For a long time, economists have used production functions to study the impact of changes in the elasticity of substitution between capital and labor in factor income distribution. When the elasticity of substitution is one the relative shares remain constant, when it is greater than one the share of capital increases and when it is less than one the share of labor rises.
Most economists believe that the remarkable stability of the relative share of capital and labor in total income experienced in capitalist countries is due to the fact that technical progress is either neutral (and the elasticity of substitution is one) or is mildly labor-saving but the relative earnings of labor in relation to capital will decline due to a relative labor abundance, thus moving the elasticity close to one. But, what will happen to capitalism if technical progress turns extremely labor-saving and labor income becomes negligible or negative?
For instance, imagine a futuristic scenario where each one of us owns personal robots better than us in all domestic and professional tasks, not just the simply tasks of cleaning and similar. Science fiction typically depicts such scenario in terms of who will be the master, us or the robot, but I will assume that humans will be the masters.
Following the law of comparative advantage we would leave to the robots the tasks where they had a comparative advantage, for both pleasant and unpleasant jobs. However, by increasing the number of robots relative to that of humans, humans would be able to skip entirely all the unpleasant tasks. Therefore, the few pleasant jobs left to humans would be mostly the design and supervision of robots and to decide on collective investments. Because these function will not occupy many people jobs for humans will be so scarce that workers might be willing to pay for the privilege to work rather than be paid.
So, in such a world, how would capital accumulation and economic exchange work? Could the six principles of capitalism survive in such world? Can we imagine exchanges to continue as usual but now with trading between robots at a speed not accessible to humans?
In such a world the accumulation of human capital (skills and education) will be driven by non-economic factors and everyone’s income is essentially determined by capital returns. Thus everyone would need to own traditional assets and robots either directly or indirectly through collective investment vehicles (e.g. pension funds) or the government.
That is, the markets for goods and services could work as they do now but the labor market would be substantially different, since humans would no longer be sellers but buyers in such market. Likewise, preferences for consumption and accumulation will be altered since in such society the leisure class will be a majority while the working class is a small minority.
There would be then three types of assets, the traditional forms of property, the human replicas (slave robots) and the embodied skills and human capital necessary to qualify to buy the right to work. The first two types of capital can be merged in two categories - traditional assets and slave robots. Therefore, one could still use the conventional two-factor model so that in a product function we were left with two single inputs, traditional capital and slave robot labor, and again define an elasticity of substitution between them in the usual way.
The only requirement is that slave robots be separable from their owners so that they may be traded like any other type of capital. In this futuristic world, private property would still be needed to drive consumption and capital accumulation, but human labor supply would no longer constrain the rate of capital accumulation and could be considered as perfectly elastic. Therefore, the personal fortune of each individual robot-owner will depend entirely on its initial endowment, investment skills and luck on selecting their portfolio of capital and robots.
The jobs for humans would be a status symbol to be achieved through other means rather than competitive markets, namely through hereditary rules, lottery or voting. All job positions could be theoretically auctioned, like old master paintings, but it would be inefficient. Such a society would resemble Ancient Rome but with robots instead of human slaves.
Nevertheless, it is unlikely that self-reproducing slave-robots could be left entirely in the hands of private individuals. Even assuming a good regulatory environment, most people might prefer state ownership fearing that robots might turn against humans.
If that happens one could no longer rely on comparative advantage, even in the context of a single factor (slave-robots) model, because that factor would be jointly owned (state owned). Moreover, slave-robots would be more homogeneous than humans which would make them less differentiated in terms of comparative advantage. So, new solutions will have to be found.
In conclusion, the ways humans chose to regulate the production of humanoid slave-robots will determine how a new economic system may differ from capitalism.