Why do professional digital cinema cameras like ARRI ALEXA, RED Epic cost that much? They record 4k so do other cheap cameras?
Look at it from a data rate point of view: a GH4 records 4K at 100 Mbps. A RED Carbon Fiber WEAPON records at 300MBps. That's 24x the data rate. Look at how very much more expensive it is to purchase a CPU that's 10% or 30% faster than "normal" and you might then have some understanding of how much more expensive it is to offer 10x or 30x the performance in a camera body.
You are probably comparing cameras that record compressed 4k video with cameras that record uncompressed video, i.e. RAW footage. The ARRI ALEXA and RED Epic belong in the latter category.
The hardware for cameras capable of recording RAW footage is more expensive. Also, it hasn't been around for as long and as with every new technology, prices start higher (for example, 4k cameras are more expensive than Full HD cameras right now). Wait a couple of years and 4k RAW cameras will most likely be available starting at much lower prices. Here's a Wikipedia list of cameras that are capable of recording RAW footage. As you can see, it's not very long yet …
The image processing of cinema cameras is done with fairly inexpensive FPGA chips, that doesn't explain a 50.000€ price difference between I.e. a gh4 and a arri Alexa. The FPGA chip used in blackmagic products is sub 10€, so even if the Red or Alexa use a 100€ fpga, that's not the point. Media storage is also not the point, since all vendors use standard media like ssd's, cf/cfast, SD card etc.
The single most expensive part in any video camera is usually the sensor, and there are very big differences in image quality when using different sensors which come at very different price points.
There are also some really big differences in manufacturing quality, also in the materials used. But the main difference is service, quality assurance and: R&D. Even when the Alexa only was available as a 2.5k version, it completely wiped the competition off the scene in the drama / feature section of cinema. That is because arri spend a lot of time and work to achieve a consistent and highest level image quality.
To give you and example from the sound world: schoeps (which produce some of the best and most expensive microphones) artifically age their mics in a climate chamber by 10 years before selling them to make sure each microphone keeps its quality over a long time... A company like rode, which sells ok quality, fairly cheap microphones could not do that or they would loose money on each sale.
Different markets have different requirements. A feature film production can easily cost a couple of million euro / dollar, so a budget of 100.000€ for the camera department is not much In comparison. What is really expensive though is loosing shooting days to a camera not working. So the focus in professional film production is not on how much resolution does camera X have but how reliable can the crew work with it.
This whole business goes as far as offering products that are not for sale but only available as rentals, like panavision cameras or the 65mm sensor Alexa.
In addition to the points above, keep in mind that cinema cameras also have a host of features not found in cell phones and lower-end cameras, such as removable lenses, better autofocus, better bodies that may be weather-resistant or weatherproof. They also have larger sensors which cost more, and the specs on the sensors are probably better than in low-end 4K cameras. (For example 3 CCD cameras with a separate sensor for red, green, and blue, as opposed to a single Bayered CMOS sensor.)