  We consider the widespread assumption that coherent pulsar radio emission is
based on extended pair production leading to plasma densities highly exceeding
the Goldreich-Julian density. We show as an example that the observed low
frequency (160 MHz) emission of the Crab pulsar is incompatible to the model of
extended pair production. Our results rule out significant pair production if a
plasma process is responsible for coherence and the radio emission originates
from inside the light cylinder.
