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2. (Principle-Agent Problem with Repeated Investment)
Consider a risk neutral manager who has no cash on hand ( = 0) and an investment
project which returns when it succeeds and 0 when it fails. The cost of investment is .
If the manager works hard the project succeeds with probability , if she shirks she gains
private benefit but lowers the probability of success to . If the first project succeeds
then a second project arises with probability .
a. Show that the pledgable income for the first-period project is larger than the expected
pledgable income for the second-period investment.
b. Suppose investors cannot pre-commit to finance in the second period when the first
project succeeds. Will financing in the second period happen more easily than in the
one-shot case?
c. Now suppose that investors can pre-commit to financing in both periods. That is,
they can write contracts that guarantee financing of the second-period project
conditional on a project arising in the second period. Compute the expected pledgable
income and write down a condition for financing.
3. (Asymmetric Information)
Extending the basic model we discussed in class, imagine that for a faction of firms if
> , but
the manager shirks the probability of success is , while for the rest it is
both types of firms have the same
, , and . This represents a different type of
asymmetric information problem, one where outsiders don’t know the true effects of
shirking.
a. Write down a condition for a manager of each type to work hard.
b. Compute the investor’s value for financing to each type separately at the lowest Rm
that that type would accept.
c. Can the investor offer a contract that induces hard work among all managers whould
accept that contract? Can we find such a hard-work-inducing contract that only one
type of firm would want to accept?
d. What is the value to the firm of financing both types at the lowest Rm that induces
both types to work hard? Therefore what is the condition for financing to occur?