It may vary due to some factors:
1st - If you are EK/RP and hunting solo.
2nd - If you are team hunting in a crowded server, or as a EK.
In the first scenario: Its worth delivery until 6,400, then loot the others in hunt in order to lower the damage. I've a 1800 EK and I was hunting solo, I bought over 12,800 essences, and after 6,400 I didn't notice any difference in the hunt.
In the second scenario: Its worth delivery 1,600 essences for each player, in order to access the lower hunting ground, in crowded servers it will be another option to hunt, and with 1600 essences the damage the EK will receive will not be substantially.