Economics will never disappear because many goods are fundamentally scarce. Fortunately, the necessities of life really aren't, so the economy could conceivably be pried away from its current position as holder of both carrot and stick (I'm defining "stick" as "withholding the necessities of life" here) and reduced to simply offering carrots. This would be an extraordinary improvement and would put capitalism on course to actually live up to the "consensual transaction" and "monotonic improvement" rhetoric so frequently brandied about by the younger members of the capitalist camp. And the communist camp? Well,
people owning the means of production is what their philosophy was about all along. If it becomes practical to achieve such a state of affairs without government enforcement then the controversial and historically failure-prone side of their beliefs becomes moot. Capitalism and communism become more or less compatible, which will be no surprise at all to the people who have familiarized themselves with both schools of thought but possibly a bit of a shock to anyone who took the highly polarized rhetoric surrounding the issue at face value. In any case, this type of thing has been thought about and discussed before at great length, but there's a strong taboo hanging over the discussion which makes it easy to inadvertently ignore.
> a single person can use automation to make everything he needs
This would require a large amount of infrastructure per person. An intermediate target would be the point at which communes become viable -- share the heavy infrastructure across some number of people larger than 1 but smaller than 8 billion (or 300M if you think the US government is already sufficiently protectionist). The macroscopic trends of "increasing automation capability" and "decreasing market value of many peoples' labor" make it inevitable that this will happen at some point, the big question is when. It's possible we're approaching or have passed the tipping point but don't know it yet because we haven't invested enough effort in developing infrastructure optimized for decentralization, which is the opposite of what current market structures require. Also, there are a few big social sticking points, namely specialists who are necessary at the margin but who are still treated well by the traditional system (doctors). If workable alternatives can't be developed then the whole endeavor will have to wait until the market turns on them as well. One way or another we'll get past the issue, but getting around the social problems could take decades longer than getting around the industrial problems.
The big danger is that we don't get to the point of viable decentralization before the automation economy makes enough people redundant to create large-scale human misery and political unrest. Arguably this has already happened, but it can get a lot worse -- and I sure hope that we don't get a chance to find out just how much worse that is.