2023美赛F题

Introduction

Background

GDP (gross domestic product) is a commonly - used indicator to measure
the growth of a country’s economy. But it has caused controversy among
many economists in recent years because these negative factors such as
pollution and deterioration of the long - term environment caused by the
per - unit amount of GDP are not taken into account.

The concept of green GDP originated from the ecological Domestic Index
(EDI) was proposed by environmental economists Daly and Cobb in 1989. It
aims to establish a quantitative relationship between the measurement of
economic relationship between economic growth and resource &
environmental protection. In 1993, the United Nations Statistical Office
(UNSO) revised the System of National Accounts (SNA), expanded the
concept of “green value” and “green GDP”, etc. Since then, various
countries continued to improve the concept of green GDP in their
sustainable development support projects.

Restatement of the Problem

For the requirements given, we restate them as follows to help better
position the focus of our work.

• We need to choose a method to calculate GGDP to measure climate
  mitigation for Task 1.

• In Task 2, we’re supposed to build a model to assess the global
  impact of the shift in climate change.

• In Task 3, compare the benefits of climate mitigation and the
  potential disadvantages of this shift.

• In Task 4, analyze the impact of this shift for a specific country,
  including resources and industries.

• In addition, we need to provide advice to the leaders of the
  selected country on whether to shift to GGDP.

Our Work

Based on the restatement of requirements, our work can be concluded as
follows:

• Establish the calculation method of GGDP and calculate the GGDP data
  of 76 major countries around the world from 1965 to 2021.

• Build a comprehensive evaluation system for climate. By predicting
  the future GGDP through time - series analysis and calculating the
  change in the proportion of climate mitigation data in the GGDP -
  calculation formula, since the environmental factors are related to
  the secondary indicators in the evaluation system, we can predict
  the global impact of climate

• Establish a nonlinear programming model to study the impact of the
  shift from the flow of production factors among various industries,
  so as to explore its advantages and resistance.

• Analyze the impact of the shift on Peru based on previous models,
  and establish a super - game model for Peru’s copper mining
  industry.

• Make sensitivity analysis for the nonlinear - programming model when
  parameters grow or shrink.

Model Preparations

• **Statistics we collect from website are actual an reliable.**Our
  data were collected from offical statistical websites and databases
  and underwent scientific pre-processing.

• **The overall situation can be estimated through samples.**Due to
  missing statistics, we are unable to study all countries in the
  world. So we need to assume that the 75 countries we study are
  representative of the global situation.

• Neglect the explosive changes when forecasting over the few
  decades. Global disasters such as severe epidemics will bring
  immeasurable impacts from all aspects, which we cannot predict.

• Indirect environmental losses are omitted. For the sake of
  feasibility and avoiding double - counting, we believe that the most
  important environmental losses come from four aspects: greenhouse
  gas, thermal power generation, waste discharge, and natural resource
  loss.

• As for greenhouse gases, we only considered carbon capture
  and $N{O}_x$. These two categories of greenhouse gases have the most
  ecological impact.

* The assumptions under specific models are given in the following
sections.

Notation

Symbol Definition Unit

$C_k$ the constant coefficient for term k -
$E_{total}$ the total electricity consumption kWh
$KtC{O}_2$ the carbon dioxide emission kt
$KW$ the mass of total waste kt
$p$ the disposal cost of unit quality waste $
$NRD$ total natural resource depletion trillion$
$G$ the value of GGDP without the impact of shift trillion$
$\hat{G}$ the value of GGDP with the impact of shift trillion$

: Table 1:Notations

* Other notations instructions will be given in the text .

Data Collection and Cleaning

Collecting sufficient data is the basis for establishing a comprehensive
index system. Our data are mainly sourced from the World Bank website,
Wind database, and national statistical bureaus. The data sources are
summarized in Table 2.

Database Website

Woeld Bank https://www.worldbank.org/
OECD thttps://www.oecd.org/
UN-DH-Libarary https://digitallibrary.un.org/
BEA https://www.bea.gov/data

Data pre - processing is divided into three steps: data filling,
handling outliers, and normalization.

