UTOPIA? “PROTOPIA”! · 2018-03-08 · system, which is defined as the product of GDP and GDH.Gross Domestic Product (GDP) and Gross Domestic Happiness(GDH) are determined by income,

MCM/ICM

Summary Sheet

UTOPIA? “PROTOPIA”!

Summary

To design a sustainable social system on Mars to achieve the goal that it will make a

better living experience than the earthly one for the migrations during the 22nd century,

seven models are developed.

In the first part, a series of metrics are defined to evaluate whether the system is

meeting its goal and how to calculate them. CSI is the ultimate metric to evaluate the

system, which is defined as the product of GDP and GDH.Gross Domestic Product (GDP)

and Gross Domestic Happiness(GDH) are determined by income, education and equality.

By analyzing the calculation model of CSI, we find that increasing the education time is

a good way to improve CSI.

In the second part, we generate a sample population of 10000 people to simulate the

first migration Population Zero to Mars firstly. Based on it, we find the total education

time of Population Zero is the decisive factor of income and education.Equality is

determined by the corruption. Based on the equation, we can motivate people to increase

their education time by increasing their income to improve CSI. Secondly, we divide

Population Zero into several subgroups per their preference. A variable called Subgroups

Satisfaction Index(SSI) is defined to measure the satisfaction with the status quo of the

subgroups The result indicates that as time goes by, SSI of each subgroups are growing

but their gap is expanding. Fortunately, the gap is always changing in a certain range that

will not lead to a humanitarian crisis.

In the third part, we establish two migration models. Phased Migration Model

determines the reasonable number of immigrations each time and Refugee Migration

Model determines the largest number of people flooding into the system. Models

sensitivity, robustness and the effect of initial value changes are also analyzed.

In the last part, we give some policy recommendations in the short term and in the

long term. Besides, the ways to strengthen our models are also considered.

T1

T2

T3

T4

2017

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Contents

1 Introduction 2

1.1 Problem Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . 2

2 Model Overview 3

2.1 Principles and assumptions of “Protopia Mars” . . . . . . . . . . . . .. . . . . . . . . . . . . . 3

2.2 Notations & Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .4

3 Part I 4

3.1 The calculation model of GDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

3.1.1 Additional assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

3.1.2 model establishing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . 5

3.2 The calculation model of GDH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2.1 The definition of GDH . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . 7

3.2.2 regression analysis to find the relationship between GDH and three

factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . .. . 7

3.2.3 The calculation model of CSI . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . 8

3.2.4 The discussion of CSI . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . .8

4 Part II 8

4.1 Generate a sample of Population Zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . 8

4.2 The model to determine the three factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .9

4.3 Subgroups’ Preference Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4.4 Model extension analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5 Part III 13

5.1 Immigration model by phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

5.2 Additional assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13

5.3 Calculation Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6 Strengths & Weakness 16

6.1 Strengths: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

6.1.1 The Model avoids main inequality existed on Earth . . . . . . . . . . . . . . . . . . . . . . .16


6.1.2 The model avoids the problem exist in current labor . . . . . . . . . . . . . . . . . . . . . 17

6.2 Weaknesses: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17

6.2.1 The influence of internal perturbation on the accuracy of model

prediction: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

6.2.2 The influence of external factors on the accuracy of model prediction: . . . . . . . .17

7 Policy recommendations 18

7.1 First 10 years . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

7.2 Following years: Policy recommendations based on the phased immigra-

tion model and the refugee immigration model: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

7.3 The policy recommendations based on the main weaknesses . . . . . . . . . . . . . . . . . .18

8 References 19

Appendices 19

Appendix A Program sources: Calculating GINI Index 19

Appendix B Program sources: Function fitting 20

List of Figures

1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 The distribution of Population Zero’s Ed . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11

4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12

6 Location of Chad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

List of Tables

1 Correlation Analyze . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7

2 Multiple Linear Regression Model of GDH . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

3 Demographic characteristics of the sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4 Reasonable immigrant per decade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16


1 Introduction

Close your eyes and imagine that you are now in 2095, the end of the 21st century. During

this century, human beings continually exploit and use the resources of the earth. At the same

time, the shortage of resources is becoming more and more intense and the environmental

problems are becoming more and more serious. “Where is the next planet?” has become a hot

topic. Fortunately, with advances in science and technology, the ability of mankind to explore

Mars has made a qualitative leap and immigration to Mars has become possible.

