We describe a simpler proof for Calvert and Keady's (C-K) theorem showing the non-occurrence of the Braess
Paradox in networks with power-law congestion costs. We extend the C-K theorem to the case of elastic demand. We then
use the methods of these proofs to develop several new theorems about the optimality of flows and the piecewise stability
of Minimal Revenue (MR)Tolls in transportation networks with power-law congestion costs, with and without fixed costs.
The stability of MR tolls is an important attractive feature. For administrators it makes the tolls cheaper to collect. For users
it makes the tolls more predictable.