EDITOR’S PROOF

Stable Constitutions in Political Transition 87

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Appendix

In this appendix we show that in the case whereLandMbargain andwM>w

the contract curve is vertical for 0<t<1. For convenience, we define the income

gap of each group relative to average available income as (^) M=wM−w≶0,
(^) L=wL−w<0 and (^) R=( 1 −γ)wR−w>0.
For 0<t<1,M’s proposalPM→L=(t′,x′)givenc=(t∗,x∗)solves the con-
strained optimization problem
max
[
vM(x)+( 1 −t)wM+tw
]
s.t.vL(x)+( 1 −t)wL−tw≥u
(
t∗,x∗
)
.
Writingμ(x′)=
∂vM(x′)
∂x
∂vL(x′)
∂x
≤0, the first order conditions for an interior solution of
this problem,x′satisfies
μ
(
x′
)

(^) M
(^) L
(3)
and the tax rate is determined as the residual satisfying
t′=
vL(x∗)−vL(x′)
(− 1 )L
+t∗. (4)
AtxM,μ(xM→L)=0 and atxL,μ(xM→L)→−∞. By continuity ofμ,aso-
lutionx′satisfying the first order conditions uniquely exists withx′∈[xM,xL).As
∂vM(x′)
∂x =−^2 |x
′−xM|and∂vL(x′)
∂x =^2 |x
′−xL|,x′only depends on the ratio^ M
(^) L.
By construction,x′is the policy level which is Pareto-optimal forLandM.Call
this policy realizationxe. It is easy to show thatL, when proposing toMselects the
same policyxe.
The optimal proposal can be interpreted as follows:xeis the policy which would
maximize the joint pay off forLandMgiven that transfers betweenMandLcan
only be achieved through the linear tax system:^ MLis the rate at whichM’s income
is converted intoL’s income as the tax rate increases. Note that a transfer rate of
greater than−1 signifies an involuntary contribution ofR.^25 If the ratio is− 1 /2, it
costs half a unit ofM’s income to increaseL’s income by one unit.μis the rate at
whichM’s utility from consumingxincreases per unit of utility decrease byL.Inan
optimum,M’s gain has to be equal toM’s cost of compensatingLat an admissible
tax ratet∈( 0 , 1 ).^26
(^25) One can show that the ratio is greater than−1ifwL+wM
2 <(w
M−wL),i.e.ifM’s wealth
exceedsL’s wealth by more than average wealth, where the latter is calculated looking atMandL
only. To demonstrate this point, note that^ MLcan be written asw
M+(wM−wL)−wR
wL−(wM−wL)−wR.
(^26) If M/L=−1, we obtain the familiar policy choice rule of selectingxhalf way between the
bliss points, see e.g. Baron and Diermeier ( 2001 ).