Version classiqueVersion mobile

The Political Economy of Sovereign Default

 | 
Sebastian Hohmann

Annexe

I. Algebra

Texte intégral

1Subheadings are as in the thesis. Each derivation is identified with the number of the equation in the main text.

2.2 The Winning Coalition’s reaction to a default

(1) Utility of a member of W loyal to a defaulting government

Image 10000000000009B00000018DAAD4EA3A.jpg

(2) Utility of a member of W deposing a defaulting government and once again member of W

Image 10000000000009B000000226D15254B4.jpg

(3) Utility of a member of W deposing a defaulting government and shut out of the new W

Image 10000000000009AF0000017CFFA0C236.jpg

(4) Expected utility of a member of W deposing a defaulting government

Image 10000000000009AF0000049CB234E2E8.jpg

(6) The deposition condition

Image 10000000000009B000000094F2D71E87.jpg

2Since 0 < δ < 1, I can multiply both sides by 1 − δ without changing the direction of the in- equality. Hence

Image 10000000000009B00000015EF6825188.jpg

(7) An increase in Selectorate size

Image 10000000000009B0000001722FFF2532.jpg

(8) An increase in the size of the Winning Coalition

Image 10000000000009B000000154BB2AFF86.jpg

2.3 The Government

(9) Expected utility of a government honouring its debt

3A government honouring its debt receives a utility of Ψ today and incurs a cost of repayment of θ. In the next period, it can then again choose to default or not. The utility from this choice-situation is gC. Since the outcome of θ next period cannot be foreseen, the government will receive a utility of gH if it again honours its debt and gD if it defaults. The probabilities of these choices are determined by the realization of θ. For θ ≤ θT, the government will choose to repay. For θ > θT default is the better option. Thus:

Image 10000000000009B000000294981A3C90.jpg

Image 10000000000009B0000002E07651F906.jpg

Image 10000000000009B0000001EF1C3B3A44.jpg

Image 10000000000009B00000020887A1ECF9.jpg

(10) Utility of a defaulting government

Image 10000000000009B000000182738C1088.jpg

(13) Threshold cost of repayment

Image 10000000000009AF00000149F165A229.jpg

Image 10000000000009B0000002C0EB15D65D.jpg

Section 4 Lenders and interest rates

(16) The competitive interest rate

Image 10000000000009B000000144370DBF1F.jpg

(17) An increase in the risk of default

Image 10000000000009B00000011C7DA2C93E.jpg

(18) Probability of default in terms of threshold cost of repayment

Image 10000000000009B0000001384F20AF07.jpg

(19) Interest rate in terms of threshold cost of repayment

Image 10000000000009AF00000140030CC932.jpg

(20) The effect of higher threshold costs of repayment on interest rates1

  • 1 Assuming that f() is continuous at (...)

Image 10000000000009AC0000044DE0277362.jpg

Notes

1 Assuming that f(Image 100000000000001F0000002BA7FEF3EE.png) is continuous at Image 100000000000001F0000002BA7FEF3EE.pngT, we can use the fondamental theorem of calculus. See Ron C. Mittelhammer, 1999. Mathematical Statistics for Economies and Business, Springer, New York, p. 52.

CC-BY-NC-ND-4.0

Le texte seul est utilisable sous licence CC BY-NC-ND 4.0. Les autres éléments (illustrations, fichiers annexes importés) sont « Tous droits réservés », sauf mention contraire.

Acheter

Rechercher dans OpenEdition Search

Vous allez être redirigé vers OpenEdition Search