ECON 448: Week 12-
1. Credit Market
(1) What is credit rationing? What are the possible reasons?
(2) SelfHelp is a newly formed credit cooperative which receives partial financing from government banks. Members of SelfHelp can deposit savings with the cooperative and they can also turn to SelfHelp for a loan if they need one. If a borrower defaults on a SelfHelp loan he is punished (which is equivalent to a loss of monetary value F) and excluded from future dealings with SelfHelp. Suppose that each borrower has a mental horizon of N periods. The value (to borrower) of the future dealings is some number S per period. However, there is no telling whether SelfHelp will survive in the future; the probability that SelfHelp continues to survive a period is p.
a. If each member is risk-neutral, what is the expected value of dealing with SelfHelp in the future?
b. If a member has an outstanding loan of L and needs to repay it the following period along with interest at the rate r, write down the value of his net gain from default. (Assume that N=2.)
c. How does the member's decision to default ('textitvoluntary default) change if r changes? Now fix the interest rate at r. Show how the survival probability of SelfHelp can affect the size of the loans it can make to borrowers.
d. Now suppose that the probability of SelfHelp's survival depends on the percentage of borrowers who repay as well as the quantum of government assistance, should a high rate of default occur. Show that in general there can be two outcomes or equilibria for the same parameters: (i) there is no voluntary default and SelfHelp survives with little or no government assistance or (ii) there are high rates of default and SelfHelp survives with low probability despite government assistance.
e. Show that a credible promise by the government to bail out SelfHelp in times of trouble can lead to a unique equilibrium in which all borrowers repay and little government assistance is actually required.
(3) There are two projects, A and B. Project A pays $1000 upon completion; project B pays $10,000 if it is successful, which only occurs at a probability of 0.1.
a. Which of the two project would a risk-averse person choose.
b. Suppose a fixed capital of $500 is required for each of the projects. With limited liability, what are the expect payoffs for a person who invests in the projects with a loan at an interest rate of 0.2? Is it possible for a risk-averse investor to choose project B over A?
c. For the rest of this question, suppose that half of all potential investors prefers A and the other half prefers B. What is the optimal interest rate that the bank should set? (Assume that there is no opportunity cost of extending a loan)
d. Let p denote the success probability of project B. For what values of p would induce the bank to set a lower interest rate?