2023 Huawei Cup Question D - Empirical Research on Carbon Emissions Peak Based on Kaya Model

I. Introduction

Fossil energy is an important factor of production that drives modern economic growth, and economic production activities are closely related to carbon emission activities. Fully understanding the relationship between economic growth and carbon emissions is extremely necessary to transform production methods and determine the path to carbon peak and carbon neutrality. Based on the existing research on the relationship between economic growth and carbon emissions, this study systematically analyzed that the process of peaking carbon emissions is essentially an inverted U curve connected by three orders: carbon emission intensity, per capita carbon emissions and total carbon emissions. The formation of a gradual peak dynamic process. That is, carbon emission levels will experience a rapid rise in the early stages of economic development, and will gradually slow down and eventually peak after the economic development level reaches the middle-to-high-income stage. At the same time, based on the static Kaya model, the study conducted an empirical comparative analysis of the carbon emission peaking process between Organization for Economic Cooperation and Development (OECD) member countries and major non-OECD economies, including China, and analyzed the carbon emission levels. Dynamic changes are analyzed in stages. Empirical results show that China and OECD member countries are in line with the basic development law of economic growth and carbon emission peaks. The relationship between carbon emission peaks and economic development stages has a continuous interrelation of three inflection points and four stages. The peak order is in sequence. are carbon emission intensity, per capita carbon emissions and total carbon emissions. When carbon emissions peak, it is a necessary process for high-quality economic development in response to climate change. Market-oriented innovative incentives and reasonable and effective policy guidance must be adhered to to achieve green development.

2. Kaya model dynamics and triple turning points of carbon emissions peaking

In the past few decades, economists and scientists have developed a large number of carbon emission factors and carbon emission peak analysis methods. The Kaya identity proposed by Kaya is very simple, but it is a highly scalable accounting analysis method. The specific expression is:

 The simple expression of the Kaya model is that we use the logarithm of both sides and perform the first-order partial derivative of time to get: carbon emission growth rate = population growth rate + per capita GDP growth rate + energy consumption growth rate per unit GDP + carbon emission growth rate per unit energy consumption . When carbon emissions peak, the carbon emissions growth rate is 0, and we get: population growth rate + per capita GDP growth rate = unit GDP energy consumption decline rate + unit energy consumption carbon emissions decline, that is, population and economic growth are decoupled from carbon emissions. Decoupling comes from improving energy efficiency and transforming the energy structure from high-carbon energy to low-carbon and zero-carbon energy.

Simplicity is the advantage of Kaya's identity, but the problem lies in the lack of dynamic analysis of changes in carbon emission trends. The starting point of this study is to clarify the inherent dynamic meaning of the Kaya model, so as to conduct a staged analysis of the dynamic changes in carbon emission levels. In order to avoid the description being too cumbersome, we merged the basic variables in the Kaya model into five, namely carbon emissions C, total population P, total output Y, per capita output Y/P, carbon emission intensity CI, and carbon emission growth rate y =population growth rate n+per capita output growth rate m+carbon emission intensity growth rate x, from which three dynamic equations are obtained.

1. The basic characteristic of modern economic growth is the continuous increase in per capita output. In the Isolo model, the economic growth rate m must be higher than the population growth rate n, that is, mn>0;

2. Carbon emission intensity CI=C(1+x)/Y(1+m). When x>m, carbon emission intensity increases;

3. Per capita carbon emissions PC=C(1+x)/P(1+n), when x>n, per capita carbon emissions rise;

After solving equations 1 to 3 simultaneously, we can find that the dynamic conclusion of the Kaya model is that the carbon emission peak process should be represented by three endogenous carbon emission inflection points consistent with the four development stages.

Inflection point 1 is the inflection point of carbon emission intensity, and energy marginal efficiency is stable. The duality of the scale effect of economic growth is the growth of carbon emissions and the accumulation of environmental and ecological pressure. As the carbon intensity CI rises, the carbon emissions per unit of output rise, which is equivalent to the diminishing marginal efficiency of energy as a production factor; when the energy structure remains unchanged, technological improvements make the marginal efficiency of energy shift from diminishing to stable, and the carbon intensity inflection point is ΔCI=0 , CI is a constant, when x=m, the growth of carbon emissions is determined by population and economic growth rates.

