APPENDIX
Proof of Proposition 1
The condition for a solution to the CA’s problem is
ψ = n-1 (1 + δ) - 2(1 - C) < 0. (27)
For θ> 0 it is also necessary that
κ = n-1 (1 + δ) - 1 + c< 0. (28)
Higher monitoring costs and default risk reduces the CA’s profit because
∂ Π* ∂δ |
= <1 ‘¢2 K 2πT < 0 (1 +δ)2ψ2 |
(29) | |
and | |||
∂ Π* d πnpv |
(1 — c )κ τ = -ə-----½2πτ < 0. t(1 +δ)ψ2 |
(30) | |
∂c |
The agent’s profit is increased since
∂π* ∂C = |
n — 1 (1 — |
c) (1 + δ) τ -----4 4∏τ > 0, |
(31) | |
and |
1 — c ¢2 τ --ɪ4πτ > 0. ψ3 | |||
∕9τΓ* dπNPV |
n—1 ( _ _ _ (n + 1)2 |
(32) | ||
∂δ |
The debt finally is reduced due to an increase in the monitoring costs
and default risk because
dDebt (⅛)2 + (l+δ)2,∩ c,2, τ f.
(33)
(34)
~∂i~ = (-----ψ3-----)(1 - tt )2π < 0,
and
dDebt n — 1 2 (1 — C )(1 + δ) τ
—— = (----)2ʌ---1-^3----22πT < 0.
∂c n +1 tψ3
27
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