Sustainability in a Risky World

How much consumption is sustainable, if “sustainability” requires that welfare should not be expected to decline over time? We impose a sustainability constraint on a standard consumption/portfolio choice problem. The constraint does not distort portfolio choice, but it imposes an upper bound on the sustainable consumption-wealth ratio, which must lie between the riskless interest rate and the expected return on wealth (and if risky capital evolves according to a geometric Brownian motion, it lies exactly halfway between the two). Sustainability requires an upward drift in wealth and consumption to compensate future generations for the increased risk they face. (JEL D63, D81, E21, G51, H43, Q01)