In my story, humanity has wiped itself off earth (salted nukes, to be precise) and survives as a large remnant civilization in the asteroid belt, with small bases on the moon and possible mars.
As the plot begins, my main character is a self employed ship owner who scavenges the remains of satellites around earth looking for microprocessors, which are one of the only things that her civilization still cannot produce. Because a processor is needed for every ship, several for a colony or for a factory, they are incredibly valuable. Ideally, one successful find can fund refuelling her ship, and supplies and rations that would last her months.
Is it plausible that a spacebound civilization, that produces rocket engines, life support equipment, tube radios, and large space stations, would be incapable of producing microprocessors, and so would pay the equivalent of millions of dollars for each scavenged unit? Would the radiation environment in space make producing computers more difficult than it is on earth?
Going off the answers to this question about recreating a computer in ancient times , building a computer is incredibly hard. My space civilization necessarily has pretty good material science and manufacturing capabilities to even survive, but I don't know if it could devote the thousands of people needed to set up a photo-lithography plant. In addition, the existence of expensive but very powerful scavenged cpus should discourage efforts to make new computers unless they can be mass produced, since a million dollar hand-made computer capable of ten megahertz can be replaced by buying access to one thouandth of the processor time of your settlement's i7 based mainframe.