>From (2.5) and the fact that P is a small party, we have RP = γ2rCP.
Imposing the consistency condition that future and current equilibrium rents (per
party) are the same, and using (3.2), we can solve (3.4) for the equilibrium rents
captured by each party in a coalition government:12
*p
C
4
γφ .
(3.5)
Thus, equilibrium rents tend to be higher: (i) the smaller is the relative weight,
γ, assigned to future rents; (ii) the lower is within-group mobility, φ, and hence
the responsiveness to welfare losses among voters.
Total equilibrium rents in a coalition government are given by
2
8
γφ .
* *Ρ
rC = 2_^ r*
P=1
3.1.2. Single-party government
Given the symmetry of the model, it does not matter for the policies chosen by
the single-party majority whether its opposition consists of a single party or two
distinct parties. Thus, the results presented in this section refer to a two-party
system, as well as a three-party system. Thus, we omit the N back subscript,
whenever there is no risk of confusion.
Equilibrium seat shares To fix ideas, consider the choices by party P =12,
resulting from the merger of legislative groups 1 and 2, when in government.
Compared to a party in coalition government, this large party twice as large a
vote share among its own voters (now groups 1 and 2) and among the opposition
groups. Its seat share and vote share is thus given by an expression similar to
(3.1) above:
SP = VP = 4[2 + X F (V J - V *J - δ)∣ .
J=1
12Here, we used the result that d∂φ~P = -1/4 for all J. Note that here we pin down equilibrium
rents through our assumption that current and future equilibrium rents are equal. But similar
results would be obtained if we took the expected value of seats as parametrically given by
RP , and assumed that the parties’ marginal utility of rents was strictly decreasing (rather than
constant as assumed here).
15
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