5. Verifiable Income

Question 1

What makes a variable verifiable?

Answer 1

A court of law are able to enforce the execution of the contract agreement. So third parties can also verify terms written in the contract

Question 2

Verifiable income

Answer 2

The principal of maximal insider incentives

Question 3

Semiverifiable income

Answer 3

Audits and bankruptcy

Question 4

Nonverifiable income

Answer 4

The threat of termination

Question 5

How is income modelled in the principal agent model Innes (1990)?

Answer 5

Random variable R distributed on the interval (0, R bar) according to the distribution p(R|e) where e>0 denotes the entrepreneurs effort

Question 6

How is the entrepreneur modelled in the principal agent model Innes (1990)?

Answer 6

Risk neutral, net worth A, disutility of effort, limited liability

Question 7

How is the contract modelled in the principal agent model Innes (1990)?

Answer 7

W(R) is the entrepreneurs reward when realised income is R; R-w(R) is lenders reward

Question 8

What does the monotone log likelihood ratio property (MLPR) state?

Answer 8

A higher income signals a higher effort

Question 9

What does the objective function give?

Answer 9

The entrepreneurs expected compensation conditional on the level of effort

Integral of w(R)p(R|e)dR -g(e)

Question 10

What is incentive compatibility constraint?

Answer 10

This is obtained after setting the derivative of the objective function wrt e equal to 0

Integral of w(R)dp(R|e)/de dR = g’(e)

Question 11

What is the zero profit constraint?

Answer 11

This is the expected loan repayment

Integral of (R-w(R))p(R|e)dR= I-A

Question 12

What is the monotonicity constraint?

Answer 12

It requires that the lender’s payoff is nondecreasing in the projects return.

R-w(R) is nondecreasing for all R

Question 13

What do mu and lambda denote?

Answer 13

The non negative multipliers of the constraints (ICb) and (IR) and ignore the monotonicity constraint

Question 14

Suppose mu >0, what does the monotone likelihood property imply?

Answer 14

That there exists a threshold income R* such that

W(R) = R if R>R*
W(R) = 0 if R<R*

Question 15

Proposition 1 live or die contract

Answer 15

The solution generalises the maximal insider incentive principle: the borrower receives nothing for R<R* and the entire income for R>R*. These type of contracts are called live or die

Question 16

What happens if we relax the lenders limited liability constraint

Answer 16

The solution would degenerate with W(R)=0 for R<R bar and spike at R bar

Question 17

Proposition 2 when is the optimal reimbursement the standard debt contract?

Answer 17

When we add the monotonic constraint the optimal reimbursement is the standard debt contract. When monotonicity is imposed the lenders limited liability constraint isn’t binding

Question 18

For a risk averse entrepreneur why is there a conflict in contract design?

Answer 18

Conflict between insuring the entrepreneur against income uncertainty and inducing effort

Question 19

What reward does the borrower get?

Answer 19

W(R)

Question 20

What reward does the lender get?

Answer 20

R-w(R)

Question 21

What is the assumption of monotonic reimbursement and why is it needed?

Answer 21

R-w(R) is nondecreasing for all R. Otherwise the entrepreneur could borrow R2-R1 from a third party and increase her reward by w(R2)-w(R1) and then repay the third party and make a profit

Question 22

If we impose the extra constraint that the lender has limited liability w(R)<=R then what is the solution?

Answer 22

W(R) = R if 1+ mu((dp(R|e)/de)/p(R|e)> lambda
W(R)= 0 if 1+ mu((dp(R|e)/de)/p(R|e) < lambda

Question 23

If mu=0 what is the optimal effort given by?

Answer 23

g’(e)= integral of Rdp(R|e)/de dR

Question 24

What is the correspondence between the fixed investment model and the verifiable income model?

Answer 24

The only differences are:
-In fixed investment there are only two states and in the verifiable income model there are a continuum of state.
-In fixed investment there is a benefit to working and in verifiable income there is a cost of working

Question 25

Does the fixed investment model satisfy the monotone likelihood property?

Answer 25

Yes because Ph is bigger than Pl and Ph indicates a higher level of effort

Question 26

What is the correspondence between the incentive compatibility constraints of the fixed investment model and the verifiable income model?

Answer 26

They are very similar. In each case increasing effort increases likelihood of higher reward but also increases costs of effort

Question 27

What is the optimal capital structure when mu=0

Answer 27

Mu is the multiplier associated with the incentive compatibility constraint. The project is so good that no incentives are needed for you to put in effort

Question 28

Would a risk averse borrower prefer to obtain funds through an equity or a debt contract?

Answer 28

Equity contract