economics//economic growth//semi-endogenous growth

Semi-endogenous growth is a class of growth models in which ideas drive long-run growth but become harder to find, so that steady growth requires the number of researchers to keep growing, and it is the standard explanation of why technological progress has been roughly exponential while research effort grew much faster. Charles Jones proposed it in 1995, after earlier models predicted that more researchers should mean permanently faster growth, which the data did not show.

Semi-endogenous growth is a class of growth models in which ideas drive long-run growth but become harder to find, so that steady growth requires the number of researchers to keep growing, and it is the standard explanation of why technological progress has been roughly exponential while research effort grew much faster. Charles Jones proposed it in 1995, after earlier models predicted that more researchers should mean permanently faster growth, which the data did not show.

On a steady path the growth rate of technology is tied to the growth of the research effort, gA=λ gL/βg_A = \lambda, g_L / \betagA​=λgL​/β in the notation of the idea production function. With a constant research population, gL=0g_L = 0gL​=0 and growth eventually stops; the twentieth century kept growing because the number of scientists and engineers kept rising.

The model makes growth depend on demography, which is why automating research is a large change: if researchers are copies of software, their number grows with compute and with the efficiency of the software, not with population.

Whether that change produces acceleration or only a faster steady pace depends on whether λ\lambdaλ exceeds β\betaβ.