The international agency, Laboratory of Interstellar Financial & Exploration Policy (LIFE)

recently completed a series of short-term planned living experiments on Mars and planned to

send the first wave of migration, called Population Zero (10000 people), to the manufactured

cities on Mars by 2100. The problem is how to design a social system for Population Zero that

will make the living experience on Mars in the year 2100 even better than the Earthly one in the

current year of 2095. Whats more, how to ensure that the system is sustainable for a long time?

How to ensure that the following immigrants can join? To answer these questions, and to build a

protopia1 , some scientific and sociological analysis and mathematical models may be needed.

1.1 Problem Analysis

To design a good social system on Mars, there are many factors to consider, such as economy,

equality and peoples happiness. Our goal is to create a social system by maximizing both

economic output (GDP) and happiness for its citizens. Furthermore, the system can be sustainable

if the number and demographic characteristics of the population change. As we know, economic

output (GDP) and happiness can be in opposition, so we consider income, education and equality

as the balancing factors.

Then, consider the following questions:

• What are the metrics to evaluate whether the system is meeting its objective and how to

calculate these metrics, especially their relationship with the three factors? • Whats the

relationship between the three priority factors (income, education, equality)?

• After generating a sample population of 10000 people to simulate Population Zero and

dividing them into several subgroups according to their preference, is there any difference

of happiness between different subgroups?

• If there are phased migrations over the next 100-years, how sensitive is the model to the

population selection for various migration phases? How to determine the number of

immigrants each time?

1 “Protopia” is a concept that Kevin Kelly——the former editor of "Wired" magazine, the famous futurist ——puts forward. Different from the Utopia. The community does not pursue a perfect static society, but follow the pace of the development of the evolution. The latter is an artificially constructed society that cannot be reached, while the former is consistent with the law and trend of historical development, so it is more lively and more likely to be the world's future appearance.


• If there is an abrupt large number of migration to the system for some reason, for example,

scientists discover a threat of a collision of Earth with a planet sized comet, is the model

still functional? Would it make a difference if migrations occurred in phases?

• Is the model enough sensitive and robust to a much larger scale migration?

• Whats the strengths, weaknesses and practical significance of the model?

To answer these questions, we design a series of methods shown in the model overview.

2 Model Overview

2.1Principles of “Protopia Mars”

1. Everyone on the earth is equal. Based on this principle , well randomly choose “Protopia”

people from earth ignore their gender income region or race .

2. The economic base determines the society structure, the main factor of our model is

economic properties. Once the economic properties are configured properly, other social

properties such as political status can be reasonably decided.

3. The principle of freedom: the community will not force members to do anything, the

achieving of our target indicators will be carried out through motivating citizens to do what

we want him to do. When the individuals are pursuing their own interests, the interests of

the whole community will be maximized.

Figure 1: Model

CSI = ×


2.2 Notations & Descriptions

Notation Descriptions

GDP Gross Domestic Product

GDH Gross Domestic Happiness

CSI Community Success Index

Lt Laborpopulation at time t

Lm The maximum capacity of the population

Edt Per capita education time at time t

T Total education time of the society

Edm Per capita education level of Population Zero

Eqt Equality at time t

Kt Capital at time t

At Resource and technology multiplier

Ii Personal income

ϕ Saving rate

δ The depreciation rate of capital

g The increasing rate of Resource and technology multiplier

SSI Subgroups Satisfaction Index

GINI GINI Index

3 Part I

3.1 The calculation model of GDP

First, we define a measurement system to evaluate whether the system can achieve its goal. These

criteria include output (GDP), Gross Domestic Happiness (GDH) and Community Success Index

(CSI). This part will demonstrate the calculation method of three standards.

3.1.1 Additional assumptions

The initial time is 2100, denoted as t0 = 0;

The labor force is equal to the total population;

Constant returns to scale2;

Ignore short-term economic fluctuations;

The level of education is expressed by the average time of vocational training: We know,The

level of education in a country is determined by the government and business investment in

education, and this can be reflected in the citizen education time, so we can use the per capita

time of education to measure a country’s educational level.

