Backstop Technology and Growth: Doomsday or Steady State?

A backstop technology provides resources at a constant marginal cost for an indefinitely long time. Healʹs formal model of a backstop technology supposed that output is produced by capital and resources. He derived the result that consumption either grows or decays exponentially, or is constant: the outcome depends on a “knife-edge” constellation of exogenous parameters. The result is puzzling because Doomsday could arrive despite the availability of a backstop technology. This paper shows that if labor is a productive factor, then a steady-state equilibrium is reached just as in standard optimal growth models.