Equilibria Under Fiscal and Institutional Logrolling
Proposition 3
When there is …scal and institutional logrolling, there can emerge
the following political equilibria:
A. If the party of the poor has higher e¢ ciency, there can be two outcomes:
A.i) When 9 a
such that both constraints 1 and 2 hold, then a) if at
r
constraint 1 still holds, the party of the rich o¤ ers support for reform in exchange
for a tax rate of
=
r
, b) if at
r
constraint 1 fails, the party of the rich
selects tax rate
=
such that
solves U (
; k
r
;
H
)+
R
2
= U (
b; k
r
; 1).
The party of the poor always accepts the …scal logrolling o¤ er, wins the election
and implements reform e¢ ciently.
A.ii) When @ a
such that constraints 1 and 2 hold, the reform is oppor-
tunistically blocked by the party of the rich, each party wins the election with a
1
2
probability.
B. If the party of the rich has higher e¢ ciency, there can be two outcomes:
B.i) When 9 a
such that both constraints 1 and 2 hold, then a) if at
p
constraint 1 still holds, the party of the poor o¤ ers support for reform in exchange
for a tax rate of
=
p
, b) if at
p
constraint 1 fails, the party of the poor
selects tax rate
=
such that
solves U (
; k
r
;
H
) +
R
2
= U (
b; k
r
; 1).
The party of the rich always accepts the …scal logrolling o¤ er, wins the election
and implements reform e¢ ciently.
B.ii) When @ a
such that constraints 1 and 2 hold, the reform is blocked
and each party wins the election with a
1
2
probability.
Proof.
Omitted, it follows directly from claim 9 and solution 1.
While these results seem very similar to those in the previous extension,
there are two important di¤erences. Logrolling allows the low ability party to
be compensated for its losses sometimes, so it reduces the area under which
reform fails, and therefore improves e¢ ciency. Logrolling on the other hand has
its disadvantages, as it may lead to opportunistic behavior by the high e¢ ciency
party.
Proposition 4
a) When logrolling occurs and constraint 1 binds, the high e¢ -
ciency party is opportunistically supporting a logrolling o¤ er that hurts its con-
stituents. Alternatively when logrolling occurs, and constraint 1 does not bind,
the high ability party may or may not be opportunistically supporting a logrolling
o¤ er that hurts its constituents.
Proof.
a) When constraint 1 binds, U (
; k
H
;
H
) +
R
2
= U (
b; k
H
; 1) =)
U (
; k
H
;
H
) < U (
b; k
H
; 1) which is the utility that the constituents would
get in the absence of reforms. ii) When constraint 1 is not binding, (i.e. when
=
r
when the part of the poor is high e¢ ciency and
=
p
when the party
of the rich is high e¢ ciency) then U (
; k
H
;
H
) +
R
2
> U (
b; k
H
; 1), which may
occur either when U (
; k
H
;
H
) 2 [U(b; k
H
; 1)
R
2
; U (
b; k
H
; 1)) in which case
the constituents are hurt by logrolling or when U (
; k
H
;
H
)
U (
b; k
H
; 1) in
which case they bene…t from logrolling.
19
Convention