DRAMs achieve high memory density by storing each bit of information with one transistor and one capacitor. That got me wondering, how expensive is a capacitor relative to a transistor?
The question isn't necessarily about the relative cost of each transistor versus each capacitor. Once the masks are made for manufacturing the silicon chips, a chip made purely of transistors wouldn't cost any more than a chip made of purely capacitors (Excepting the number of steps in the manufacturing process, which a mixed chip would need all steps anyway).
Image pulled from the SRAM wikipedia page.
Alternatively, we can use a DRAM cell. As you mentioned, DRAM uses one transistor and one capacitor, which means we can fit many more of these two-component storage cells onto a single chip than the six-component storage cells. DRAM is cheaper because it can be made significantly more dense than SRAM, not because of the relative cost of the transistors and capacitors on the silicon chip.
If you're asking this question from a VLSI perspective then it certainly is going to depend on the process, but it will be a complicated question to answer. It looks like a typical DRAM memory is constructed by a process that's designed to make densely packed DRAM cells, and in a modern DRAM the capacitor is built above the transistor such that they have a similar cost. A more typical CMOS process doesn't have the facility to make small area capacitors like this, and is optimized to make small transistors and no capacitors at all.
People who may have designed or used DRAM cells or a DRAM process are likely to be under NDA and unable to talk about the particulars like cell sizes.
We relate area to cost because a larger silicon chip requires more materials and more effort to produce, but also because it presents more opportunities for a defect to destroy it reducing yeilds and requiring a large portion of the production to be thrown out.
Taken literally the question is quite meaningless since parts of a DRAM cell cannot be "sold" separately.
In terms of R&D effort, the single biggest investment in making a DRAM chip is the resolution of the process, which applies to all the structures inside a chip, transistors and capacitors alike. Then comes the layout: that's what allows packing more individual DRAM cells on a given area, and again, it cannot be attributed to only transistors or only capacitors.
In terms of the real estate on a chip (which defines production costs), the most important structure is the interconnect matrix (bitlines, wordlines and contacts) rather than DRAM cells themselves. If we consider only DRAM cells, then capacitors are typically larger so they are more expensive in that sense.
DRAMs ... how expensive is a capacitor relative to a transistor?
Please see my answer as an extension to Dmitry Grigoryev's answer:
Your question seems to be based on the false assumption that microelectronic circuits consist of single parts the same way a soldered circuit does.
However, this is not the reality.
In reality, microelectronic circuits consists of areas where the material has a certain chemical composition.
If you read that some integrated circuit has about 1500 transistors, then this actually does not mean that this IC is built of 1500 parts, but it means that there are maybe 10000 different areas on the IC. These 10000 different areas work like a soldered circuit made of 1500 single transistors would work.
I have already seen a cut drawing of a DRAM cell: It is nearly impossible to tell which area belongs to the transistor and which one belongs to the capacitor because some larger areas are both there for storing charge (capacitor) and for controlling the resistance in another area (transistor).
This means that these areas are both parts of the capacitor and the transistor!
By the way:
The capacitance of the DRAM cells is very small. Larger capacitances on an integrated circuit are rather expensive. This is because larger capacitances require more space and the price of integrated circuits grows with the size, not with the number of parts.
For this reason ICs like the MAX232 don't have the capacitors built in but external capacitors are used.