This exercise illustrates the case of Lemma 5.2.1 in the model of Diamond (1991). Take \(L=R=1, \pi=\frac{1}{2}, X=1 \frac{3}{4}, C=0, f=\frac{1}{2}\), and \(f^{d}=\frac{1}{3}\).

(a) What are the face values of a short-term and a long-term debt contract?

(b) Show that in this example there will be no liquidation.

(c) What is the payoff of a good project financed with long-term debt?

(d) What is the probability that a good project receives a downgrade at \(t=1\) ?

(e) What is the payoff of a good project financed with short-term debt?

Data From Lemma 5.2.1:-

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Lemma 5.2.1 (Diamond, 1991). Comparing two debt contracts issued at t = 0, neither of which involves liquidation on a downgrade at t = 1, the one with the higher value at that point in time given a downgrade, Vd, is preferred by the entrepreneurs of good projects.