It doesn't take much to start a construction company. Most of them have foremen who are perfectly able to quitting and starting their own company. Both the new and existing company will hire a few new people (zero experience needed, start today at $18/hr - or some wage that gets people in) and so there are more in construction overall.

As such builders will try, but once lumber prices go down a bit they will probably lower prices to attract customers. Plumbers and the like might get a little more many as they are harder to train up, but for the most parts there is enough competition that passing savings on to customers is going to happen.