Saving rate ϕ = 6%2;

2 It indicates: α+β = 1. 2

Data source: The average of Saving Rate in the US from 2010 to 2016 published in FRED Economic Research


Depreciation rate δ = 15%3;

Resource technology growth rate of g = 9.75%4;

Resource technology growth rate mainly refers to the resource growth rate: Technological

progress and resource development have a positive effect on the production output, so take these

as the multiplier of the technical resources. And during the first 10 years, as the early stages of

economic development, technological progress can be ignored.

3.1.2 Model establishing

The Douglas production function is a classical model to study the economic output, which shows

that the total GDP is determined by the input factors of capital and labor force, and its function

form is:

Y = AKαLβ (1)

On this basis, Considering the effect of education on the improvement of labor force quality,

technological progress, a increase in resources, and the impact of GDP growth, the GDP model

is as follows:

GDPt = F(Kt, Lt, Edt, At) (2)

Where Kt is the capital stock at time t, Lt is the quantity of labor at time t, Edt is the average

vocational training time at time t, At is the technical resource multiplier at time t. Combining the

form of the Douglas production function with the constant returns to scale,(α + β = 1), the

Equation (2) can be expressed as:

GDP (3)

1. Capital growth function

The increase in capital stock is equal to the household savings in current year minus the

depreciation of capital,

the savings rate ϕ > 0, the depreciation rate δ > 0, wi is a single resident wage, yt is the sum

of the total wage this year, So the capital increase function can be:

Kt+1 − Kt = ϕ × yt − δ × Kt, ϕ > 0,δ > 0 (4)

3 Data source:Refer to the depreciation rates for various industries in the US Bureau of Economic Analysis (BEA) 4 4.Calculation process:Take the first 156 years after the “Mayflower” emigrated to the North American as the

reference time. Because the situation that the “Mayflower” initially landed in North America is like ours. Infrastructure

is scarce but land and resource growth is extremely high. Assuming that the Cultivation level and food needs of the

“Mayflower” migrants were equal to those of the UK at that time and the per capita arable land in the early 1700s was

about 0.2 acre, so the North American colonies initially had 50×0.2=10 acres of land. When the United States was

founded, the land was about 20 million acres, so the average growth rate g =9.75%.


yt =∑ 𝑊𝑖𝑛𝑖=1 (5)

From (4),(5) we get,

(6)

In the function q = 1 + ϕ

2. Labor force growth function

Considering that natural resources, environmental conditions and other factors may block

the population growth, Population Zero growth on Mars in line with Blocking Growth

Model, the Logistic model. This model considers that the population growth rate r

decreases with the increase of population x.

The basic function form is:

(7)

After transformation, the equation can be expressed as:

(8)

Where x(t) is the population in year t, xm is the population capacity, that is the natural

environment and resources can accommodate the maximum amount, x0 for the initial

number, r is the population growth rate, t is time.

According to Equation (8),assume the initial population is L0, population capacity is Lm,

take the population data of United States during 1790-1940 years as samples4, the fitting

result is:

(9)

3. Education

(10)

4. Production factor growth function

During the first 10 years after immigration, economic development is in the early stage ,

the technology level is relatively stable, the growth rate is 0, and the resources increase

with the land development, the resource growth rate is g1; In the long run, considering the

limited resources, the rate of technological progress is g2, assuming g1 + g2 is a fixed value

g. Considering during first 10 years g2 is a constant, while g1 equals to 9.75%.

At = (1 + g)t × A0 (11)

4 Data Source: American Census Network.


A0 is the initial technical resource level in 2100.