• Data Filling: If there is a relatively strong correlation with
  other years, we use the regression interpolation method, or we use
  the average value of other years to fill in the missing ones.

• Handling Outliers: We analyzed each indicator and deviated from
  the abnormal data that may damage the accuracy and efficacy of our
  models.

• Data Normalization: We normalize the data of different
  indicators so that they can be compared on the same scale. We
  classify the used indicators into benefit attributes and cost
  attributes and scale them to $[0,1]$.

The Calculation of GGDP

The calculations of GGDP

Green GDP aims to provide a more comprehensive measure of economic
performance by accounting for the negative externalities of economic
growth, such as air and water pollution, deforestation, and depletion of
non - renewable resources.

There is no single “official” calculation method for Green GDP. We
choose ANI as the basis of our approach because it is an expansion
of GDP. The part of measuring ecological development is added to the
basis of GDP. However, there are also many forms of the formula of ANI.
To avoid controversy, we revised GGDP into two parts: GDP and
environmental destruction cost[@stjepanovic2019green].

$$GGDP=GDP-c(C{O}_2)-c(Ele)-c(Wa)-c(RD)$$

The first deduction means the costs of $C{O}_2$ pollution (as $C{O}_2$
emissions times carbon market price), second the costs of energy
pollution, third the opportunity costs of one tonne of waste that could
be used in the production of electrical energy), and a fourth is the
adjusted savings of natural resource depletion as a percentage of the
gross national income per country.

More specifically, the formula can be rewritten as:

$$GGDP=GDP-C_1\cdot KtC{O}_2\cdot PCDM-C2\cdot (1-\delta )\cdot E_{total}\cdot Pelect-C_3\cdot TW\cdot p-\left(\frac{GNI}{100}\cdot \%NRD\right)$$

where $C_k$ represents the constant coefficient for term $k$, $KtC{O}_2$
represents the carbon dioxide emissions expressed as kilotonnes, $PCDM$
is the average volume - weighted price for carbon in PPP, $E_{total}$ is
the total electricity consumption, $TW$ is the mass of total waste and
$p$ is the disposal cost of unit quality waste. GNI (Gross national
income) is the sum of value added by all resident producers plus any
product taxes (fewer subsidies) not included in the valuation of output
plus net receipts of primary income (compensation of employees and
property income) from abroad. NRD represents natural resource depletion
as a sum of net forest depletion, energy depletion, and mineral
depletion.

Global Statistics

We need the data on GDP, $C{O}_2$ emissions, power consumption, and
mineral and forest consumption of each country to calculate the GGDP.
Due to the large degree of missing statistics, we finally select $75$
countries as the representation of the global situation from $1965$ to
$2021$. The shift from GDP to GGDP is fundamentally a change in the
country’s attitude towards environmental protection. That is to say, the
country attaches great importance to environmental protection. Hence,
the impact of the shift can be studied through those most
environmental-consciously countries.

We choose ten countries with the highest GGDP - to - GDP ratio in 2021.
The global average value and the ten countries’ average value of GDP and
GGDP are shown in Figure 2. As shown in the figure, the trend of the
average GDP of the ten most environmental - consciously countries is
similar to it in other countries, so we can deduce that the shift will
not change the development trend of GDP overall.

The ratio of GGDP to GDP can be used to measure countries’ environmental
protection degrees. The left subfigure of Figure 3 reflects the average
ratio of the ten countries in half a century, showing the trends that
are primarily synchronized and eventually approaching a limit.

Compared to the rest countries, these ten countries show a clear
cyclical growth trend. As first - mover countries, their growth is
mainly due to progressively better environmental policies. We can use
this cyclical trend to predict the impact of GGDP as a policy shift for
each country. We make the mean curve of these ten countries (the right
chart of Figure 3 ), and name it as ratio life - cycle curve. We
summarize the following rules through curves of more countries:

• There is an upper limit of the ratio, and it can be assumed that all
  countries will reach this upper limit in the future.

