Geoff Willis

Risk Manager

Geoff Willis

Laser Econodynamics:

Relieving Poverty

by Modifying Income

and Wealth Distributions

Income Wealth Distributions - Assumptions

• Boltzmann / gamma distribution base

• Power law tail

Human Abilities

• Normally distributed

• Large offset from zero

Fig. 2 Offset Normal Distribution

Proportion

Average Value

Skill

Fig.3 Boltzmann distribution

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 50 100

150

200

250

300

350

400

450

500

550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

1200

1250

1300

1350

1400

1450

1500

Weekly Income ($)

Pro

po

rtio

n

x*exp(-x)

half mean

mode

mean

Income Distribution

• Boltzmann– Skewed distribution– Top decile far above bottom decile

• Rich earn many times more than the poor

– Mode below Median• Majority of people have less than ‘average’ wealth

– Approx 15% less than half mean• 15% permanently below ‘ relative poverty line’

Income Distribution

• Boltzmann– skewed distribution– ‘unfair’ distribution

• Boltzmann with Power Tail– even more skewed– even more ‘unfair’ distribution

Income Distribution

• Boltzmann– Maximum entropy output– Independent of microscopic interactions– Difficult to change

Traditional methods of redistribution

• ‘Communist’ methods– need totalitarian control– poor growth– still have poverty

Fighting entropy – does not work

Traditional methods of redistribution

• ‘Socialist / Social Democrat’ methods– need high levels of control– high levels of taxation– high welfare spending

Fighting entropy

– does not work well, expensive

Income Distribution

• Boltzmann– Why a skewed distribution?

Because– Closed at zero

• Negative wealth / income not usually allowed

– open ended in positive direction

so Assymmetrical distribution

True of most physical systems – but not all

-E

+E

Fig. 4

-E4-1

+E5-

4

Fig. 5

E1

E4

E5

Non lasing material

Energy exchange to upper levels possible

Lasing material

Energy exchange to upper levels not possible

Simulated Energy Distributionssix atoms - 24 units of energy

0

0.2

0.4

0.6

0.8

1

1.2

Energy

No

of

ato

ms

(av

era

ge

ov

er

50

sim

ula

tio

ns

)

no upper limit

Modified Distribution

• No Upper Limit– Boltzmann distribution

• Introduce Upper Limit– Maximum 6 energy units– Any interaction that results in more than 6

energy units is prohibited

Simulated Energy Distributionssix atoms - 24 units of energy

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Energy

No

of

ato

ms

(ave

rag

e o

ver

50 s

imu

lati

on

s)

no upper limit

upper limit 6 units

Modified Distribution

• Do same with income distributions:

• Introduce Upper Limit– Maximum income per year– If a person earns more than set amount in 1

year (including fringe benefits etc)• Criminal offence• Sent to prison

– If set max wealth at double mean wealth• Should get symmetrical distribution

Fig. 6

Proportion

Average wealth

w 2w

Upper boundary

Fig. 7

Proportion

Average wealth

w1.5w

Upper boundary

Fig. 2 Offset Normal Distribution

Proportion

Average Value

Skill

Problems

• Isolation– People affected by cap move to other country– Would need severe restrictions on freedom

or very good international cooperation

• Existing Rich would lose lots of money– Influential people!– Perceived to be unfair by many others

UK NES Data 1992

• 121,000 people

• Average income £297pw

• Maximum £1600pw– In reality will be much higher

• 5% above £600 – double maximum– Influential people!

Stepped Cap

• Lowest cap level at 1.5 times average– Raise with wage inflation

• Highest cap level at current maximum– Not raised at all (effectively decreased)

• Steps between max and min– Raised with cost inflation

• Bottom end should slowly ‘pressurise’

Apply similar process to wealth

Possible Solutions

• Stepped Caps• Caps on wealth

– Eventually would reduce need for cap on income– But people allowed current wealth, and also locked

wealth for retirement age (also capped)

• Maximum wealth limits split on inheritance– (£1,000,000 could be split into two limits of £500,000

for two children)

Problems

• Isolation– International agreement would take long time

to resolve– Severe restrictions on freedom

• Existing Rich would lose lots of money– Influential people!– Perceived to be unfair by many others– Stepped cap would take long time to have

affect

Local Isolated Systems(Welfare Systems)

• Set Up Required Conditions– Welfare scheme

• (say 100 people)

• Allowance– Only Recipients have allowance

• Isolated System• (say Allowance of 120 units each)

– Maximum Wealth– Pressurisation

Local Isolated Systems(Welfare Systems)

• Coupon– Issued by government

• Independent Unit of Wealth• (say 10,000 coupons issued each week)• (equivalent to 100 per recipient)

– Exchangeable• Freely Interacting

Local Isolated Systems(Welfare Systems)

• Coupon– Can only be cashed in by people with

allowance

But– Distributed through Private Employers

• Competition• Market Efficiency

Local Isolated Systems(Welfare Systems)

• Government Give Allowance to Beneficiaries

• Government Sells Coupons to Employers

• Employers give Coupons to Beneficiaries– in exchange for labour

• Beneficiaries cash in Coupons– But only to value of Allowance

Local Isolated Systems(Welfare Systems)

• Ratio of Coupons to Allowance

Only 100 Coupons for each 120 Allowance

– Pressurisation– Competition– Inverted Distribution

Proportion

Average wealth = Total Coupons Total Allowance

w

Maximum Allowance

Upper boundary

Problems

• Simplistic

• Expensive

• Separation of Society

• Collusion

• Cheating

More details: cond-mat/0408227

Conclusions

• If, Income / Wealth systems are– ‘thermodynamic’– maximum entropy

• Apply ‘thermodynamic’ solutions– use models from physics, engineering etc

Conclusion

•Do not fight entropy

•Use entropy

New Scientist- March 1993

Geoff Willis