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# 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

## (6) The deposition condition

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

# 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:

# Section 4 Lenders and interest rates

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

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

## Notes

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

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