• The development of the ratio in each country can be divided into
  three stages: the initial stage, the growth stage, and the maturity
  stage. These three stages are closely related to the country’s
  performance in environmental protection and comply with the growth
  of the country’s environmental protection capacity.

• In the initial stage, the country attaches great importance to
  economic growth, and lacks of environmental protection awareness, so
  the ratio is low and stable.

• In the growth stage, as a mature economy, the country begins to pay
  attention to sustainable development, and the ratio also increased
  rapidly.

• Finally, in the maturity stage as the country’s performance in
  environmental protection has been perfect, the ratio will keep
  approaching its theoretical upper limit.

• The theoretical upper limit can raise slowly. It is related to the
  development degree and resource endowment of environmental
  protection technology in the current world. When science and
  technology keep improving and the utilization of resources is
  constantly optimized, the upper limit of the ratio will climb at a
  slow speed.

The Forecast of GGDP

Prediction Method

According to the ratio life cycle theory in the previous section,we can
predict with the following steps:

• Step 1,identify the stage by the rate of a country over five years.

• Step 2,predict the development of the ratio life cycle curve.

• Step 3,the time series is used to predict the GDP of the country,
  and the multiply the GDP by the ratio to obtain the future GGDP.

In this way, we implicitly divide all countries into three categories,
giving them corresponding prediction rules. Until 2050, the global GGDP
is shown in the figure below. We also mark the predicted 2050 GGDP on
the map.

Forecast Cnclusions

• Replacing GDP with GGDP as the most important evaluation indicator
  of the economy has a significant effect on promoting the increase of
  global GGDP.

• For each country, the impact of the shift is different, which is
  related to the stages of the ratio life cycle.

• In the short term, the countries in the growth stage benefit most,
  whose GGDP - to - GDP ratio will start to rise rapidly.

• In the medium term, considering the stage transition, more countries
  will enter a new stage and benefit from the shift, and the global
  GGDP will have a significant increase.

• In the long term, almost all countries will be in the mature stage.
  Due to the development of science and technology and society, the
  upper limit of the ratio can continue to increase, and the global
  environmental protection level will usher in a new leap.

Model $1$:Evaluation Model of Climate Mitigation

Climate mitigation refers to efforts aimed at reducing greenhouse gas
emissions and thus slowing down the rate of climate change. Climate
mitigation involves reducing the amount of GHG emissions from human
activities such as energy production, transportation, agriculture, and
deforestation, etc. There are various strategies and techniques that can
be used for climate mitigation, such as increasing the use of renewable
energy and improving energy efficiency. Here we establish an indicator
system to measure the impact of the shift on climate mitigation.

Establishment of AHP model

Standars of Evaluation Model

The climate mitigation evaluation model for a country or region of
climate mitigation should satisfy the following requirements:

• The evaluation model is universal, and it can be used to measure any
  one country or region.

• The model should be comprehensive, exhausting various aspects of
  climate mitigation.

• The selected indicators are reliable and representative, with no
  duplication between them.

Indicators Selection

The comprehensive performance of a country or region in climate
mitigation is related to many factors. The most important pollutant
emissions because greenhouse gases have a direct impact on the
atmosphere. Human waste may also cause irreversible harm to the
environment. Besides, energy consumption—the more efficiently, the
more the country contributes to climate mitigation. In addition,
scientific and technological development can also help to improve
climate problems and save the environment. Other factors related to
climate mitigation include forests, policy, and public awareness.

Based on the above description, we establish an AHP model and compile
six main factors and select 15 indicators that measure climate
mitigation.

Calculation of Weights

Determination of the weights is essential to evaluate the different
contributions of the indicators. Consequently, two weighting models are
adopted to calculate the weight vector.

The traditional AHP model uses Group Decision Method (GDM) to
determine the weight of each indicator. This method requires experts to
give the comparison matrix of all main factors. GDM has its rationality,
but it is very subjective.

The entropy weight method (EWM) is another commonly used weighting
method. It assumes that the greater degree of dispersion, the greater
the degree of differentiation, and the more information can be derived.
Thus, a higher weight should be given to the indicator, and vice versa.

