Transcript Entrepreneurship and Incentives

Entrepreneurship and Incentives
James Mirrlees
Chinese University of Hong Kong
[email protected]
At National Tsing Hua University,
Taiwan
11 December 2007
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Outline…
• Profits provide incentives for
entrepreneurs, i.e. business men.
• Do they provide the right incentives?
• Two theories of the way that incentives
operate for entrepreneurs: a search theory,
and a competition theory.
• If the theories are right, taxes on high
incomes from business should be high –
approaching 100%. Alternatively, CEOs’
etc. income should relate that way to
profit.
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Work and incentives
• We believe that the prospect of higher
income encourages people to work longer,
harder, more productively, and to seek to
do more demanding jobs.
• Everyone knows this argument in favour of
income inequality, or, more specifically, the
argument for marginal tax rates that are
not too high.
• But we need to allow for the different kinds
of labour supply, especially at high
incomes.
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How high should taxes be?
• Many economists have argued that total
marginal tax rates – all the taxes paid out
of an additional unit of labour income –
should be less than 50%. Some say 25%.
Hong Kong has less than that.
• In UK, it is over 70% for many people with
children, and nearly that for high incomes.
• Average taxes less subsidies are less than
40%.
• This is probably broadly right for UK.
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What entrepreneurs do…
• They think of things to do.
• They find and select the factors of
production.
• They monitor their workers (and possibly
suppliers too).
• The last is like working at making things or
providing services.
• The others are not like ordinary labour
supply.
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Incomes of the creative
• Creative people – inventors, artists,
sportsmen, entrepreneurs, do not, or
should not earn their income from the
number of items they produce or the
number of hours they work.
• It is mainly the quality of what they achieve
that matters; and quality relative to others.
Incentive arguments are then different.
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Three theories of enterprise.
• 0: Simple theory assuming the
entrepreneur supplies unobservable effort.
• I: A theory assuming limited search for
projects.
• II: A theory assuming direct competition.
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Theory 0
• If the entrepreneur just chooses what to
do, we might think he chooses the actions
that will maximize his profit.
• Simple economic theories say that we
want firms to maximize profit, so it seems
that the entrepreneur should receive a
constant proportion of profit.
• But the entrepreneur may be too risk
averse.
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• Approximation: Lenders to the firm, and
the government (receiving a proportion of
profit as tax) want expected profit to be
maximized.
• If the entrepreneur is risk-averse, he will
not maximize expected profit.
• So offset risk by letting the entrepreneur
keep more profit when it is high, or low,
less when it is medium?
• This doesn’t allow for incentives properly.
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Incentive theory.
• If the entrepreneur is thought of as
applying effort, a natural model has gross
profit (before deduction of the
entrepreneur’s income) a function of effort
and the state of nature.
• In a plausible version, the entrepreneur’s
income would be minimized for the worst
outcomes.
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Theory I: bounded rationality
• Simon proposed satisficing as a model of
limited rationality.
• People cannot consider all possible
choices. They may consider one or two,
and when they think they will not find
anything much better, they will choose
from the ones they have considered.
• Search is similar; and there is a good
economic theory of optimal search.
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Search theory for entrepreneurs
• The entrepreneur examines a number of
possible projects, which come to him
randomly. Defining, forecasting and
assessing any particular project has a
cost. He stops when the prospects of
better do not justify the cost of further
search.
• A neat integral equation defines the
threshold project-value.
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Search theory and moral hazard
• The threshold value depends on the
reward system for the entrepreneur. If
incentives are powerful, a project’s
attractiveness will increase greatly with its
expected profitability. So what he will do
depends on the reward system.
• And the rewards must be, on average,
good enough to attract (good enough)
entrepreneurs into business.
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• The question is, what kind of reward
system will yield the highest expected
residual profit to the economy -- subject to
making business more attractive than the
alternatives; and taking account of the kind
of decisions entrepreneurs will make.
• This is known as a moral hazard problem.
• Under quite general assumptions, it turns
out that rewards should be bounded
above, a surprising result. The
entrepreneur is made more risk-averse.
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Optimal falling marginal tax rates
• One implication is that, for high
entrepreneurial income, marginal tax rates
should approach 100%.
• At the other end of the scale, it is implied
that, after tax, entrepreneurial income
should be as small as possible in the
lowest range of outcomes: i.e. the State
should not compensate for large negative
profit
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Optimal incentives with search
• Suppose a project of type z has profit
probability density f(y,z). z has probability
density g(z).
• We have a reasonably simple model to
solve for the optimal payment schedule.
We maximize the expected value of profit
less pay, subject to the search rule, and
the requirement that the manager’s payoff
be sufficient to attract him.
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The optimal reward schedule
1
C
 A
where h( y ) 
u '( x( y ))
h( y )
(or x  0 if h is small enough)


