Nodal prices, congestion revenues, transmission capacity rights, and c
ompensation for wire ownership are key concepts used to formulate clai
ms about proposals to organize competitive and open transmission acces
s. Underlying those claims are implicit assertions (folk theorems) con
cerning the regulation of transmission access, the determination of po
wer flows, properties of economic dispatch, and the operations of comp
etitive nodal markets for power. The paper has two objectives. We firs
t formulate these folk theorems as explicit mathematical assertions. W
e then prove that some of these assertions are true, and we present co
unterexamples to other assertions. The counterexamples are interesting
because they negate plausible propositions, including: (1) uncongeste
d lines do not receive congestion rents (defined through node price di
fferences); (2) nodal prices clear markets for power only if the alloc
ation is efficient; (3) in an efficient allocation power can only flow
from nodes with lower prices to nodes with higher prices; (4) strengt
hening transmission lines or building additional lines increases trans
mission capacity; (5) transmission capacity rights are compatible with
any economically efficient dispatch.