After dropping the standard general-equilibrium assumption that preference
orders discount future consumption faster than the economy grows and droppi
ng continuity and weakening utility representation, we establish commodity
prices and consumptions that approach approximate equilibrium to within any
practical tolerance. The Weizacker-overtaking criterion defines the best-k
nown non-standard-discounting orders we admit over discrete-time. determini
stic consumption paths and over continuous-time, stochastic consumption pro
cesses. We also perturb preferences to qualify all approximate equilibrium
as full equilibrium, thus showing some well-known non-existence examples ar
e singular, and so are inadequate defence of standard assumptions. Classifi
cation Numbers: C60, C62. (C) 2000 Academic Press.