After all, Equation (3) can be shown below:

(12)

3.2 The calculation model of GDH

3.2.1 The definition of GDH

To measure the happiness index of residents, we define the Gross Domestic Happiness value

(GDH), the higher the value, the higher the happiness of residents. And then find its relationship

with the three factors (Income, Education, Equality). It is assumed that GDH is linearly related

to the three factors, and can be expressed as:

GDH = ω0 + ω1 ×𝐺𝐷𝑃

𝐿+ ω2 × Ed + ω3 × Eq (13)

3.2.2 regression analysis to find the relationship between GDH and three factors

Based on the data in the survey World Happiness Report2016 by the U.N., we can get the values

of GDH, GDP per capita, GINI Index, government corruption and average life expectancy of

countries in 2014. Take GDP per capita as a measure of income, GINI Index and the perception

of government corruption as a measure of equality, “Its never too old to learn”, so we assume that

the average life expectancy can be used as a measure of the education. In order to get the most

significant factors of GDH, these variables were analyzed for correlation, the results are in Table

1:

Table 1: Correlation Analyze

Factors GDP per capita Healthy life expectancy corruption GINI Index

Correlation 0.792 0.805 -0.610 0.474

So we choose GDP per capita Healthy life expectancy corruption as factors ,take multiple linear

regression analysis using SPSS, the multiple linear regression model is in Table 2:

The significance test result shows that all the Index are significant and the linear relationship is

also significant, which indicates that the linear relationship of three factors to GDH is reasonable.

Considering that regression analysis uses government corruption perception as a variable to

measure equality, it is negatively related to equality. That is, inequality will reduce happiness.

Therefore, we change the equality in GDH calculation model to inequality, the model results are

as follows:

GDP

GDH = 0.35 + 0.07Ed − 1.07INEq − 1.27 (14)

L


Table 2: Multiple Linear Regression Model of GDH

Independent Variable Dependent Variable

GDH

GDP per capita 0.35

(0.0005)***

Healthy life expectancy at birth 0.07

(0.0000)***

Perceptions of corruption -1.07

(0.0012)***

Constant -1.27

(0.0279)***

Number of observations 129

Adjusted R-squared 0.705

F-statistic 102.8214

(0.0000)***

3.2.3 The calculation model of CSI

To create a sustainable society by maximizing both economic output (GDP) and happiness(GDH),

we define a parameter Community Success Index(CSI). Community Success Index (CSI) is equal

to the product of GDH and GDP. The function is as follows:

CSI = GDH × GDP (15)

Considering the Equation (12), (14) and Equation (15) can be obtained:

CSI

ω0 = −1.27, ω1 = 0.35, ω2 = 0.07, ω3 = −1.07;

3.2.4 The discussion of CSI

1)From Equation (16) we can see that the higher the level of education, the longer the vocational

training time per capita, not only can increasing GDP, but also can increasing the GDH to improve

CSI. In the absence of population moving in and out, the capital and labor meet the growth pattern

over time, resource technology multiplier is established, the equality remain unchanged in short-

term, only education is controllable factors. Therefore, CSI is improved mainly by raising the

level of education.

2)We need to discuss the value of 𝛂. It comes down to the constrained maximization problem as

follows.

𝐬. 𝐭. 𝑲𝟎 > 𝑳𝟎

𝐦𝐚𝐱 𝐂𝐒𝐈 = 𝐆𝐃𝐇×𝐆𝐃𝐏

When 𝛂 = 𝟏, CSI is biggest. But in fact, 𝛂 cannot be equal to 1. Considering 𝟏 − 𝛂 is smaller

than 𝛂 by a Magnitude, 𝛂 can be 0.9.

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4 Part II 4.1 Generate a sample of Population Zero To simulate Population Zero, a sample population of 10,000 people is generated by using

Excel. We define demographic characteristics such as gender, age, educational level, and income.

Based on our principle 1, we generate the sample totally according to the demographic

distribution in America.

From this figure we could find that the average education level is high school graduate; and most

people have an income around $67500 per year, as for the equal principal, the gender is 50%male

vs 50%female; and the age distribution is much uniform.