t
f ( y, z ) g ( z )dz
f ( y, t )
1/u΄ is a bit like x, so this is instructive. h is
obviously positive. If fz/f is increasing in y,
it can be shown that h is increasing in y.
Then C has to be positive, to ensure that x
is increasing.
Therefore x is bounded above; may be 0.
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Theory II: competition
• Another account of entrepreneurial
behaviour allows for competition with
others. The most extreme examples are
inventors and innovators, who must try to
be first. The first to patent a particular
invention gets all the rewards, through
royalties. The first entrepreneur into a new
market generally gets the largest payoff in
that line.
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Winning the race
• This means that, in some ways, business
is like an auction, although the secondand third-best usually get significant
rewards in business.
• The important feature is that it is the
entrepreneur’s efforts relative to
competitors that determine his profit.
• Good competitors provide an incentive to
do well. How fast you run depends on the
prize; and also on the next man’s speed.
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Marginal tax rates
• In an extreme version of this model, it
turns out that optimal marginal tax rates on
the highest incomes should be 100% -- at
that level, all the incentive is provided by
the second-best.
• This is too strong, but in general, the case
for high tax rates is stronger because of
the alternative source of incentives.
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Competitive incomes in general
• It seems that many of the highest incomes
in the world are the result of competitive
behaviour. Not just businessmen and
inventors, but sportsmen, musicians,
lawyers; and, at a lower income-level,
academics.
• The implications for high-income tax rates
are clear.
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Intellectual property rights.
• Similarly, we might argue that patentholders and copyright-holders who get
high cumulative income from their
creations should have shorter patent- and
copy-right lives.
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Appendix
• The following pages are not for
presentation at the lecture.
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Appendix: Optimal incentives with
search
A project of type z produces y with probability density f ( y, z ).
z must be measured in such a way that f changes nicely as z
changes: e.g. larger z -distribution dominating smaller. z occurs
with probability density g ( z ). The manager chooses a threshold
t for z so that

  [u ( x( y)) f ( y, z )  u ( x(t )) f ( y, t )]dy.g ( z )dz  c
and we must have  u ( x( y )) f ( y , t )dy  u .
t
0

1
The owner maximizes
[ y  x( y )] f ( y, z )dy.g ( z ) dz


1  G (t ) t
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The first-order conditions for x( y ) take the form
1
f ( y, t )
C
 AC 
 A
u '( x( y ))
h( y )
f ( y, z ) g ( z )dz

t
This must imply that x is a nondecreasing function of y for
the solution to be valid. If f z / f is increasing in y, and C  0,
that is indeed true. Proof:
z
f ( y, z )
 z 


 exp  
ln f ( y, v)dv   exp   f v / f dv 
 t

f ( y, t )
 t v

is increasing in y when z  t. Hence

1
h( y ) 
f ( y, z ) g ( z )dz

t
f ( y, t )
is increasing. If C  0, 1/ u ' is increasing, as required.
Then x is bounded above: u '( x)  1/ A.
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If u (0) is finite, we might have x( y)  0 for some values of y. We do
get a solution in all reasonable cases, and it is not the first-best.
An interesting special case: y normal, with mean z, and z normal.
Then we can show that h is concave (as well as positive and
increasing). Thus 1/ u' is concave, and with constant relative or
absolute risk aversion, x is a concave function of y.
Applying to income-tax theory, the marginal tax rate should be
increasing, with limit 100%.
It is unreasonable to assume that projects can be ordered by
dominance, even the weak dominance that f z /f is increasing in y.
To be more realistic, one would need to have multidimensional
search.
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