Optimal Rent Extraction in Pre-Industrial England and France – Default Risk and Monitoring Costs



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*
d πnpv

∂δ

= <1   ‘¢2 KT < 0

(1 +δ)2ψ2

(29)

and

Π*

d πnpv

(1 — c τ

= -ə-----½2πτ < 0.

t(1 +δ)ψ2

(30)

∂c

The agent’s profit is increased since

π*
NPV _

∂C =

n — 1 (1
(n + 1)2

c) (1 + δ) τ

-----4 4∏τ > 0,
ψ
3t

(31)

and

1 c ¢2 τ

--ɪ4πτ > 0.

ψ3

∕9τΓ*

NPV

n1 (

_ _ _

(n + 1)2

(32)

∂δ

The debt finally is reduced due to an increase in the monitoring costs

and default risk because

dDebt    ()2 + (l+δ)2,∩   c,2, τ f.

(33)


(34)


~∂i~ = (-----ψ3-----)(1 - tt )2π0,

and

dDebt n — 1 2 (1 — C )(1 + δ) τ

—— = (----)2ʌ---1-^3----22πT < 0.

∂c n +1 tψ3

27



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