Table 3: Demographic characteristics of the sample

Education Attainment

Population 18 to 24 years Percentage

Less than high school graduate 14.40%

High school graduate (includes

equivalency)

29.70%

Some college or associate’s degree 46.10%

Bachelor’s degree or higher 9.80%

Population 25 years and over Percentage

Less than 9th grade 5.70%

9th to 12th grade, no diploma 7.60%

High school graduate (includes

equivalency)

27.80%

Some college, no degree 21.10%

Associate’s degree 8.10%

Bachelor’s degree 18.50%

Graduate or professional degree 11.20%

Age Percentage

Under 5 years 6.19%

5 to 9 years 6.37%

10 to 14 years 6.42%

15 to 19 years 6.57%

20 to 24 years 7.07%

25 to 29 years 6.99%

30 to 34 years 6.74%

35 to 39 years 6.34%

40 to 44 years 6.29%

45 to 49 years 6.49%

50 to 54 years 6.95%

55 to 59 years 6.78%

60 to 64 years 5.93%

65 to 69 years 5.00%

70 to 74 years 3.57%

75 years and over 6.29%

IncomeperYear Percentage

Less than $10,000 7.20%

$10,000 to $14,999 5.30%

$15,000 to $24,999 10.60%

$25,000 to $34,999 10.10%

$35,000 to $49,999 13.40%

$50,000 to $74,999 17.80%

$75,000 to $99,999 12.10%

$100,000 to $149,999 13.10%

$150,000 to $199,999 5.10%

$200,000 or more 5.30%

Gender Percentage

male 50%

female 50%

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4.2 The model to determine the three factors

1. The education time per capita of Population Zero can be obtained by dividing the total

education time T by the population L:

2. Because raising the level of education can improve CSI without a population moving in

and out, how can it motivate people to improve their education? The first incentive we

consider is income.

By using the data of the total education time T and the personal income I of Population

Zero, the relationship between personal income I and education time T is(fitted by Matlab):

I = 14640e0.072T

3. The level of equality is determined by the perceived corruption per World Happiness

Report 2016.

4. Based on our sourcing method of Population Zero, the distribution of education time T in

Population Zero is similar to that in the United States and is Normal distribution. Using the

actual data , equation parameters can be fitted, and µ =

6.92, σ = 4.33.

Figure 2: The distribution of Population Zero’s Ed

The equation of average educational time Ed over time t is:

(17)

4.3 Subgroups’ Preference Analysis

Everyone has different perceptions of the same thing because of different values. We now

classify Population Zero into subgroups by means of preference features, and use differential

equations to measure differences in satisfaction that are generated by different preferences. In our

model, our main control factors are Education, Equality, Income, so we mainly consider the

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differences in satisfaction degree of the subgroups due to the differences in preferences of these

three factors.

First, in terms of education, we do not consider the impact of the length of education on

happiness, because not many people feel that “learning makes me happy.”

Then income, satisfaction and income are assumed to be linear relationship, the higher the

income, the higher the satisfaction.

Finally, Equality, happiness and fairness is also assumed to be a linear relationship, more fair

the community is, the happier the citizens will be. The fairness is quantified by GINI Index:

SSli = A × (1 − αi) × ω + αi × GINI (18)

A is the multiplier to ensure that ω and GINI have the same magnitude. A is chosen as 10.

Suppose the citizen’s preference for money is not related to the money he now has, so .

GINI Index formula is:

(19)

The relationship between the wage level and the level of education is as follows:

I = 14640e0.072T (20)

So the GINI Index on Mars is equal to 0.161;

Program is in Appendix A

Let α be linearly distributed between 0 and 1,that is αi = 0.01 × i(i = 1to100) So, we can get

the distribution of SSIi:

Figure 3:

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SSImax/SSImin = 1.61 And Canada’s GDH divided by Greece’s GDH is 1.61, so we can not

think that the happiness of the subgroups in our model is not much differentiated; At last, we

consider that as time goes by, what changes will happen to GDH of the subgroups? At this case,

the time t is between 0 and 10. Take into it:

Figure 4:

It’s obvious that as time goes by, GINI Index is increasing. The curve that indicates the change

of total GDH of the subgroups over time is as follows:

Figure 5:

It’s obvious that the total GDH is increasing over time.

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Then what about the GDH differentiation degree SSImax/SSImin? SSImax is totally

determined by GINI Index and SSImin is constant, so the biggest differentiation degree is 1.75

when t = 10. Cananda’s GDH divided by India’s GDH is 1.75, so the GDH differentiation of the

subgroups will not lead to a humanitarian crisis.

4.4 Model extension analysis

People will not only have different preferences for Ed, Eq, I, but also for the other needs of

daily life. For example, some people like movies, some people like electronic products, some

people like music. But the community can not understand and meet all the individual needs

through central decision-making.

