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Entrepreneurship and Incentives

James Mirrlees

Chinese University of Hong Kong

jam28@cam.ac.uk

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/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.

( , ) ( )1 where ( )

'( ( )) ( ) ( , )

(or 0 if is small enough)

tf y z g z dzC

A h yu x y h y f y t

x h

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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 second- and 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 patent-holders 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 produces with probability density ( , ).

must be measured in such a way that changes nicely as

changes: e.g. larger -distribution dominating smaller. occurs

with proba

z y f y z

z f z

z z

0

bility density ( ). The manager chooses a threshold

for so that

[ ( ( )) ( , ) ( ( )) ( , )] . ( )

and we must have ( ( )) ( , ) .

1The owner maximizes [ ( )] ( , ) . ( )

1 ( )

t

g z

t z

u x y f y z u x t f y t dy g z dz c

u x y f y t dy u

y x y f y z dy g z dzG t

t

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The first-order conditions for ( ) take the form

1 ( , )

'( ( )) ( )( , ) ( )

This must imply that is a nondecreasing function of for

the solution to be valid. If / is increasin

t

z

x y

f y t CA C A

u x y h yf y z g z dz

x y

f f

g in , and 0,

that is indeed true. Proof:

( , )exp ln ( , ) exp /

( , )

is increasing in when . Hence

1 ( ) ( , ) ( )

( , )

is increasing. If

z z

vt t

t

y C

f y zf y v dv f f dv

f y t v

y z t

h y f y z g z dzf y t

0, 1/ ' is increasing, as required.

Then is bounded above: '( ) 1/ .

C u

x u x A

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If (0) is finite, we might have ( ) 0 for some values of . We do

get a solution in all reasonable cases, and it is not the first-best.

An interesting special case: normal, with mean , and norm

u x y y

y z z

al.

Then we can show that is concave (as well as positive and

increasing). Thus 1/ ' is concave, and with constant relative or

absolute risk aversion, is a concave function of .

Applying to income

h

u

x y

-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 / is increasing in .

Tzf f y

o be more realistic, one would need to have multidimensional

search.