Uzawa’s theorem states that all technological change in a balanced growth path must be labor augmenting. The intuition behind this is surprisingly simple — since capital accumulates, and labor does not, and there exists some optimal ratio between the two, technological change will simply lead to greater capital accumulation to exactly counterbalance the change in technology. If you think of there being some residual multiplying capital and labor, BK and AL, K will change to make B stay the same. Thus, technology improves labor. It follows from this that all technological progress must, in the long run, increase wages. Any excess return to capital will be competed away by accumulation. Chad Jones and Dean Scrimgeour have a short note explaining this, if you are interested in more.

A similar result underlies the famous (okay fine, “famous”) Chamley-Judd results. Their argument is that, in a Ramsey model with infinitely lived and homogenous agents, and two factors of production K and L, it is optimal to tax labor only, and leave capital totally untaxed. This result is simply because capital accumulates in the model, and labor doesn’t. Thus, we should tax the thing which inelastically supplied.

I do not, however, believe that this is economically relevant. L is not labor, and K is not capital, as we would understand them. Labor is an awful lot like capital, insofar as we accumulate skills, or human capital, over time. We have no real way of separating out capital returns and entrepreneurial labor, so there goes the tax argument. The infinitely lived agents is also a far too strong assumption to be the basis of anything serious.

But this is besides the main point, which is that it is perfectly possible for technological change to send wages to zero, if the rate of technological change persistently outstrips that of capital accumulation. This is the logic of Anton Korinek and Donghyun Suh’s paper “Scenarios for the Transition to AGI”. They note that, obviously, if all possible tasks are automated, human wages are zero; and if there is a long and thick enough tail of complex tasks which humans can perform, it is possible for wages to rise indefinitely. While we are on the way there, though, the future of wages is determined by a race between capital and automation. If the rate of automation is faster, wages fall to be equal to the rate of return on capital. Since multiplying an AI is cheap, the return to capital is also small.

If you say that humans require a certain amount of output to maintain, and we expect wages to drop below that subsistence level for a period, then whether humans will survive will depend on the discount rate of the AI, or on how many of us are capital holders, or on the ability of the state to appropriate enough resources. In short, it is perfectly possible for wages to fall to below subsistence. Do not let modeling conveniences mislead you!