6. Semiverifiable Income

Question 1

How is income modelled in the semi verifiable 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 standard debt contract

Answer 4

A standard debt contract specifies 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.

Question 7

Proposition 1 what is the optimal contract under deterministic audit?

Answer 7

Under deterministic audit the optimal contract is the standard debt contract

Question 8

Why can’t the reimbursement in an auditing zone exceed D?

Answer 8

Because if it did then the entrepreneur would be better off reporting an income in non audit zone

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

Question 10

How is the contract modelled?

Answer 10

y(R hat) distributed [0,1] is the probability of no audit conditional on the report R hat.

Question 11

What is the entrepreneur’s reward when realised income is R, report is R hat and there is no audit

Answer 11

Wo(R hat, R) = R-Rl^0 x (R hat)

Question 12

What is the entrepreneurs reward when realised income is R, report is R hat and there is an audit

Answer 12

W1(R hat, R)= R-Rl^1 x (R hat, R)

Question 13

What is R?

Answer 13

True realised income

Question 14

What is R hat?

Answer 14

Reported income

Question 15

What is the objective function?

Answer 15

Integral of w(R)p(R)dR

Question 16

What is the incentive compatibility constraint?

Answer 16

W(R)= max y(R hat)Wo(R hat, R) +(1-y(R hat))w1(R hat, R)

Question 17

What is the zero profit constraint?

Answer 17

Integral of (R-w(R)-(1-y(R)K)p(R)dR>=I-A

Question 18

How can W(R) be written in terms of Wo and W1?

Answer 18

W(R)= y(R)Wo(R,R)+ (1-y(R))W1(R,R)

Question 19

Can an equity induce truth telling?

Answer 19

Yes it can but it’s extremely costly. Every single report is audited.

Question 20

Why do deterministic contracts dominate stochastic contracts?

Answer 20

Because they reduce auditing costs by imposing a penalty