Limited Punishment

It was one lecture absence from last leacture I attended. Today's topic was limited punishment; in real sociaty, it is difficult to punish appropriately because of social system and cost. To achieve efficiency, some rewards should be used otherwise problem of commitment will rise.

This model's implication is useful for relation worker and employ, and entrepreneur and investor. And it also can be applied in justification of controling, defferences of credible system between developed and developing countries, needs of education for alter signaling of money.





Limited Punishment:
Commitment problem can be avoided if “cheating” is punished strongly enough. However, nowadays there are limits to both physical and economic punishments.
Which limit? ;death penalty, economic penalty.
Why are there such limits?; cost(because it is difficult to measure degree of punishment according to each crime. Difference of preference(because value of money or time is different among people, it is impossible to set appropriate punishment. Law(because law should be made before crime is made)

Therefore, in order to deter cheating, there must be a reward for good behavior. Sometimes, the required reward is so large that the parties have to live with the commitment problem.

Example 1:Efficiency Wages
Player: a employer and a worker.
B(e)=outcome of the work
C(e)=cost of the work
W(e)=wage
e=｛eh,eh｝
L=limit of wage

A Employer maximize B(e)-W(e), and a worker maximize W(e)-C(e).
If L is large enough and C(el) is low enough, the worker has no incentive to work with eh, because if she work with el, she can get at least L. It means inefficiency is caused by limitation of wages, and it is impossible to reach efficient equilibria.

To generalize the case, we can assume
B(eh)-C(eh)>B(el)-C(el)>0 (=eh is better than el)
Consider the contract:
W(el)=L, W(eh)=C(eh)
This contract induces effort eh if
W(eh)-C(eh)>W(el)-C(el), sufficient condition is C(el)>L (L is useless)

Interpretation: the contract will always be signed, and effort will always be efficient.

General Analysis of Limited Liability Case;
Suppose now that L>C(el). Then, the above contract does not work. The cheapest way to induce high effort is to set w(el)=L (as before) and set w(eh) to solve. (this means minimum wage is indifferent from w(el) because L is same as w(el))

W(eh)-C(eh)=L-C(el),
: eh and el gave same incentive for a worker.
That is
W(eh)=L+C(eh)-C(el)
:this is cheapest way to reach efficient equilibria.
Incentive wage should be consist of limit wage and difference of cost between motivated and not.

Example2:Corporate Finance
Player :an entrepreneur, an investor
I=investment cost
A=equity
R=gross investment return
b=private benefit to entrepreneur
p=probability of success
w=entrepreneur’s compensation in case of success

Assumptions;
If the entrepreneur works, p=h and b=0.
If the entrepreneur shirk, p=l and b=B>0.
Working good for welfare (h-l)R>B (=hR>B+lR
(work is better than shirk for the worker)
Shirking never supportable: lR-I+B<0(= net revenue of shrink is less than –B)
(shrink is not supportable if net return of shrinking case is more minus than private benefit of entrepreneur.)

Analysis;
Social optimum: Invest iff hR-I>0
Entrepreneur works iff(h-l)w>B(= hw>B+lw)

Rp=R-W=R-B/(h-l); expected return is net return minus wage for entrepreneur.
hRp>I-A; expected high revenue is more than investment cost minus asset of an entrepreneur.

Insight;
B=reputation of an entrepreneur, A=asset of an entrepreneur. It says good reputation and large asset is important for investment.

Investors control:
Monitoring cost (but it is non-monetary)is γ and it increase output by τ, there is funding if
hRp+τ＞I-A
If hRp0 ( it means hw is more than monitoring cost ofγ)

Implications:
Investor control may be justified when entrepreneur has little equity, and when investor control will not impose an excessive burden on the entrepreneur.
(because τ makes it easier to invest ifγ is not so heavy for entrepreneur)

Poor entrepreneur with large funding needs retain few control rights.(no money means no right)

In countries with weak legal enforcement of creditors’ claims, there is scope for other enforcement mechanisms. (development countries has many private finance)

Wealthy entrepreneurs relinquish few control rights( prefer to raise funds through bonds and bank loans with weak covenants)


Broader implications;
Imperfect credit markets imply poor people’s talent.(If someone is poor, she cannot get investment even if she has good talent)

The choice between production and crime is affected by the worker’s labor market prospects( low-skilled worker tends to commit a crime)

Absent sufficient punishment, even selfish rich people may favor some redistribution in order to prevent crime.(if punishment is not enough, not only worker but also employer (usually richer than worker) needs redistribution to prevent crime or shrink.


Words:
Argument; a set of reasons that show that something is true or not. The act of disagreeing of questioning something