Here is a list on what levels pokemon will obey you.

1 Badge
(Pokémon level 1-25 will obey you)
(Final stage Pokémon can now be leveled up to 20 or their base level +10, whichever is higher.)

2 Bages
(Pokémon level 1-30 will obey you)
(Final stage Pokémon can now be leveled up to 25 or their base level +10, whichever is higher.)

3 Badges
(Pokémon level 1-32 will obey you)

4 Badges
(Pokémon level 1-35 will obey you)
(Final stage Pokémon can now be leveled up to 30 or their base level +10, whichever is higher.)

5 Badges
(Pokémon level 1-40 will obey you)

6 Badges
(Pokémon level 1-45 will obey you)
(Final stage Pokémon can now be leveled up to 40 or their base level +10, whichever is higher)

7 Badges
(Pokémon level 1-50 will obey you)
(Final stage Pokémon can now be leveled up to 50 or their base level +10, whichever is higher)

8 Badges
(Pokémon level 1-100 will obey)
(Final stage Pokémon can be leveled up to level 60 or their base level +10, whichever is higher)