  We examine various predictions of the minimal supersymmetric standard model
coupled to minimal supergravity. The model is characterised by a small set of
parameters at the unification scale. The supersymmetric particle spectrum at
low energy and the spontaneous breaking of the standard model itself are then
generated radiatively. The previously considered predictions of the model now
include the neutralino relic density which in turn provides bounds on the scale
parameters. We find a remarkable consistency among several different
constraints which imply all supersymmetric particle masses preferably within
the reach of future supercolliders (LHC and SSC). The requirement that the
neutralino be the dominant component of (dark) matter in the flat Universe
provides a {\em lower} bound on the spectrum of supersymmetric particles beyond
the reach of LEP, and most likely also the Tevatron and LEP 200.
