As noted in some initial comments (but I feel fine answering, as I had the exact same ideas when I read the question), this is a general progression of technology but there are two very specific factors for RAM:
Core Memory -> Integrated Circuits
While many different, very expensive, systems were used in the first computers, including mercury delay lines, CRT storage tubes and magnetic drums, the primary memory technology from roughly 1955 - 1975 was core memory. Still lives on, for some of us, in terminology such as "core dump".
There were no "personal computers" in 1955, at least not based on cost! In the 1960s mainframes and minicomputers both used core memory. Some of the first minicomputers were used in a single-user/single-task/single-operator mode, so arguably they fit the "personal computer" term, though arguably it wasn't until the days of the 8080 and 6502 that there were affordable & functional personal computers.
Because core memory required actual physical separate wires running through tiny little magnetic cores, there were both limits to the achievable density (smaller = cheaper, at least in cost of materials) and limits in speed of the manual labor involved in actually threading the wires through the cores.
Integrated circuits were the next (and still current) major form of RAM. Individual transistors were actually not a major advantage over core, because the physical space needed for transistors was larger than needed for core memory, on a bit-for-bit basis. Integrated circuits changed that. For those who don't know, while Intel is most famous for its CPU chips, it started making memory chips for mainframe computers. Which leads us to Gordon Moore and...
Moore's law is the observation that the number of transistors in a dense integrated circuit (IC) doubles about every two years
Memory chips (Static RAM vs. Dynamic RAM vs. various types of Flash) vary in terms of how many transistors needed per bit. However, within each type, the improvements based on Moore's Law have resulted in consistent improvements in both capacity and cost.
In fact, I would argue that Moore's Law has had more of an impact on memory than on any other type of chip. Improvements in CPUs now depend as much, if not more, on improved design - pipelining, cacheing, predictive branches and so many other things - where improvements in RAM largely come down to using smaller transistors and more of them in each chip.
It was simply impossible to produce today's RAM chips 50 years ago - integrated circuits had transistors on the order of 2,000 times the size they are today (10 µm vs. 5 nm). And if you could build a gigabit chip in 1971, it would have been physically too large to be useful.