We combine these two methods to determine the weights for our evaluation
model, which both increase credibility and reflect the importance we
attach to each factor.

• First,we use EWM to find the weights of all secondary
  indicators. The specific steps to calculate each first - level
  indicator are as follows. For a first - level indicator $k$, there
  are $n$ second - level indicators of $m$ country.

  1. For the indicator $i$, calculate the probability $p_{ij}$ of
     country $j$, where $x_{ij}$ is the country $i$’s value of
     indicator $i$.

     $$p_{ij}=\frac{x_{ij}}{\sum _{j=1}^m{x}_{ij}}$$

  2. Calculate the entropy value $E_i$ of indicator $i$.

     $$E_i=-\frac{\sum _{j=1}^m{p}_{ij}\cdot \ln p_{ij}}{m}$$

  3. Calculate the weight $w_i$ of indicator $i$.

     $$w_i=\frac{1-E_i}{\sum _{i=1}^{n}1-E_i}$$

  4. Add the values of each second - level indicator by weight, then
     get the value of the first - level indicator $k$.

     $$X_{kj}=\sum _{i=1}^n{w}_i\cdot x_{ij}$$

  With second - level indicators’ weights obtained, we can calculate
  each first - level indicator. Similarly, we obtain the weight vector
  of first - level indicators.

• Second, we use GDM to subjectively determine the weight of each
  first - level indicator. Three experts vote on the importance of
  the six first - level indicators for climate mitigation, and
  specific steps are as follows.

  1. Pairwise comparisons between different factors

     Three experts voted to compare the importance of the main
     factors. $$\text{Greenhouse Gas}>\text{Energy}>\text{Waste Discharge}>\text{Forest}>\text{Technology}\approx \text{Social\&Policy}$$

  2. Calculation of comparison matrix

     With the relationship discussed before, we get our comparison
     matrix $(b_{ij}{)}_{6\times 6}$. $$\left(\begin{array}{cccccc}{F}_1& F_2& F_3& F_4& F_5& F_6\\ 1& \frac{1}{3}& \frac{1}{5}& \frac{1}{7}& \frac{1}{9}& \frac{1}{9}\\ 3& 1& \frac{1}{3}& \frac{1}{5}& \frac{1}{7}& \frac{1}{7}\\ 5& 3& 1& \frac{1}{3}& \frac{1}{5}& \frac{1}{5}\\ 7& 5& 3& 1& \frac{1}{3}& \frac{1}{3}\\ 9& 7& 5& 3& 1& 1\\ 9& 7& 5& 3& 1& 1\end{array}\right)$$

  3. Consistency Test

     We can calculate the eigenvalues and eigenvectors of the matrix
     before. Next, we need to perform consistency test with the
     maximum eigenvalue ${\lambda }_{max}$.
     $$CI=\frac{{\lambda }_{max}-n}{n-1}$$ $$CR=\frac{CI}{RI}$$ where
     $RI=1.26$ when $n=6$. For the above comparison matrix, we
     obtain $CR=0.044<0.1$, thus the comparison matrix is
     acceptable.

  4. Calculate to obtain weights

     Having passed the consistency test, we can get the weights of
     the main factors by the eigenvector corresponding to the maximum
     eigenvalue: Greenhouse Gas(0.475), Energy(0.257), Waste
     Discharge(0.135), Forest(0.068), Technology(0.033),
     Social&Policy(0.033).

• Third, We combine the two sets of weights. With the principle of
  Minimum Relative Information Entropy, we establish an
  optimization model to minimize the relative deviation of the results
  under the two decision methods.
  $$\text{min}\sum _{j=1}^n{w}_j\left(\ln w_j-\ln {\alpha }_j\right)+\sum _{j=1}^n{w}_j\left(\ln w_j-\ln {\beta }_j\right)$$
  $$\text{s.t.}\{\begin{array}{l}\sum w_j=1\\ w_j>0\\ j=1,2,\dots ,n\end{array}$$ Lagrange Multiplier Method is used to solve the above
  optimization problem, and we got the final weights:

  $$w_j=\frac{{\left({\gamma }_j{\alpha }_j\right)}^{0.5}}{{\sum }_{j=1}^n{\left({\gamma }_j{\alpha }_j\right)}^{0.5}}$$

In the following figures, we show the results of our evaluation model.
The left figure reflects the weight of every indicator, and the right
one shows how the 10 representative countries in our rating system
scored in 2021.