Therefore, we must introduce a certain degree of market mechanisms, but start-up must have

start-up capital. Because Mars immigrants initially are proletarian without collateral, and the

community is not easy to assess the quality of entrepreneurial projects and entrepreneur credit

value, so we must introduce New financing modalities.

We think that “crowdfunding” is the best way to fully decentralize decision-making and use

the market for information understanding to promote the release of individual needs.

The specific operation is: the community provides a public platform to raise the good idea of

the public. You can crowdfund both the products and the stock to meet the needs of the minority.

5 Part III

5.1 Immigration model by phase

For the case of population immigration in phases, we use the GDH to calculate the maximum

population size on Mars.

5.2 Additional assumptions

1. Immigration occurs every ten years;

2. The proportion of all income declined temporarily to support move-ins to survive,

3. the GINI Index is not affected by immigration;

4. The growth pattern of immigrant population is similar to Population Zero.

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5.3 Calculation Process

In Part I we get GDH and GDP calculation model

GDH = ω0 + ω1 ×𝐺𝐷𝑃

𝐿+ ω2 × Ed + ω3 × Eq (21)

(22)

Take Equation (21) into Equation (22):

GDH

Data of Equation (23) is same as the data in Part I.

1. g = 0.0975;

2. α = 0.9,β = 0.1;

3. Eq is the GINI Index, equals to 0.013;

4. Regression coefficient ω0 = −1.27, ω1 = 0.35, ω2 = 0.07, ω3 = −1.07;

5. Education level per capita Edt take the level of education per capita in the United States.

Considering the environment differences between Mars and the Earth, the Edt takes a

reduction treatment, slowly return to normal level. Its function equation is:

(24) Figure 6: Location of Chad

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6. Mars has a hot, dry and relative lack of infrastructure environment, so select the African

country Chad happiness as Population zero Initial happiness, that is 3.41. So there Mars

initial GDH

GDH (25)

So we get,

(26)

7. L is the current population of Mars, in line with the population growth model:

(27)

Where Lm is the population capacity of the environment, linearly increases with time, L0 is

the initial population, determined by the current population of Mars, t is taken as 10 years,

L is the total population of Mars after 10 years.

After the phased resettlement plan started, the number of immigrants per stage is ∆L, Mars

GDH can not lower than the average happiness of the Earth 5.455, there is:

From this we can calculate the reasonable number of immigrant every ten years:

As we can see, the model has a strong Sustainability and practical significance, and can be

used as a reference for population migration policy.

Refugee Immigration Model

If the population in the Earth needs a large-scale migration due to disaster avoidance, the

GDH can also be used to measure the max number of population, we take the happiness of the

world’s lowest happiness in 2014 (2.69) as the Lowest GDH of Mars population in which does

not lead to social unrest.

GDH

Compared with the above conclusions, Mars single maximum immigrant allowances is 1.9

times than the reasonable immigrant number at the same decade, if immigrant more than this

value, it will lead to social unrest and other issues.

Then analyze the GDH formula in the model:

5 Data Source: 2016 World Happiness Report by The United Nations

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GDH

5.4 Discussion

educational level of immigration is improved, then the average education level of Mars will

increase, and the GDH will increase, that is, Mars can allow more immigrants. If the Table 4:

Reasonable immigrant per decade

Table4：Reasonable immigrant per decade Year 2110 2120 2130 2140 2150 2160 2170 2180 2190 2200

Immigrant 3600 22661 66222 186872 525633 1478223 4158509 11709166 33045274 93794410

average educational level of the population moving into Mars is lower, the population capacity

will decrease, but the effect is not significant. According to the above formula, increase the Edt

by one year, ∆L increased by only 1.17%.

If the number of Population Zero changes, it will directly affect the number of immigrants

allowed. Since the growth of capital in this model is constant, the initial population increase will

result in an acceptable reduction in the number of immigrants in the preceding decades, but In

the long run, the impact is very small, the following table for the initial population increase 10%,

after 2170, the reasonable population has no relationship with the initial population.

