[Costly State Verification(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 Incentive Compatibility (IC) constraint on the entrepreneur and an Individual Rationality (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 first-best outcome? What is the expected pay- off the entrepreneur in this outcome?

(b) Find the optimal standard debt contract. What is the expected pay- off the entrepreneur?

(c) Construct a non-debt contract that is also optimal. What feature of a standard debt contract does it violate?