The main factor that matters most is greenhouse gas emissions. The rise
in the concentrations of greenhouse gases will directly lead to the rise
in the temperature of the earth. The main cause of global warming is
that human use of fossil fuels (such as coal, oil, etc.) in nearly a
century, and emit a large number of greenhouse gases such as $C{O}_2$.
While energy efficiency and natural resources are also vital.

Through rigorous calculations, we obtained a combined weight score for
all countries based on the entropy method and AHP. Ten countries
representing each situation were selected to show the scores. According
to our evaluation results, the country that performs best in climate
mitigation is Switzerland, which gets a score of 0.72.

Evaluation results

For Task 2, we need to use the previous prediction results and
evaluation model to estimate the impact on climate mitigation after
switching indicators. In Section 3.3, we predict the development of GGDP
$\hat{G}$ with the shift. The development of $\hat{G}$ involves both
natural economic growth and policy shocks. In this part, we predict
another GGDP $G$ directly based on historical data by ARIMA. This means
that $G$ only takes into account the natural growth of the economy and
is not subject to policy shocks, which is the counterfactual result of
$\hat{G}$. Hence, the difference between them reflects the effect of the
policy.

$$\Delta G=\hat{G}-G$$

At the same time, based on our previous deduction, GGDP is affected by
both GDP and environmental damage, and the implementation of the policy
will not significantly change the trend of GDP growth. So treatment
effect $\Delta G$ can be used to explain the impact of the conversion on
environmental damage.

As is stated before, environmental damage is mainly caused by greenhouse
gas emissions, thermal power generation, waste discharge, and resource
destruction, so the impact can also be decomposed into these four
aspects. We evenly distribute this part of the impact to these four
aspects, so that the value of carbon dioxide emissions reduction,
electricity savings, waste reduction, and resource savings can be
estimated.

Finally, we obtain that if this happens in 2019 ($\Delta G=10.6$
trillion), the world can reduce carbon dioxide emissions by 4425 million
metric tonnes, save electricity by 2376.22 TWh, reduce waste emissions
by 7898 million metric tonnes by 2050. What is more, the global
consumption of minerals, metals, fossil fuels, and biomass will be
reduced by 23 billion tons, and the recycling rate of raw materials will
increase from $8.6\%$ to $19.7\%$.

We plug these values into our climate mitigation evaluation models, the
impact will benefit climate mitigation globally in the following ways:

• The most direct impact of this shift is the substantial reduction of
  greenhouse gases. Considering the huge negative effect of greenhouse
  gases on GGDP, enterprises, and governments will actively or
  passively adopt pollution treatment devices. We calculate that by
  2050 carbide gas emissions will drop by $27.61\%$ and NOx gas
  emissions by $49.71\%$.

• Governments will implement more stringent environmental protection
  policies. Moreover, they will substantially increase investment in
  environmental protection. According to the indicator weight
  calculation, enterprises polluting the environment will pay an
  additional price of $300.00\%$. The public will also have higher
  environmental awareness, and the proportion of citizens with high
  environmental quality may increase from 6.23

• This shift will also promote human beings’ attention to forest
  resources. We estimate that the forest area in some deforestation
  areas (such as the Amazon rainforest, etc.) will stop negative
  growth, the global forest area will increase by $4.00\%$ by $2050$,
  and the health of the forest ecosystem will increase by $20.16\%$.

• Developed countries will have a trans - epochal improvement in
  carbon capture technology and waste disposal technology.
  Unfortunately, these technologies may not be affordable for a large
  number of developing countries. Even so, global waste disposal will
  rise to $35.55\%$ by $2050$.