Table5：Reasonable immigrant per decade adjusted Year 2110 2120 2130 2140 2150 2160 2170 2180 2190 2200

Immigrant 2414 22483 66175 186859 525629 1478222 4158509 11709166 33045274 93794410

6 Strengths & Weakness

6.1 Strengths:

6.1.1 The Model avoids main inequality existed on Earth

1. For the disabled people on the Mars. Their employment problem can be partially solved

through the Social Enterprise approach. Nonprofit Organization will be set up by the

community where disabilities could provide social services to people and get paid by public.

2. The equal problem between men and women, income entirely decided by your work

“competence”, that is, the vocational training time, economic inequality can be solved very

well. The current solution in the U.S. is like the “Green Ways” approach, which is like our

model by strengthening the training to women work competencies. But women will still

be discriminated in the current workforce system with a full degree of competency,

meaning that the workforce’s worth after training is wrongly estimated. But in our model,

it equally reflects the relationship between a person’s work competency and his income,

without being affected by gender disparities. In other words, the economic equality of men

and women has been resolved to the greatest extent.

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3. For the stratum solidification problem, the income in our model is only related to the degree

of competency, and it can weaken the inequality caused by the solidification of stratum to

a certain extent.

4. As for the education time, we have linked the education time to income, and it has a strong

correlation. It will promote people’s motivation to receive education. Just as the Far East

experienced the crisis in the 1960s.The acceptance of higher education was regard as the

primary indicator of the rise of the class, which has greatly promoted the enthusiasm of

people to take examinations. Because it is the community to provide training opportunities,

it will not show inequality like “educational stratification”, which appear in the current U.S.

6.1.2 The model avoids the problem exist in current labor

Unemployment problems in the economic cycle are not averaged across the workforce, Some

certain subgroups of the population are still likely to be unemployed at a high risk. After

analyzing these subgroups, it is found that they really lack the work competency.

By extending its training time, the work competency, that is the ability to perform a rigorous

job can be greatly enhanced ,the economic level and the living conditions can be improved in our

model.

Many people could not find jobs because of the pessimistic outlook, the longer they stay

unemployment, the harder they regain the opportunity to work forming a vicious feedback loop.

In our model, it is also through the direct link between “work competency” and income to avoid

this vicious feedback continued to strengthen.

6.2 Weaknesses:

6.2.1 The influence of internal perturbation on the accuracy of model prediction:

1. The main weakness of this model is how the T reflect the quality of education. We assume

that a person’s training time is a good reflection of the quality of the person’s training, but

as Goodhart’s law points out: when a measure of economic development becomes the goal

pursued by a country, its capacity of measuring economic development will be

substantially reduced, just as GDP in China is overvalued the same. This may occur with

our T, In the following policy recommendations, we will give a solution.

2. the normal distribution curve for the T, the parameters may be different from our estimates.

The standard deviation wont change, but on Mars, due to the technical level required far

more than on the Earth, the after the first 10 years may be more than 13.84 years. Since T

value is important to our model, this mean deviation is an important weakness in our model.

3. Allowing a certain degree of free trade effects. Because we introduce a certain degree of

freedom in the community, people can trade according to their own preferences, so that the

actual income of each person will be different with their wage income. People good at

business will take higher wage level, and our GINI Index will be biased, this affecting the

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Eq of the entire community. We will give a solution in the following policy

recommendations.

4. The deviation of g2. We estimate technological progress g2 with g1+g2 = constant, but this

is likely to show exponential growth, as Ray Kurzweil said in “Singularity Is Near” that

technology is not a linear growth but an exponential explosion. If the size of g2 is too large,

since g is a coefficient of exponential function, the value of g2 can have a significant effect

on our model outcome.

6.2.2 The influence of external factors on the accuracy of model prediction:

Since the actual environmental capacity of Mars is not known, we estimate the environmental

capacity of Mars according to the Earth’s capacity level, which may be biased, and this is the

main external effect.

7 Policy recommendations

7.1 First 10 years

1. Demographic structure: Increase the initial population size or enhance the education level

of the first immigrants cannot increase the immigration capacity in the long run.

2. Build a crowdfunding platform.Then,we can use crowdfunding for products or stokes to

satisfy the individual needs without the community loading to the entrepreneur As a result,

the satisfaction of subgroups will be increased.

