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

The agent’s profit is increased since

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.

~∂i~ = (-----ψ3-----⁾⁽¹ - t_t )2^π < 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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