(*) Consider a wealth-constrained firm and a lender operating in a two- period model (ty and...
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(*) Consider a wealth-constrained firm and a lender operating in a two- period model (ty and t2) with no discounting. At date 1, the initial invest- ment 1 yields income R₁ with probability p and 0 with probability 1-p. At date 2, the initial investment if not terminated yields expected income R₂ to the entrepreneur. If the project is liquidated in t₁, the lenders receive liquidation value L. Assume 0≤L≤ I. Moreover, liquidation is inefficient so that L < R₂. We will now look for the optimal contract in competitive capital markets. (i.e., the contract that maximizes the borrower's expected payoff subject to IC and IR). Let yo [0, 1] be the probability of continuation when there is no repay- ment at t₁ (note: the entrepreneur always repays 0 if the first-period return is 0). Consider a contract that specifies a repayment equal to D≤ R₂ if first-period income is equal to R₁, together with a probability of continu- ation y if D is repaid. The repayment of D must be incentive compatible so that R₁ - D + y₁R₂2 R₁+yoR2 (₁30) R₂2 D. The optimal contract solves the following program: Max(p(R₁D+91 R₂)+(1-p)(yo R₂)} with respect to (30-31, D) subject to; - IC: (91-30) R₂2 D - IR: p[D+ (1 -y₁) L + (1 -p)(1-yo)L 21 - and D< R₁, which we will consider not binding (i.e., R, is large.) Please: (a) Show that IR must be binding. (b) Show that IC must be binding. (c) Solve for yo (or for 1-0) and for D. Note: The entrepreneur repays nothing in the last period (12) as long as return 0 is a possibility (otherwise the entrepreneur repays the minimal value of second period income). R₂ can be treated as a deterministic pri- vate benefit. (*) Consider a wealth-constrained firm and a lender operating in a two- period model (ty and t2) with no discounting. At date 1, the initial invest- ment 1 yields income R₁ with probability p and 0 with probability 1-p. At date 2, the initial investment if not terminated yields expected income R₂ to the entrepreneur. If the project is liquidated in t₁, the lenders receive liquidation value L. Assume 0≤L≤ I. Moreover, liquidation is inefficient so that L < R₂. We will now look for the optimal contract in competitive capital markets. (i.e., the contract that maximizes the borrower's expected payoff subject to IC and IR). Let yo [0, 1] be the probability of continuation when there is no repay- ment at t₁ (note: the entrepreneur always repays 0 if the first-period return is 0). Consider a contract that specifies a repayment equal to D≤ R₂ if first-period income is equal to R₁, together with a probability of continu- ation y if D is repaid. The repayment of D must be incentive compatible so that R₁ - D + y₁R₂2 R₁+yoR2 (₁30) R₂2 D. The optimal contract solves the following program: Max(p(R₁D+91 R₂)+(1-p)(yo R₂)} with respect to (30-31, D) subject to; - IC: (91-30) R₂2 D - IR: p[D+ (1 -y₁) L + (1 -p)(1-yo)L 21 - and D< R₁, which we will consider not binding (i.e., R, is large.) Please: (a) Show that IR must be binding. (b) Show that IC must be binding. (c) Solve for yo (or for 1-0) and for D. Note: The entrepreneur repays nothing in the last period (12) as long as return 0 is a possibility (otherwise the entrepreneur repays the minimal value of second period income). R₂ can be treated as a deterministic pri- vate benefit.
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a To show that IR must be binding lets consider the two cases Case 1 IR is not binding ie the inequa... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
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