military technology could help to describe the ensuing conflicts and attempts to annex all or part of neighboring territories. We will not consider here such conflicts but will
keep focus on efficiency explanations of the size of a given unitary club-state facing first heterogeneity due to distance.
III. Heterogeneity Due to Distance and the Size of a Unitary State
We first characterize the monopolistic solution Section III, first part and then we provide a comparison with the program of surplus maximization Section III, second
part.
The Unitary State as a Monopolist In this framework, the objective of the government is to maximize its discretionary legal
control over citizens, with respect to the radius of the state. Such a government is neither a dictator nor a benevolent social planner. It is a monopolist that must take into
account both the increasing costs of territorial control and the decreasing individual willingness to abide by its law as the size of the state increases:
P
ROGRAM
1: A monopoly unitary state solves max
r
j
2r
j
f~r
j
2 g~r
j
. 5
The government thus maximizes its total discretionary power over each citizen, mul- tiplied by their number, taking into account non-discretionary costs associated with the
control of the territory. Endogenous frontiers associated with the optimal radius r
j
are such that
f~r
j
1 r
j
f 9~r
j
5 g~r
j
1 r
j
g9~r
j
6 The second-order condition is
r
j
f 0~r
j
1 2f 9~r
j
2 r
j
g0~r
j
2 2g9~r
j
0, 7
which is verified for instance if f0 ¶ 0 and g0 Ä 0. The left side of the first-order condition describes the marginal consent to the constitutional power of the state. The
right side represents the marginal cost of control of the territory. Frontiers are deter- mined by Equation 3 where the radius is such that Equation 6 is satisfied. The extent
of constitutional power amounts to
t
j
5 f~r
j
. 8
It delineates the range of constitutional control over the private domain, and Figure 1 illustrates it. It represents the right side of state j, but should be mirrored at the left side.
To compare the monopolist constitution with the planning solution, it is convenient to conduct the analysis in terms of surplus extraction or maximization.
Comparison with Surplus Maximization We still consider that capital j is exogenously located. The objective is such that the
radius r
j s
is obtained by maximizing total surplus: P
ROGRAM
2: A benevolent unitary state solves 504
Unitary States and Peripheral Regions
F
IG
. 1. Monopolistic and social-pla6nning s solutions.
505 J
OSSELIN AND
M
ARCIANO
max r
j
2
E
r
j
f~u 2 t
j
du 1 2
E
r
j
t
j
du 2 r
j
g~r
j
. 9
It amounts to maximizing
E
r
j
f~udu 2 r
j
g~r
j
. 10
The frontier i
f s
on either side of j is such that f~r
j s
5 g~r
j s
1 r
j s
g9~r
j s
, 11
for which individual willingness at the frontier equals the marginal cost of territorial control. Surplus maximization thus implies a degree of constitutional power
t
j s
5 f~r
j s
12 Compare Equation 11 to Equation 6 to verify that r
j s
. r
j
and t
j s
, t
j
. The surplus-maximizing solution provides a larger optimal territory than the monopolist
government does; at the same time, there are more restrictions on the power of the government in the benevolent setting see Figure 1 for a graphic illustration.
We now move on to the comparison of surpluses. First, citizens gain D
i
5 2uj 2 i
f
u~t
j
2 t
j s
1 2
E
r
j
r
f s
~ f~u 2 t
j s
du, 13
when a benevolent government replaces the monopolist one, whereas government loses D
j
5 2 2uj 2 i
f
u~t
j
2 t
j s
1 2
E
r
f
r
f s
t
j
2 ~ g~u 2 ug9~udu 14
when it chooses to maximize total surplus, providing that D
j
is negative. An important assumption that has been made until now is the invariability of the
functional forms of cost and willingness throughout the whole territory constituting the state. The following developments consider what happens when that assumption is
lifted, thus dealing with a second kind of club heterogeneity.
IV. Discontinuities in the Spatial Pattern of Preferences
