Well, think of it this way, your cost is composed of three parts:
- Food
- Operations (labor, rentals, travel, etc.)
- Overhead (rent, insurance, licenses, taxes, and everything else to stay in business)
Your price = your costs plus your desired profit.
Food cost is pretty much directly related to the number of people, i.e. $xx/person, so that is pretty constant.
Operations is a little less related to the number of people and is more "step like" than food costs, i.e. 1 cook and 1 server can probably handle 2-8 or 10 people unless it is a real complex menu, as the number increases, you have to add BOH and FOH personnel, but in steps, it IS hard to hire 1/2 or 1/4 of a person.
Overhead has NO relationship to the number of people, it is often called "fixed costs".
Say for a typical three course menu for N people, food cost is, oh say, $10/person, operations (the fee for my wife and I) is $400 and my overhead is, um, $20/day ($400/month divided by 20 days, then my "costs" are:
$10*N+$400+$20 = $10*N+$420
Now, let's see how the cost per person varies with the number of people:
- For 2 people: $10*2+$420 = $20+$420 = $440 and $440/2 = $220/person
- For 4 people: $10*4+$420 = $40+$420 = $460 and $460/4 = $115/person
- For 6 people: $10*6+$420 = $60+$420 = $480 and $480/6 = $ 80/person
- For 8 people: $10*8+$420 = $80+$420 = $500 and $500/8 = $ 62.50/person
At that point, I have to add to the operations costs for BOH and FOH.
Obviously, if the number of people is greater than, say, 20-40, the overall difference is much smaller. That is why restaurants/caterers, who's volume is much greater, have no problem charging $/person. A few, more or less, has little impact on their daily income. Foe a private or personal chef that charges $/person WITHOUT A GUARANTEED MINIMUM, there is a distinct risk of ending up with no profit and, maybe, even not getting your fee.
I do NOT charge $/person, I charge $/job. That way I KNOW how much I will make if I get the job!