Simon Fraser University Prof. Karaivanov
Department of Economics Econ 855, Spring 2009
FINAL EXAM (April 14, 2009)
This is a closed book examination. To get full credit you need to answer ALL questions.
Please always explain how you obtained your answers – no credit will be given for numerical
or other answers with no explanation. You have 2 HOURS to finish the exam. The total
number of points is 100.
I. TRUE/FALSE – explain your answers! (5 pts each, 30 pts in total)
1. If sharecropping is inefficient due to incentive problems, a good policy is to help the
tenant get a loan from public sector banks and buy off the land from the landlord.
2. The empirical work on foreign aid shows that aid can help generate growth in
developing countries but only when combined with sound macroeconomic policies.
3. The fact that richer countries have been found to exhibit more trust and social capital
than poorer countries implies that governments should spend to promote social capital building
4. The theory of perfect insurance suggests that individual consumption should co-move
one-to-one with aggregate consumption but not with individual income.
5. The adoption of a more efficient technology may be blocked by local monopolists who
hold the political power since they would lose their profits from operating the old technology.
6. If entrepreneurial talent is uniformly distributed across people of different wealths, then
the fact that the probability of starting a business is an increasing function of wealth implies
that financial markets are imperfect.
Problem 1 (35 pts)
An agent with wealth w ≥ 0 can engage in an ’entrepreneurial’ activity which requires a
fixed capital investment of I 1. The uncertain revenue from this activity is H 0 with
probability p and 0 with probability 1 − p. If less than I is invested the project yields zero for
sure. The probability of output equaling H (‘success’) equals the individual’s effort e, i.e.
p e. Denote by ce the cost of putting effort e, where ce He with ∈ 0, 1. The
agent’s initial wealth w can be either used as capital investment in the entrepreneurial activity
or deposited in a bank at a gross interest rate of r. If w 1 the agent can also borrow from the
bank I − w and, due to competition, it is assumed that he can obtain funding at an interest rate
that makes the bank just break even (it is assumed the bank’s opportunity cost of funds is r as
well). The bank cannot observe or stipulate the effort level put by the borrower. There is also
limited liability – the borrower cannot pay back anything if his project fails. Let w denote
the gross interest rate per unit borrowed charged by the bank to a successful borrower with
wealth w 1 ( is an endogenous amount to be determined later in this problem).
(a) Given w what is the total amount a borrower (w 1 must pay back to the bank in
case of success? In case of failure?
(b) Solve for the optimal effort level chosen by the borrower given the interest rate
schedule w quoted by the bank.
(c) What effort level will be supplied by wealthy agents, i.e. the those with w ≥ 1?
Compare this level to that in (b). Explain the intuition.
(d) Write down the equation that the bank would use to determine the interest rate w for
a borrower with wealth w 1 (Hint: Remember that the bank needs to earn an expected return
of r to break even). Solve for the optimal repayment rate schedule, w implied by this
(e) Would there be some agents (i.e. with certain range of wealth) to whom the bank would
not want to lend at any interest rate? If no, why? If yes, who are they? Explain your answers.
Problem 2 (35 pts)
Consider the following variation of the model of group lending. Borrowers are risk averse
and have a utility function uc ln c where c is consumption. Output from the project is y.
Let R be the total repayment amount the bank requires from a person. Borrowers do not save,
and have no other source of income. Therefore, consumption equals output from the project
less any repayment to the bank. There are no informational problems, but contract enforcement
is very costly – the only punishment that the bank can inflict is not to lend to this borrower
ever again. A borrower will repay only if the benefit of defaulting (which is $R worth of extra
current consumption) is less than the discounted net value of continued access to credit from
this lender, B.
(a) Solve for the critical level of output from the project such that the borrower will choose
to repay a standard, individual liability loan. Let this be denoted by ŷ IL . How does it depend on
R? What is the intuition?
(b) Now suppose that under joint liability loans for groups of size two unless the bank
receives 2R from the group, both borrowers are cut off from future loans forever. Solve for the
critical level of output from the project such that a joint liability borrower will choose to repay
his and his partner’s loan if the latter does not repay. Let this level be denoted by ŷ JL . How
does it compare with ŷ IL ? Explain the intuition.
Suppose now that output y can take two values with probabilities p and 1 − p respectively:
a high value of H and a low value of L where R L H (so that even when output is low
borrowers can repay if they are willing).
(c) Suppose H ŷ JL and L ŷ IL . What is the repayment rate (i.e. the fraction/probability
of repaid loans from all loans given) under joint liability and individual liability? Which one is
greater? Does your answer change if ŷ IL H ŷ JL and L ŷ IL ? Explain the reasoning.
(d) Discuss briefly, based on your answers in (c), the potential costs and benefits of using
joint liability vs. individual liability lending in a limited enforcement setting.