Ultimatly, you are responsible for having the permits.
Often Builders get them because they do not want to get held up or stopped for not having them.
Electrical & Pluming/mechanical permits would be taken out by the person doing the work. If you are doing it, then you get the permit. If the builder hires pros, then they get the permit so, the Inspection Department can make sure they are licensed.
Permits are posted on the property where the work is being done. If, in your contract, your builder was supposed to get them, you should look at them before any work starts.
In some cases, depending on the size of the job, the contractor will try to get by without one.
It later comes back on to the homeowner and sometimes the work has to be torn out.