In hypothetical situation where self-repairing solar-powered robots farm food for everyone, is the cost of living, or at least food, now free?
Historically the primary reason given for why people have to work has been “to put food on the table.”
Robotic labour however is not free. There is the initial capital cost of creating and initializing (or teaching) the machine, and there is the ongoing costs of energy consumption and maintenance. The former is comparable to the costs of hiring and training workers, while the later is comparable to the wages and salaries of existing human workers. Thus it would be expected that if humans and robots were to compete for jobs, it would actually drive wages down.
It is much more likely then that the market will establish a new equilibrium in which human and robot are both competitive in particular niches.
Perhaps one could construct a morally ideal utilitarian world where robots who are happy to serve do all the drudge labour in society, while humans are free to do as they please.
Though, such a society would have to have a completely different economic system, than one where survival depends on labour. In a way, one could truly abolish wage slavery this way. Two possible systems could occur, a capitalist system with each person owning robots that can do their work for them, or a socialist system where all the robots were owned by the state and a guaranteed income supplied to everyone based on the robot labour. A third communist system where the robots were free to just give their labour to people in need might also work, as robots would actually have a nature in which voluntary work was desirable. Most likely a mixed economy would evolve, as corporations would try to buy all the robots, and so the government would have to step in with the minimum income to deal with widespread unemployment.