Why would the company pay more when they can just not pay more? The only things I can see happening is they might lower prices as competition ramps up, or in general as there is more supply for the same cost.
To try and explain one path: Company A doesn't raise wages but makes 5% more money. Company B pivots from Industry B into construction (because suddenly construction is having 5% fatter margins), and hires workers at more competitive wages to poach them from Company A. Company A forces to raise wages.
If there's a demand ceiling on housing it's a different story though.