How can flights operated by the same company have such different prices when marketed by another?

Codeshares usually work in that way, that an airline buys a number of seats on a flight operated by another airline. In your example, both Virgin and Air France bought each a set of seats from Delta, which they can now sell under their own flight number, within their own fare rules and fare scheme. Depending on how many seats they bought and already have sold, they can end up with completely different prices. Here, most likely Air France doesn't have many more available seats within their allotment, so the price is higher than with Virgin.

If you can't find the flight directly with Delta, than most likely Delta has already sold all of their "own" seats.

There's also that factor that many airlines and aggregators adjust prices by your search history. Example: I got a price much higher than one I had seen before. I closed the tab (but not the browser), deleted cookies from that site, went back to the site, did the same search and got the same flight for the same lower price I had seen earlier. (MUCH lower)

And then on another flight search engine search (mine) for the same flight, the cheapest flight is a different airline altogether, no Delta flights exist (matches yours) and Virgin Atlantic is actually more expensive. Go figure ;)

The number of providers between the airline and the website can be several layers deep. As a result, with commissions, different classes of economy seating, bulk buying of seats (like Virgin's purchase of seats from Delta in this case), all affect prices.

In this example, Delta has as someone else pointed out, likely sold out of seats, or possibly has sold them all out to other airlines in their codeshares. As a result, Virgin has the 'best' seats.

It's also possible that from the bulk price that Virgin bought them at, on that route they're prepared to make a lower profit than say, Air France, who might have a higher price for the same seats (in this case it seems they're out too, but it was just an example).

On Jetstar sales in Aus, for example, our site sometimes has lower, sometimes higher prices than Jetstar itself, and almost always lower on Malindo air than say, skyscanner. So the layers from the airlines through different flight providers to the end user also complicate the price on top of the airlines' own complications.

There's a great MIT paper from a few years back on the complexity of air fares, which I still like to refer back to until I lose it about 20 pages in....

The short answer is "economics". The long answer is to do with price versus demand.

If you run an airline you have to publish schedules in which you commit to flying a certain number of times each day along each route. The costs of doing this are pretty much fixed regardless of whether the planes fly full or empty (a full plane takes a bit more fuel, but that's about it). Now you need to maximise the amount of revenue you get for those seats.

If you charge a flat rate per seat then you get a certain amount of money. However if you adjust this downwards to the point where all your seats are full then most of the people on the plane would have been willing and able to pay more, some of them a lot more, if only you could persuade them to. The art of airline seat sales is to find ways to get those people to stump up the extra.

Some of the ways airlines do this are:

• Charge more for higher levels of service; first vs business vs coach. But that costs more to operate as well.

• Charge more for the later bookings; people who book later are less sensitive to price.

• Charge different amounts for return flights that include a weekend; most passengers are businessmen who want to be home for the weekend.

• Sign exclusive deals with middlemen who will then direct your customers to you rather than to your competitors, so you can charge them more.

The last one gets positively Byzantine. People who are able to pay more might not be prepared to do all the legwork of hunting around for a cheaper flight, so they will be steered towards the Air France flight and take it instead of spending another hour digging around the schedules. They may also not notice the "operated by Delta" in the fine print and think they are going to get Air France service levels, legroom etc.

A big factor in this is that the people taking the flights are often not paying for them. Most transatlantic passengers are flying on business, so when someone takes the Air France flight for convenience its their employer who pays the extra. It can also be that the employer has signed an exclusive deal with a travel agent (outsourcing your travel arrangements is common these days), and that travel agent is getting kickbacks extra commission from Air France, so will book its clients with them if possible. Meanwhile the travel agent will be justifying its work by showing how it has negotiated a 10% discount with Air France, so on that £956 flight they actually saved the client £95.60, which enables the company purchasing department to justify their existence.

And so on.

Note that the seats may not be identical. Well, the physical seats may be the same, but for example you might get more hold luggage allowance with one carrier or the other. I've experienced this, where I was allowed two hold items on a code-share but the person stood behind me in the queue had to pay extra for their second suitcase.

This is explained very well an entertaining 2004 article by Joel Spolsky called "Camels and Rubber Duckies".

(What do you know; air fare appears as an example; I didn't remember that!)

The basic idea is if you want to maximize profit, you have to somehow offer the product at multiple price points to different consumers. If you have a single fixed price for something, like $100 dollars, then you're failing to capture the "consumer surplus" from those customers who would easily have paid $150 for the same thing. At the same time, you're not profiting from the legions of bargain hunters who will jump on the product if it can somehow be had for $75, but otherwise ignore it if it costs $100. If you still make a profit at $75, it's better to sell at $75 then to keep asking $100 and not move a unit.

With Southwest airline, they preallocate seats at different rates. Say 33% at bargain, 33% at mid level, and 34% at top price. (I am guessing at the percentages.) But when all of the bargain seats are gone, they are gone. Order early and you get the better price. Order late and you pay top price. I noticed that the cheap seats to Providence are now over $110, while seats to Boston can be had for $49. Next time that I go to Providence, I am going to Boston and taking the commuter train back.