expected ex-post collection of the announced fees: (1+δ) θ~θ(⅛-λ+λs) .32
At stage one, the CA therefore solves
max n-ɪ (a - θ(1 - λ + λs))2 +(1 - ca - θ(1 - λ + λs)
θ n +1 4b t (1 + δ)2b
The solution is
a n! (1 - λ + sλ)
θ* = -----a------(1 - ^+ɪʌ-----------)).
2(1 - λ + sλ)v φ ,
_(1-c ) n _1
where φ ≡ 2(1+δ) - n-(1 - λ + sλ) > 0 for a solution to exist.
The agent’s profit is equal to
(22)
(23)
-'
πNPV =
2 (1 c ) πτ
n + 1 φ2(1 + δ)2
(24)
the CA’s profit is equal to
ΠNPV =
(1 - c)2
(1 + δ) (1 - λ + sλ) φ ^,
(25)
and the debt is given by
c
Debt =
(1 - C)2(n-1 (1 - λ + sλ) - ⅛) T
(26)
----------------------------------------------Z7Γ
φ2 (1 - λ + sλ)
Proposition 3 An increase in the probability to commit to the agent in-
creases the use of ex-post payments, the debt issued and the CA’s profits,
and reduces the agent’s rent.
Proof. See Appendix. ■
Consider an increase in the probability to commit to the agent, i.e., a
reduction in λ. The CA’s response is to increase the announced fee such
the agent’s expected profit is reduced. In other words, the CA increases
the use of direct collection within the government. This change increases
32To emphasize that the default risk, δ, and the probability to commit to officials,
λ, yield the same qualitative results we treat them as independent of each other.
24
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