• Building energy efficiency and industrial production energy
  efficiency both increase by $10.13\%$. With the development of
  electric vehicle technology and the phase - out of fuel vehicles,
  the fuel efficiency of vehicles will increase by $68.33\%$.
  Meanwhile, fossil fuel power generation will only drop by $80.79\%$
  following climate countries. The share of fossil fuel in total
  energy is expected to.

In conclusion, the shift significantly improves all six dimensions in
the AHP model, which will lead to a significant increase $(44.18\%)$ in
the global Climate Mitigation Score. As shown in Figure 7, according to
the research of the IPCC (Intergovernmental Panel on Climate Change),
global temperature change is directly related to carbon emissions. So
the shift will also help meet the United Nations’ goal of 1.5 degrees
Celsius of global warming by 2050.

Model $2$:Nonlinear Programming Model of Global Impacts

In 3.3.2, we prove the increasing positive impact of the shift on
sustainable development over time. In Section 4, we analyzed the impact
of the shift on climate mitigation in details. Moreover, in this
section, we describe the global impact of the shift in more aspects and
analyze the advancement and weakness respectively.

Flow Analysis of Production Factors

Analyzing the impact of a policy can also be conducted by studying the
development of different industries. Replacing GGDP with GDP will have a
huge impact on traditional industries with high energy consumption and
pollution. At the same time, it will also greatly encourage the
development of certain industries, such as new energy industry.
Globally, the most damaged industries are manufacturing, transportation,
energy and mining, which we name sunset industries of the shift. The
three most benefited industries are service industry, technological
industry and new energy industries, which named sunrise industries.

Considering the two most important factors of production, capital and
labor, we can use their flows to analyze the impact of shift on each
industry. Although the output value of all industries is increasing
every year, the country’s development will be tilted from sunset
industries to sunrise industries. Globally, affected by the shift,
capital and population will move from the sunset industries to the
sunrise industries, as shown in the figure below.

Although the shift has taken place, the short - term development goal of
countries in the world is still to maximize the total output value. The
total flow of capital can be estimated by $\Delta G$, because $\Delta G$
represents not only the value loss caused by environmental damage, but
also the loss of high - pollution and high - energy - consuming
industries. Production factors will flow to other industries. Based on
the flow relationship of production factors among industries, we can
build a nonlinear programming model.

Optimization Model for Production Factors Flow

Before we build the model, we need to make some specific assumptions:

• We only consider the two factors of production, capital and labor.

• Affected by the shift, the production factors will flow from sunset
  industries to sunrise industries the sunrise industry.

• The flow occurs at the end of each year.

• Every industry has labor load limit.

• After the flow, each industry has a fixed annual growth rate of
  capital and labor.

The value of output per year can be calculated using the Douglas
Production Function. For each industry, we use the last five years of
data to estimate the parameters in the production function.

$$Q=A\cdot K^{\alpha }{L}^{\beta }$$

With the above rules, we can build a flow optimization model.

 Symbol           Type         Definition

  $i$             index        the index of sunset industries
  $j$             index        the index of sunrise industries
$x_{ij}$    decision variable  capital flow from industry $i$ to industry $j$ in one year
$y_{ij}$    decision variable  labor flow from industry $i$ to industry $j$ in one year
 $Q_i$      decision variable  total output value of industry $i$ at the end of the year
 $E_i$      decision variable  total labor of industry $i$ at the end of the year
 $P_j$      decision variable  total output value of industry $j$ at the end of the year
 $F_j$      decision variable  total labor of industry $j$ at the end of the year
 $p_i$          parameter      total output value of industry $i$ at the beginning of the year
 $e_i$          parameter      total labor of industry $i$ at the beginning of the year
 $q_j$          parameter      total output value of industry $j$ at the beginning of the year
  $n$           parameter      total capital flow due to shift

$\lambda$ parameter industry output fluctuation range coefficient
${\omega }_i$ parameter annual labor value growth rate of industry $i$
${\delta }_j$ parameter annual output value growth rate of industry $j$
${\alpha }_i$ parameter The first exponent of the Douglas production function of industry $i$
${\beta }_j$ parameter The second exponent of the Douglas production function of industry $j$
$k$ parameter The annual growth grate of industry labor

