  We derive Price inequalities for harmonic forms on manifolds without
conjugate points and with a negative Ricci upper bound. The techniques employed
in the proof work particularly well for manifolds of non-positive sectional
curvature, and in this case we prove a strengthened Price inequality. We employ
these inequalities to study the asymptotic behavior of the Betti numbers of
coverings of Riemannian manifolds without conjugate points. Finally, we give a
vanishing result for $L^{2}$-Betti numbers of closed manifolds without
conjugate points.
