still $10, but some of the people in the community don't have a job anymore, so they can't buy it.
Of course, then a competitor shows up, driving the product price down to $4.50. The original company has to adjust, so it fires some more people and cuts down the paychecks for the rest.
The end result is: the product is cheaper, but the community is poorer, and some of its members don't have a job anymore.
But hey, isn't this the whole point of optimizing business through competition? Isn't the goal to make more with less resources and less people?