The Leisure Economy: The Future of Growth and Population under a Binding Energy Limit

This paper analyzes where productivity gains go when output is bounded but humanity is still innovative. We build a modified Ramsey growth model with endogenous fertility and an endogenous allocation of time between work, leisure and child rearing, in which a renewable resource is essential in production but limited in supply. When the resource constraint binds, the income share of the resource rises and is increasingly captured by a scarcity rent. We denote this pattern as Baumol's Energy Cost Disease. This mechanism decreases the labor share and productivity gains translate into work time reduction and the emergence of a leisure economy. Calibrating our model to the global economy for 1960--2020, we illustrate the quantitative effects for the coming centuries and show that population growth is reduced in anticipation of a resource-constrained economy. The welfare criterion then governs how many people share the bounded output. In two extensions we show that a total utilitarian planner chooses larger populations at lower per-capita consumption, and that the transition mechanisms carry over when endogenizing the research process, provided the energy constraint is reached before ideas run out. JEL codes: E25, J11, J13, J22, O41, O44, Q43