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Diamond (1989) - Reputation Acquisition In Debt Markets (view source)
Revision as of 19:02, 29 April 2010
, 19:02, 29 April 2010no edit summary
'''Lemma 1''': At the final period <math>T\,</math>, (a) all borrowers offer a debt contract with the lowest interest rate that provides an expected return of <math>r\,</math>; (b) all borrowers who can repay do so; and (c) Only borrowers for whom beliefs suggest a high enough probability of being a <math>G\,</math> type will get a loan in period <math>T\,</math>.
===More than One Periods===
There are a series of lemmas that follow directly and need essentially no explanation:
*If at time <math>t\le T\,</math> a borrower is revealed to be a type <math>B\,</math> or <math>GB\,</math>, then he will get no loans afterward
*If a loan is made at date <math>t\,</math> then <math>r_{t}\in [r,G]\,</math>
*If returns are above <math>r_{t}\,</math> then borrowers repay exactly <math>r_{t}\,</math>, while if returns are below <math>r_{t}\,</math> then the project is liquidated.
*Any payment less than <math>r_{t}\,</math> at time <matht\,</math> leads to no loans for all <math>t^{\prime }\ge t\,</math>.
*All surviving borrowers at time <math>t\,</math> offer the same rate <math>r_{t}\,</math> that gives lenders an expected return of <math>r\,</math>.
To characterize the equilibrium we need to specific the actions of <mathGB\,</math> types and show that the rate sequences are best responses to these actions.