: Notations of Nonlinear Programming Model

$$\max \sum _{i=1}^3{A}_i\cdot P_i^{{\alpha }_i}{E}_i^{{\beta }_i}+\sum _{j=1}^3{A}_j\cdot Q_j^{{\alpha }_j}{E}_j^{{\beta }_j}$$
$$\{\begin{array}{l}n={\sum }_{i=1}^3{\sum }_{j=1}^3{x}_{ij}\\ P_i=(p_i+{\sum }_{j=1}^3{y}_{ji})(1+{\omega }_i),\forall i\\ F_j=(f_j+{\sum }_{i=1}^3{y}_{ij})(1+k_j),\forall j\\ Q_i=(q_i-{\sum }_{j=1}^3{x}_{ij})(1+{\delta }_i),\forall i\\ E_i=(e_i-{\sum }_{j=1}^3{y}_{ij})(1+\lambda ),\forall i\\ F_j\le f_j(1+\lambda ),\forall j\\ x_{ij},y_{ij}\ge 0,\forall i,j=1,2,3\\ \text{All decision variables }>0\end{array}$$

It is an annual decision model of the flow of production factors. Its
results are based on the changes in the output value and labor
population of each industry. Due to the expansion of the industry scale,
the labor population will increase every year. Therefore, we use the
historical five - year data of the population to linearly fit it to
estimate the population increase. In addition, the annual total flow of
capital is $\Delta G$ of each year estimated in the previous model.

On this basis, we apply our nonlinear model to estimate the development
of industries in the next ten years as the flow chart shown below.

According to the results of our model, the changes in total output value
of the six industries are shown in the figure below. The total output
value without shift is a convex function, and the growth is mainly
determined by the manufacturing industry. For better observation, we lay
a straight line as a reference. In the short term, the growth of the
other shift sectors is shown in the broken line in the figure below.

In addition, the ratio of each industry’s output value and labor,
comparing with the predicted value of conventional growth after ten
years, is shown in the figure below.

Results of Impact

Through the nonlinear programming model of the flow of production
factors, we quantitatively analyze the short - term impact of the shift.

• The shift will have a restraining effect on the development of the
  global economy, reducing the growth of total output value of the 6
  industries by 5

• The impact of the shift on the output value varies from industries.
  Among them, sunrise industries such as service industry, new energy,
  and technology are expected to increase by 30.53

• The shift will lead to the redistribution of labor among industries,
  which may cause a large number of unemployment and spark workers’
  protests.

• The inhibitory effect of shift on certain industries will inhibit
  the economic development of countries that rely on them as pillar
  industries.

Besides, the shift also has some other push resistance. As for the cost,
a huge administrative costs will be caused. As for technology, it is
quite difficult to measure the environmental loss accurately. Therefore,
it can be inferred that the shift is a huge burden for economically
underdeveloped countries.

In the long run, since the parameters of the production function change
greatly over time and cannot be ignored, we quantitatively analyze the
impact of the shift.

• In the long run, the traditional energy industry is constantly being
  replaced by the new energy industry. The mining industry has reached
  a steady state after shrinking. The growth of high technology can
  alleviate the damage caused by the manufacturing and transportation
  industries to the environment. The global industrial optimization
  and upgrading has been completed, and the shift leads a new wave of
  economic growth.

• The scale of the sunrise industry has expanded, and the jobs
  provided are sufficient to solve the unemployment caused by the
  shrinkage of the sunset industry.

• High technology has developed by leaps and bounds, and at the same
  time global education has also been greatly improved.

• Energy regulation has been strengthened, breaking the resource
  monopoly of some countries and promoting global equity.

The shift can improve the well - being of people around the world in the
future. Combined with its effect of climate mitigation, $q_v$ fully
prove that the shift is worthwhile at a global scale.

Case Study:How Peru Survives The Shift

Sensitivity Analysis

::: appendices
::: memo
This is a memorandum.
:::

First appendix

Here are simulation programmes we used in our model as follow.
MATLAB source code:

Second appendix

Python source code:

:::