From Moore’s Law to Eroom’s Law: Power Constraints and the Productivity Slowdown

Economic growth depends on combining existing inputs into new inventions. However, these combinations are not always physically feasible. One important example is dark silicon, where power and cooling limits prevent all the transistors on a chip from operating at once. I develop a growth model motivated by these limitations and establish conditions for a unique balanced growth path where electronic miniaturization and power efficiency grow at the same rate. When power-efficiency research becomes harder, both total research employment and productivity growth fall on the new balanced growth path. With gradual adjustment of research employment, I construct a local equilibrium transition in which more researchers temporarily coexist with slower productivity growth. This Eroom’s law result holds for small shocks in a two-dimensional design space with sufficiently similar industry constraints.