Sep 19, 2017

(LONG-TERM PROSPECTS AND THE SOFT BUDGET CONSTRAINT). PERFORM THE SAME ANALYSIS AS IN EXERCISE…

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(long-term prospects and the soft budget constraint). Perform the same analysis as in Exercise 5.3, with the difference that the date-0 choice of the entrepreneur does not affect the salvage value, which is always equal to 0. Rather, the date-0 moral hazard refers to the choice of the distribution of the second-period income in the case of continuation. This income is RL  0 or RH = RL + R, where R  0 is a constant. The distribution of RL, G(RL), or G(R ˜ L) is determined at date 0. Assume that g(RL)/g(R ˜ L) is increasing in RL. As usual, let pH and pL denote the probabilities of RH when the entrepreneur works or shirks ex post. And let ρ1 ≡ pHR and ρ0 = pH(R − B/∆p). Assume that RL is publicly revealed at date 1 before the continuation decision. Solve for the optimal state-contingent policy in the absence of the soft-budget-constraint problem. Show that the soft-budget-constraint problem arises (if it arises at all) under some threshold value of RL.

Exercise 5.3

(asset maintenance and the soft budget constraint). Consider the variable-investment framework of Section 5.3.2, except that the date-0 moral hazard affects the per-unit salvage value L. Date-1 income is now equal to a constant (0, say). Assets are resold at price LI in the case of date-1 liquidation. The distribution of L on [0, L] ¯ is G(L), with density g(L), if the borrower works at date 0, and G(L) ˜ , with density g(L) ˜ , if the borrower shirks at date 0. We assume the monotone likelihood ratio property

The borrower enjoys date-0 private benefit B0I if she shirks, and 0 if she shirks. The timing is summarized in Figure 5.11. As usual, let ρ1 ≡ pHR and ρ0 = pH(R − B/∆p). And le

(i) Determine the optimal contract {ρ∗(L), ∆(L)} (where ρ∗(L) and ∆(L) are the state-contingent threshold and extra rent (see Section 5.5.2)) in the absence of the soft budget constraint (that is, the commitment to the contract is credible). Show that

• ∆(L) = 0 as long as ρ∗(L) ≤ ρ1 − L;

• conclude as to when rewards take the form of an increased likelihood of continuation or cash (or both)

(ii) When would the investors want to rescue the firm at date 1 if it has insufficient liquidity? Draw ρ∗(L) and use a diagram to provide a heuristic description of the soft-budget-constraint problem. Show that the soft budget constraint arises for L ≤  L0 for some L0 ≥ 0.

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