If robots are really used everywhere, then 90% unemployment isn't deprivation -- it's liberation.
If robots build everything, including themselves, and the only things still requiring human labor are things like art, science, and designing the next generation of robots, then that's the world set free from want. It's almost like having a replicator from Star Trek without the technobabble physics. If robots can do it all, every machine can ultimately be made starting with rocks, air, sea water, and sunlight. Things not directly manufactured (like food, natural fibers, and timber) can at least be tended and harvested by robots in place of farmers, ranchers, and fishers.
It isn't, because you still need raw materials which are an awful lot more exotic than you think they are (such as neodynium for example) and very large quantities of other materials, and there's still scarcity of those, and the sources of the materials are owned by a tiny ultra-wealthy fraction of the world's population. Then there's the problem of capital expenses; a fabrication plant capable of building state-of-the-art chips costs billions of dollars to build and lots of money to keep running, and that's with the specialist equipment required being bought in from third parties that can spread their development costs across multiple fabs and companies. Even normal robot factories are hardly cheap.
I would identify 3 broad areas that necessarily contribute to the cost of producing material goods. They are the costs of raw materials, energy, and labor. Supposing that robots can perform all labor necessary to produce anything that is manufactured today -- a big supposition, to be sure -- then we are left with costs of energy and raw materials.
Energy is effectively free because if robots can build anything for free, they can build solar panels, batteries, nuclear reactors, and other energy generation and storage devices too. The rate at which energy can be produced is still limited by thermodynamic considerations or (more pressingly) the available planetary surface area per person, but the cost of manufacturing and operating energy systems is zero.
Finally, what of raw materials? Today it is important to work concentrated ores to extract mineral products because energy, machinery, and labor have substantial costs. If those costs are near-zero than the initial concentration and distribution of mineral resources is much less important. Better to extract aluminum from backyard rocks using your free energy and unpaid robot-labor than to pay a bauxite mine owner for access to his more concentrated mineral resources.
With free energy and robot labor, the only mineral resources that aren't accessible from common rocks are those that are both rare on Earth and strongly concentrated by geochemical processes. This includes, in my opinion, tellurium, indium, bismuth, tungsten, silver, gold, and the platinum group metals. These metals are technologically useful but can be substituted in almost all applications at some modest cost to performance. It does
not include relatively common and widely dispersed elements like gallium and the rare earth elements that nonetheless command a high price at present and thereby seem scarce. Neodymium itself, for example, is about 3 times as abundant as lead in the Earth's crust.
By way of example, look at
this analysis from the USGS of basalt located near Portland, Oregon. There are over 480 trillion tons of similar basalt in the Columbia Plateau spread over thousands of square kilometers of the northwestern United States. One ton of this type of rock, literally more common than dirt, contains about $70 worth of minerals at current market prices (mostly from the vanadium, molybdenum, cobalt, and rare earth elements). The reason it's not exploited at present is that it costs more than $70 in machinery, labor, and energy to separate the desirable elements from bulk rock. But if the labor is as free as self-duplicating robots and the energy is as free as sunshine, these "rare and valuable" elements actually prove common and nearly as good as free.
This finally takes me back to my original statement:
if you have robots that do nearly everything, including building copies of themselves, the price of most material goods collapses because they can be reproduced at nearly zero marginal cost, like MP3s. If the self-reproducing robotic systems have a small footprint it's conceivable that everyone could have one in their back yard. If they have a large footprint, they'll need a friendly nation to operate in, one that would benefit more from the abundant free energy and goods from "pirated" robotic systems than from adhering to international treaties about trade and intellectual property. Fortunately, there is no shortage of nations in the latter category, and their goods will cross borders regardless of law, just like Americans can get cheap (if not completely free) high-quality DVD bootlegs from Chinese suppliers. Either by vote or by violence, the robotic abundance will eventually spread worldwide, because there is no continent where intellectual property owners and the rich outnumber hourly workers and the poor.