geoff willis risk manager. geoff willis laser econodynamics: relieving poverty by modifying income...
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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
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