The premise of your question is not a certainty. Whether and how much of a price increase occurs depends on how much of a margin there is, and what price points are being targeted. If a widget costs $3 to make and sells at $10, then increasing the production costs to $5 may only change the profit, and not the final price. If a widget costs $9.50 to make and sells for $10, then the same $2 increase in per-unit production price would increase the price.

Which scenario we're in depends on the industry, but overall I don't trust the rhetoric of costs always being passed down to society as a whole, because it works to undermine any labor gains.