Inflection point 2 is the inflection point for per capita carbon emissions, and the impact of economic growth on carbon emissions shifts from scale effect to income effect. Modern economic growth has created higher factor efficiency, the level of carbon emissions per unit output during the production process has declined, and the increase in per capita income has led to higher per capita energy consumption and higher per capita carbon emissions, with x<m>n transformed into m>x>n. When the economic growth rate m is higher than the carbon emission growth rate Per capita carbon emissions PC. In Figure 1, from PC0 to PC1, PC1*P(1+n)>Ct0, the total carbon emissions increase. Per capita carbon emissions PC remains unchanged, reaching the second inflection point when ΔPC=0. Since m>n>x, the increase in per capita income level is decoupled from the growth of per capita carbon emissions. When the population growth rate n>0, total carbon emissions continue to rise.

Inflection point 3 is when total carbon emissions peak. When economic development reaches a higher per capita income level, the growth rate of factor marginal income is higher than the population growth rate, the income effect of carbon emissions disappears, and total carbon emissions peak, forming the third turning point. As an important symbol of economic growth transformation, the continuous improvement of energy efficiency has caused the decline rate of per capita carbon emissions to exceed the population growth rate, that is, PC0/PC1>n.

From this, the dynamic expression of Kaya's identity can be expressed as: within a closed interval, an increase in per capita income level corresponds to a higher level of marginal return of factors. In the four stages of economic development, carbon emission intensity, per capita carbon emissions and carbon emissions are reached in sequence. The three inflection points of total emissions form three inverted U curves that are connected sequentially.

In Figure 1, the S1 stage expresses that modern industrial civilization originated from the extensive use of fossil energy, accelerated industrialization and urbanization, and the rapid expansion of output scale. Economic growth and high carbon dependence occur simultaneously, the ecological environment deteriorates, and carbon emission intensity, per capita carbon emissions, and total carbon emissions are all on the rise. Entering the S2 stage, the economic growth mode switches between the peak of carbon intensity and the peak of per capita carbon emissions. The growth rate of total carbon emissions shifts from slowdown to decline. Industrial structure adjustment and technological innovation gradually constitute a new growth mode. However, due to the The cumulative effect will often lead to sudden deterioration of environmental pollution and ecological environment within a certain period of time. The S3 stage is the transition stage between the peak of per capita carbon emissions and the peak of total carbon emissions. With the advanced industrial structure and energy structure and the wider use of new technologies, the income effect of carbon emissions gradually weakens, and higher per capita income corresponds to the higher per capita income. The growth of carbon emissions is slowing down, but as long as the rate of decline in per capita carbon emissions is lower than the rate of population growth, total carbon emissions will still rise. In the S4 stage, total carbon emissions peak, carbon emissions are decoupled from economic growth, per capita income continues to increase, per capita carbon emissions decline at an accelerated pace, and economic growth and carbon emissions change inversely. The stronger the industrial upgrading capabilities and the faster the technological progress, the more significant the changes in the energy structure caused by the energy revolution will be. The proportion of fossil energy will decrease, electricity will become the main energy source, and renewable energy power generation will become the mainstay of electricity. This stage is not a constraint on economic growth, but a growth process that uses innovation and higher factor efficiency to replace the traditional high reliance on quantitative factor inputs. It is also a response to traditional industrialization and urbanization, over-consumption of natural resources, and over-reliance on fossil energy. Reflection and containment of production and lifestyle.

 Article source: Shenzhen Social Sciences

 For detailed problem solving process, please refer to:

2023 Huawei Cup Mathematical Modeling Question D Question 3 - Carbon Emission Path Optimization (Detailed process of constructing a multi-objective optimization model for energy consumption structure adjustment + model assumptions (reproducible))_Zhixin_ROL's Blog-CSDN Blog

 2023 Huawei Cup Mathematical Modeling Question D - Analysis of the current situation of regional carbon emissions and economy, population, and energy consumption (how to establish indicators and indicator systems 1, detailed modeling process of carbon emission influencing factors)_Zhixin_ROL's Blog- CSDN blog

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