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First class and business pays for the economy seats
While that's true, and so First Class and Business Class subsidize private jets more than Economy Class does, that doesn't change the fact that Economy also subsidizes private jets.
TL;DR: Yes, you subsidize, because the amount each seat pays is proportional to their ticket price, but it's a small amount per flight. But you also need to think about what you consider "fair" in this instance.
Sorry, been offline for a few days. I'm curious, so let's check the math:
Their example is a flight from Atlanta to Orlando. The most common flight on that route is a Delta B757-2001. SeatGuru can provide us with the most common seating layout: 24 First class, 21 Comfort+, and 135 Economy.
The tax that the NYT Editorial Board is looking at is mostly likely the 7.5% Passenger Ticket Tax, which is about 1/3 of total fees on a two-leg itinerary2.
Looking at Delta's fares for about two months out on randomly chosen dates in October, I see economy fares of about $270, economy plus at about $350, and first at about $570 (I tried to take a median, but it's very approximate). Those fares are round-trip, so let's cut them in half for $135/175/285. At 7.5%, the tax comes out to ~$10.13/13.13/21.38 per seat. That tallies up to $2156.40 when we multiply out by the number of seats, pretty close to the $2300 value the video claims, so I'm comfortable saying my numbers are "right enough" for the example.
Depending on how one structures the ownership of their private jet, the equivalent tax for them is zero dollars (they are exempt).
There are then taxes that both flights would pay on a per flight basis or based on fuel consumed. A private jet would pay proportionally more of those than a commercial airliner (due to the lower % passenger weight of total weight), but those are a small part of the total fees, especially for the commercial flight. (I'm seeing about $300 per plane, so I think NYT was counting some of those fees but not all, as they said that the private jet would be paying about $60 in fees).
The problem with the whole "subsidizing" conversation is that it depends on what perspective you take. If you look at it on a person-by-person basis, then sure, each passenger on the commercial flight probably pays less than the passengers on the private jet (assuming 2 ppl or something).
But FAA resources aren't provisioned on a "per-passenger" basis, they're provisioned on a "per-flight" basis, with some modifiers based on:
Let's be generous and say that our B757-200 takes 4x the ATC resources that the private jet does (I would bet the real factor is closer to 1.5-2.5x). So for a total of 5 units of ATC resource, 4 are used by the commercial jet, and 1 is used by the private jet.
The commercial flight therefore pays $(2156.40+60)/4=$554.10 per ATC resource, and the private jet pays $60 per ATC resource. Equal distribution would be $(2156.40 + 60 + 60)/5=$455.28. So the private jet is receiving a "subsidy" of $455.28-60=$395.28 per flight.
If we divide that subsidy over all of the passengers on the flight by fare, then we get about $1.81/2.34/3.81 based on seat class. That isn't much of a subsidy per passenger, about 1.4% of your ticket price.
But let's think about the other side of the equation: Chartering a plane from Atlanta to Orlando costs about $12,5003. Taking on an extra $395.28 would be an additional 3.2% per flight, which is admittedly more than the 1.4% of the fare for the commercial passenger.
And hold on... we are talking about passenger transport when we're talking about both flights... so let's look at how efficiently those FAA resources are used. Keeping that 4x factor for a flight of the same distance, we have 4 FAA resources spread over a flight with a capacity of 180, let's assume 80% full for 144 passengers, using about 0.03 FAA resources/person. Now let's look at the private jet, which recall uses 1 FAA resource for the same flight plan. Let's be generous and assume 6 passengers. That's 0.17 FAA resources/person. The commercial jet is more than 5x more efficient in its use of FAA resources.
These are people who literally create complex corporate structures for their private jets just to avoid that 7.5% excise tax, AND they tend to have much more disposable income. I think they can pay the extra $400 for their inefficient use of FAA resources.
If I were making the rules (which is absurd because not only am I not an expert but I am also Canadian), I would make the FAA fees per-itinerary filed with the FAA and incorporate three factors:
The FAA has a whole section on their website about airport planning, so I would use that to figure out how to apportion these factors to best approximate the factors required for FAA resource allocation. I'm sure there are planners at the FAA that have this all broken down already.
So yes, unless you get a super-discount fare, you are subsidizing private jets assuming that the fair apportionment of costs is based on how FAA resource capacities are planned. It's not much per passenger, but it adds up across all of society, and is another way that the US economy moves wealth from the lower classes to the upper class.