From what I understand, the engine is usually the most expensive part of each rocket, excluding payload.
I'm struggling to understand how SpaceX can have one of the cheapest launchers on the market when it flies on a 9 engine configuration, while many other launchers have fewer engines.
Isn't the cost of producing nine separate Merlin engines "theoretically" nine times more expensive than making one big engine?
No, on the contrary. The larger the engines get, the more expensive they get. Just look at the massive amount of full-scale tests they needed to get the F-1 engines of the Saturn V main stage running smoothly. Now imagine, you spend all this money to design a huge engine, and you want to manufacture it. You will need a top-notch machine park to do that. Making such an engine includes a lot of steps, like getting a huge chunk of space alloy, and milling almost all of it away, closing the cooling channel using a slow galvanic process, maybe some electron ray welding here and there.
Simply put, to make a huge engine, you need huge amounts of raw materials, huge machines and a huge permanent staff to operate all of them.
Now, on the other hand, if you want to make several small engines, the design becomes less risky and you don't need such huge machines. What's more, since you now need many more engines, you have something resembling a production line, and all machines are operating at the same time, rather than each engine going through a process like in a manufactory.
At almost every step of the way you save money, but several smaller engines are generally heavier. An even greater downside is that, if you need every engine to work for your rocket to reach orbit, you end up with a larger chance of failure.
SpaceX has some redundancy planned in, but that comes at a further cost in terms of payload.
In the end it comes down to cost per kilogram to a target orbit to the customer, and the amount of factors that have an influence here is way too large for an SE answer. SpaceX bet on clustering, Europe will continue to go with large engines. Only time will tell who made the better call.
Traditionally, engines are expensive because they require lots of manual labor to build. Because they are built in small numbers, there's no point in investing in an automated factory that can build them cheaper. They are also optimized for maximum performance, requiring complex constructions and expensive materials.
SpaceX wants to change that equation. By building 10 engines per rocket, it becomes cost-effective to set up a production line. They've also designed the engines to be cheap to produce, even if that reduces performance a bit.
In addition to the other answers, I think its also worth noting a few extra points:
Landing. It takes just one of those engines, throttled all the way down to its minimum thrust to land the stage for re-use (a key design feature). Any more than this amount of thrust would make the landing even more difficult. Thus if one large engine were used instead of the 9 merlins, then it would have the additional design requirement of being able to throttle down all to an equivalent level of a merlin at minimum thrust, which would presumably add to the cost. Or have a dedicated small engine for landing, which would add weight and cost.
Stage 2. The 2nd stage of this launch vehicle uses one merlin. If one large engine was used for stage 1, then there would be 2 engine designs instead of one.
Redundancy. From wikipedia:
Like the Saturn series from the Apollo program, the presence of multiple first-stage engines can allow for mission completion even if one of the first-stage engines fails mid-flight.
A single large engine could not satisfy this safety/reliability design requirement by means of redundancy. So it would have to have that extra required reliability as an inherent part of its design, which would also increase cost.
It depends on so many things. SpaceX chose many instances of a smaller engine, which is generally simpler than a single larger one to build and complexity is related to cost.
They chose a fuel and fuel cycle that is simpler than most. They chose an injector that is reliable and simple. Liquid Hydrogen is very hard to work with and very expensive. So an RS-68/68A in comparison would be much more expensive. An SSME is in a class of its own for costs.
So the real comparison would be something like a pair of RD-193's or a single RD-180 whose aggregate thrust is on the order of 800,000lbs of thrust. Each Merlin is approaching 180,000lbs of thrust, having started at 75,000lbs of thrust.
Additionally, SpaceX has said that they brought in process engineers from Tesla to focus on issues related to building large numbers of engines, taking advice from the auto industry on reducing costs.
If you make a grand total of 10 engines a year, then all the staff costs for the facility is spread as the cost of those 10 engines. If you make 400 (SpaceX's stated goal) it is spread over more.
SpaceX's cost, in addition to all of the other items noted, is cheaper because they build everything in house, and have made a deliberate effort over the years to reduce their cost. Most of the other players aren't working much to reduce their costs, and not nearly as hard as SpaceX. SpaceX uses many non-space rated components which have been found to work through experimentation. All of this reduces the costs
There is the fact that they already designed the rocket engine for single engine launches. Strapping 9 together is the kind of agile work done by a company that disrupts slumbering Giants.
