Cobrar a

Cobrar a
 

Hi,
Is the use of the personal a correct here?
"Cobra menos a los alumnos."
(He charges his students less.)

In this sentence the preposition 'a' is required.

Whether or not it is a case of personal a depends on whether 'los alumnos' is a direct object or an indirect object.

If "cobra menos a los alumnos" = "los cobra menos", this is a case of personal a marking a direct object.

If "cobra menos a los alumnos" = "les cobra menos", this may be an indirect object, and all indirect objects are introduced by a preposition, which often is 'a'.