Why do cheap flights with a layover get more expensive when you split them up into separate flights? [duplicate]

One obvious and common interpretation is that people going to Moscow (from London or Tokyo) are often prepared to pay for the additional convenience of a non-stop flight (especially if they are flying on an expense account). On the other hand, people flying between Tokyo and London have no reason to prefer flights with a layover and require another incentive in the form of a cheaper fare.

Similarly, the airline wants to charge as much as possible to each individual client. That means charging higher fares to business travelers and for non-stop flights where they don't face competition. Reducing fares on the very same flights if and only if they are combined with a layover is a way to fill them up and get some money from price-conscious travelers without damaging the revenue from business travelers (the technical term for this is “price discrimination”).

But as @choster noted, airline yield management is often counterintuitive and fare rules can often produce side effects so you shouldn't expect any “rule” to hold in all situations.

In practice, I am not aware of any surefire way to identify potentially free or cheap stopovers. You can try to read fare rules but it's not especially quick or practical. And, once you have identified a potential layover (perhaps through a regular “round-trip” search), you can enter the details of the connection you want using the “multi-city” feature (i.e. not as separate tickets) to see how much it would really cost.

Is there a reason for this?

It's a complicated supply and demand equation. Usually, a major factor is that:

• The direct flights are a premium product. Of the people in London wanting to get to Moscow (or the people in Moscow wanting to get to Tokyo), the ones with the deepest pockets, most urgency or most flexible expense accounts will favour the direct flights and will pay more for the speed and convenience. These tickets are priced based on estimates of what these customers will pay.

• The indirect flights are a less premium option, sold in a more price-conscious market. There usually aren't enough people willing to pay a premium for direct flights to fill most long-haul routes, so the airlines aim to fill the remaining seats from the market of people looking for slower, more economical routes for a longer journey, by setting lower prices for legs of indirect routes.

  The market for ~15-24 hour indirect flights from London to Tokyo has many many airlines across many routes (via Moscow, Qatar, Frankfurt, Vienna, Helsinki, Amsterdam, Istanbul, Zurich, Seoul...), targeting price-conscious customers who have likely already rejected the premium ~12 hour direct flights. It may be much further than London-Moscow, but these customers have much more choice and willingness to shop around than, say, someone who must be in Moscow by 11am that day and whose company is paying.

There's usually more to it than that - supply and demand is complicated - but this is a reason why they're usually more expensive.

Is there a convenient way to find flights which purposefully extend layovers for a day or so?

There are a few:

• For up to 24 hours, which (depending on the airport location, local transport reliability, and immigration rules) may be enough for a little sightseeing, some flight comparison sites, e.g. Kayak, allow you to specify a minimum stopover time and specify specific stopover airports.

• Beyond 24 hours, most flight comparison sites allow you to build "Multi-stop" or "Multi-city" flights. Check specific airline websites as well, which sometimes include options not available to 3rd party comparison sites (IIRC Air New Zealand have a very good flight builder). For example, on SkyScanner:

These generally cost more than equivalent singles and returns where it is counted as a layover, but are often cheaper than booking "premium" direct flights. Why? Because supply and demand is complicated.

Airlines make most money with customers on direct flights. The problem is, offering direct flights between every pair of cities in the world is not economically viable. Having layover passengers enables an airline to offer a flight from A to B on a plane with e.g. 100 seats when only 50 people actually need that flight, as the other 50 seats could be filled with passengers who fly A to B as a leg.

As a layover is an obvious inconvenience for the passenger, such flights have to be offered at a discount to make them competitive. Airlines may earn very little while doing this (or even do it at a loss), to avoid a bigger loss from flying a half-empty plane.

Besides the other reasons given, if there's a problem and the airline has to put you on another flight then it's a lot better for them if they only have to get you to Tokyo rather than having to specifically go though Moscow.

With one you are buying London to Tokyo, probably stopping in Moscow along the way but maybe not. With the other you are buying London to Moscow to Tokyo for sure. That certainty is more valuable to you, and higher risk of additional costs for the airline so it's perfectly reasonable for the price of the ticket to be higher.