3. According to its own labor needs, the community start training courses, to ensure the

workforce has a full degree of competency.

7.2 Following years: Policy recommendations based on the phased immigration

model and the refugee immigration model:

1. if government want to achieve a certain amount of population immigration, the

Government should gradually expand the scale of immigration, rather than immigrate the

same number of people each time.

2. Mars single maximum immigrant allowances is 1.9 times than the reasonable immigrant

number at the same decade, if immigrant more than this value, it will lead to social unrest

and other issues.

3. if you want to effectively enhance the number of immigrants, you should take measures to

enhance the technological level of growth in Mars settlements, (the value of g2) .

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7.3 The policy recommendations based on the main weaknesses

1. To prevent the Good hart effect, our community managers cannot raise the T as the lower

officer for the KPI. T can monitor the changes, but should not draw human intervention.

2. After the first group of immigrants arrived in Mars10 years later, statistical T every other

year to adjust the normal distribution of the value.

3. after the end of the first decade, as the French economist Picardy suggested, starting taxing

on capital.

(1, To alleviate the Matthew effect in free market .2, the specific operation ruled by the

economic policy makers in that time.)

8 References

(1) Jiang Qiyuan,Xie Jinxing,Ye Jun. Mathematical Models[M]. Higher Education Press,2011

(2) Transforming U.S. Workforce Development Policiise For the 21th Century

https://www.kansascityfed.org/~/media/files/publicat/community/workforce

/transformingworkforcedevelopment/book/transformingworkforcedevelopm entpolicies.pdf,

2015

(3) http://www.economist.com/blogs/freeexchange/2012/01/chinas-labour-force

Appendices

Appendix A Program sources: Calculating GINI Index

Here are programmes to calculate GINI Index python

sourcecode:

from scipy.special import erf from

scipy.special import erfinv from random

import random import numpy as np n = 10000

um = 13.84 r = np.log(10)/(np.exp(10)-1) c

= r-np.log(6.92)

uf = lambda t:um-1./(np.exp(r*np.exp(t) + c))

def q(x,u,s): return 0.5*(1+erf((x-u)/(s*1.414)))

s = 4.33 u = 6.17 def tr(u,s):

ans = -1 while ans < 0: y =

random() ans = erfinv(y*2-1)*(s*1.414)+u

return ans #

print tr(u,s)

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def about_time(t): u = uf(t) data = [14640*np.exp(0.072*tr(u,s)) for i in range(n)]

data.sort() print data[0],data[-1] print ’data’ sum = np.sum(data) print ’sum’ _s = 0

for i in range(n):

for j in range(i+1): _s += data[j]

if not(i%(n/10)):

print str(int(i/(n/10))) + ’0%’,’done’ pass

return 1 - 2* _s/sum/n

aans = [about_time(i/1.) for i in range(11)] print aans

import matplotlib.pyplot as plt plt.plot([i/1. for i in

range(11)],aans,’r’) plt.show()

Appendix B Program sources: Function fitting

Here are programmes to fit function python

sourcecode:

import numpy as np data =

[(1790,3.9), (1800,5.3), (1810,7.2), (1820,9.6), (1830,12.9), (1840,17.1), (1850,23.2), (1860,31.4), (1870,38.6), (1880,50.2), (1890,62.9), (1900,76), (1910,92), (1920,106.5), (1930,123.2), (1940,131.7)]

def x(t,_xm,_r): return _xm/(1+(_xm/3.9-1)*np.exp(-_r*t))

def e(xm_,r_): return np.sum(map((lambda i:(x(i[0]-1790,xm_,r_)-i[1])**2),data))

min = 1000000000000000 ans =

(1,) www = (1,) for i in

range(100): for j in range(100): xm = 224.5 + (i-50)*0.1 r = 0.05 +

(j-50) * 0.001 w = e(xm,r) if w <

min: min = w www = (i,j) ans =

(xm,r)

print ans print

www print min

Documents

UTOPIA? “PROTOPIA”! · 2018-03-08 · system, which is defined as the product of GDP and GDH.Gross Domestic Product (GDP) and Gross Domestic Happiness(GDH) are determined by income,