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What it takes to get explosive economic growth

Economic growth is determined by the supply and demand of investment capital; technology determines the demand for capital, while human nature determines the supply. The supply curve has two distinct parts, giving the world economy two distinct modes. In the familiar slow growth mode, rates of return are limited by human discount rates. In the fast growth mode, investment is limited by the world's wealth. Historical trends suggest that we may transition to the fast mode in roughly another century and a half.

Can some new technology switch us to the fast mode more quickly than this? Perhaps, but such a technology must greatly raise the rate of return for the world's expected worst investment project. It must thus be very broadly applicable, improving almost all forms of capital and investment. Furthermore, investment externalities must remain within certain limits.

Introduction
Many technological enthusiasts, impressed by the potential of various envisioned technologies, have speculated that technology may soon become so productive as to induce a "singularity", a period of extremely rapid growth. (A collection of speculations can be found here and here.)

How rapid? Over the last few centuries, population has doubled roughly every 70 years, per-capita consumption has doubled roughly every 35 years,and scientific progress has doubled roughly every 15 years. In contrast, computing power has doubled roughly every two years for the last half-century. Many have speculated that perhaps economic growth rates will soon match or even greatly exceed current computing-power growth rates.

What would it take, exactly, for a technology to make the economy grow this fast? This paper offers a simple economic analysis intended to illuminate this question. We will find that while very rapid growth is possible in principle, this requires enabling technologies to meet some strong conditions. It is hard to see how any single new technology could do this, though historical trends suggest that the accumulation of all new technologies over the century and a half might.