6. Semiverifiable Income

Question 1

How is income modelled in the costly state verification model?

Answer 1

Random variable R distributed on the interval (0,infinity) according to the distribution p(R)

Question 2

How is information modelled in the costly state verification model?

Answer 2

Income is costlessly observed by the entrepreneur but lenders can only verify income by incurring an audit cost K

Question 3

Revelation principle

Answer 3

In designing a loan contract there is no loss of generality involved in focusing on contracts that require the entrepreneur to report income. Furthermore, the contract can be structured again without loss of generality so that the entrepreneur has an incentive to report the true realised income

Question 4

Definition 1

Answer 4

A standard debt contract specified a debt level D, no audit if D is repaid and an audit and no reward if it is not

Question 5

What does W(R) denote?

Answer 5

The entrepreneur’s expected reward when realised income is R and the report is true

Question 6

Why does the payment have to be fixed in a no auditing region?

Answer 6

If it isn’t the case then among all the potential reports in the no auditing region the one with the lowest repayment will be chosen. Notice that 0 will not be reported given that it is audited

Question 7

Proposition 1

Answer 7

Under deterministic audit the optimal contract is the standard debt contract

Question 8

Why can’t the reimbursement for an R in R1 exceed D?

Answer 8

Because if it did then the entrepreneur would be better off reporting an income in R0

Question 9

Why is renegotiation always welfare reducing when the initial contract is complete?

Answer 9

Because it only adds additional constraints in the mechanism design problem