From Book 1, Chapter 9 of The Wealth of Nations, by Adam Smith:
"In reality high profits tend much more to raise the price of work than high wages. If in the lininen manufacture, for example, the wages of the different working people...be advanced two pence a day; it would be necessary to heighten the price of a pice of linen only by a number of two pences equal to the number of people that had been employed about it...that part of the price of the commodity which resolved itself into wages would...rise only in arithmetical proportion to this rise of wages. But if the profits...should be raised five per cent that part of the price of the commodity which resolved itself into profit would...rise in geometrical proportion to this rise of profit.
"Our merchants and master-manufacturers complain much of the bad effects of high wages in raising the prices, and thereby lessening the sale of their goods...They say nothing concerning the bad effects of high profits. They are silent with regard to the pernicious effects of their own gains. They complain only of those of other people."
What a shock--that the complaints of Management are directed at Labor, and vice-versa.
This happens to be a third-order functional result of the Materialism Society in which we live.
Of course, in the case of GM, which has now decided to abandon profits entirely, nobody is complaining. Curious, eh?
Your argument ends in the first sentence.
Who is to say that a manufacturer's profit would rise if the cost of labor quadruples?
Just because the shoes, that fewer people are going to buy, cost more money, that does not mean that the profit margin is higher.
If shoe manufacturers could raise profit by hiring $30 per hour unionized labor, they would have done it years ago.