Question
(CSV model) An entrepreneur has a project that requires an investment of 60 at time 0. The entrepreneur has no funds, so must raise the
(CSV model) An entrepreneur has a project that requires an investment of 60 at time
0. The entrepreneur has no funds, so must raise the required investment from investors.
At time 1, the cash flow from the project will be 160 with probability 1 /2 and 40 with
probability 1/2
The entrepreneur privately observes the cash flow and makes a report to investors.
If he reports a cash flow Ys, he must transfer Ts to investors. In addition, investors may
choose to audit the report, at a cost of 20. If they audit and the entrepreneur has lied,
he forfeits the entire remaining cash flow. That is, throughout the problem, assume the
maximal penalties feature | any time the investors know that the entrepreneur has lied,
all remaining cash flow is given to them, leaving the entrepreneur with zero.
As in class, an optimal contract maximizes the expected utility of the entrepreneur,
subject to an IC constraint on the entrepreneur and an IR constraint on the investors.
That is, the capital market is perfectly competitive on the supply side, so investors earn
zero surplus.
We assume the following
-Both entrepreneur and investor are risk-neutral.
-The discount rate is zero.
- The entrepreneur has limited liability, but the investors do not.
- Audits must be deterministic. That is, if ps is the probability of an audit in state
s, either ps = 0 or ps = 1 for each state.
(a) What is the rst-best outcome? What is the expected payo of the entrepreneur in
this outcome?
(b) Find the optimal standard debt contract. What is the expected payo of the en-
trepreneur?
(c) Construct a non-debt contract that is also optimal. What feature of a standard
debt contract does it violate?
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