Sustainability in a risky world

How much consumption is sustainable, if \sustainability" re- quires that welfare should not be expected to decline over time? We impose a sustainability constraint on a standard consump- tion/portfolio choice problem. The constraint does not distort portfolio choice, but it imposes an upper bound on the sustain- able 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.