reform, it follows from claim 9 that if the high e¢ ciency party accepts the o¤er,
it wins the election. For that reason, the high e¢ ciency party compares the
political and e¢ ciency bene…ts of reform to the …scal concessions it has to make
in order to ensure reform. That is, it compares its expected utility levels under
each alternative and accepts the low e¢ ciency party’s o¤er when
V (
; k
H
;
H
; R)
U (
b; k
H
; 1) +
R
2
(15)
In period 3, the decision for the low e¢ ciency party depends on whether it
can …nd a …scal policy which maximizes its utility, subject to the high e¢ ciency
party still accepting. The low e¢ ciency party, therefore solves the following
program:
maxU (
; k
L
;
H
)
(16)
subject to U (
; k
H
;
H
) +
R
2
U (
b; k
H
; 1) (constraint 1)
and U (
; k
L
;
H
)
U (
b; k
L
; 1) +
R
2
(constraint 2)
where the …rst constraint is a reexpression of equation (15) and states that the
o¤er must be acceptable for the high e¢ ciency and the second constraint states
that the bene…t from the …scal bene…t, along with the e¢ ciency gains from
reform must at least o¤set the electoral loss from supporting reform.
In order to understand the mechanics of this program it helps to recall how
changing taxation a¤ects utility.
Remark 3
Notice that each party represents one social class and any equilib-
rium …scal policy lies between
r
;
p
. It follows from claims 1 and 2 that if
@U ( ;k
L
;Z)
@
? 0 ()
@U ( ;k
H
;Z)
@
7 0. For that reason, when the low e¢ ciency
party represents the rich (poor), it reduces (increases) taxation until the point
where either constraint 1 binds or the tax rate is the one preferred by the rich
(poor) party.
From the following remark and the constraints one can construct the solution
to the program.
Solution 1
i) Whenever the low ability party represents the rich, it reduces
until the point where constraint 1 binds, whichever occurs …rst. If at that
level, constraint 2 holds, then a solution is found, if constraint 2 does not hold,
then there is no solution to the problem and the party simply blocks reform. ii)
Whenever the low ability party represents the poor, it increases
until the point
where either either
=
p
or constraint 3 binds. If at that level, constraint 2
still holds, then a solution is found, if constraint 2 does not hold, then there is
no solution to the problem and the party simply blocks reform.
From the previous remark and solution, a central proposition can be con-
structed.
18
Convention