### The ecological footprint

$$ Ef = N times ef = N times r_{j} times y_{j} times mathop sum limits_{i}^{n} aa_{i} = N times r_{j} times y_{j} times mathop sum limits_{i}^{n} left( {frac{{c_{i} }}{{EP_{i} }}} right) $$

(1)

In eq. (1), *Yes* is the province’s Ecological Footprint before trade adjustment (hm^{2})^{29}, *NOT* is the total population of the province, *yes* represents the per capita Ecological Footprint of the province (hm^{2}), *I* is the type of consumption in accounting, *yy*_{I} is the actual area of ecological production land per capita occupied by consumption in the article *I* (hm^{2}), *vs*_{I} is the annual consumption per capita in employment *I*, *PE*_{I} is the annual national average production of consumer goods of item *I* (kg/hm^{2}), *there*_{I} is the yield adjustment factor, *r*_{I} is the land cover equilibrium factor, *I* is the type of ecological productive land, among them, j=1, 2, 3, 4, 5, 6 represent fossil energy land, cropland, grassland, forest land, water area and completed land respectively .

### Ecological capacity

The measurement of ecological capacity by the ecological footprint refers to the principle of not compromising the productivity and functional integrity of ecological systems. Total area of ecologically productive land that a region can have. That is, the ecological carrying capacity of the region. This article adopts the calculation formula proposed by Xie Hongyu and other researchers to calculate the ecological capacity based on the actual production of ecological products and the ecological service capacity provided by the earth in one year.^{17}.

$$ AC = mathop sum limits_{i}^{n} frac{{P_{i} }}{{overline{{EP_{i} }} }} times r_{j} $$

(2)

In eq. (2), *THAT* is the ecological capacity (hm^{2}), *P*_{I} is the amount of resources produced *I* ecological product in the *I* ecological productive land (kg), (overline{{EP_{{text{i}}} }}) is the national average individual yield (kg/hm^{2}) from *I* type of ecological product in the *I* category of ecological productive land, *r*_{I} is the land cover equilibrium factor, *I* is the type of ecological productive land (*I*= 1, 2, 3, 4, 5, 6).

### Yield adjustment and equalization

Since the productivity of similar ecologically productive land varies from country to country and region to region, the actual area of similar ecologically productive land in various countries and regions cannot be directly compared and must be adjusted by multiplying the area of its ecologically productive land by the factor yield. Since the productivity of each type of land is different, the area of each type of land should be multiplied by its own equivalent factors, then the equivalent area of each type should be added to obtain the value of the footprint and the regional ecological capacity^{36}.

$$ y_{j} = frac{{P_{j} }}{{EP_{j} }} $$

(3)

In eq. (3), *P*_{I} is the production of class j ecologically productive land in the region, *PE*_{I} is the national production of ecologically productive land in the category *I* . In order to accurately reflect the different productive capacities of different types of land use in Guangdong Province, the Guangdong Province balance factor calculated by Liu Moucheng based on primary productivity^{37} is selected (cropped land is 1.36, forest land is 0.68, grassland is 0.57, water area is 0.45, and construction land is 1, 36).

### Trade adjustment

This study refers to the macro-trade adjustment method proposed by Bai Yu et. al. to adjust the ecological footprint of Guangdong Province^{13}. The calculation method is mentioned in the equations. (4–6)

$$ EF = c_{b} times EF_{b} + c_{e} times EF_{e} $$

(4)

In eq. (4), *EF* is the total consumption of the ecological footprint, *vs*_{b} is the trade adjustment coefficient of the biological resources account, *Yes*_{b} is the ecological footprint of the biological resources account, *vs*_{and} is the trade adjustment coefficient of the energy account, *Yes*_{and} is the ecological footprint of the energy account.

$$ c_{b} = frac{EC times H}{{G_{p} + G_{F} }} $$

(5)

$$ c_{e} = left( {frac{{E_{F} }}{E} times frac{EC times H}{{G_{F} }} + frac{{E – E_ {F} }}{E} times frac{C – EC times H}{{G – G_{F} }}} right) times frac{G}{G – A – W} $$

(6)

In the eq. (5) and (6), *THIS* is the Engel coefficient (the proportion of total food expenditure to total personal consumption expenditure), *H* is household consumption expenditure, *g*_{p} is the GDP of primary industry, *g*_{F} is the GDP of the food processing industry, including the agricultural and secondary products processing industry, the food manufacturing industry and the beverage manufacturing industry, *E* is the total energy consumption, *EF* is the energy consumption of the food industry, *VS* is total final consumption, including consumption by residents and consumption by general government, *g* is the gross national product, *A* is the total capital investment, *O* is the total wages of the workers.

### Ecological deficit and ecological surplus

By comparing the ecological footprint occupied by resources, energy consumption and waste disposal of a region or country with the ecological capacity it possesses, there will be an ecological deficit (the ecological footprint is greater than the ecological capacity, which means that the human load in the region exceeds its ecological capacity and shows an unsustainable state) and ecological surplus (the ecological footprint is less than the ecological capacity, which means that the ecological capacity of the area is sufficient to support its human load and is in a durable condition)^{2}.

$$ ED/ES = EF – AC $$

(seven)

In eq. (seven), *OF* is the ecological deficit, *ES* is the ecological surplus.

### Ecological footprint of ¥10,000 GDP

To better reflect the efficiency of local natural resource use in Guangdong Province, this study combines the ecological footprint of ¥10,000 of GDP to conduct a comprehensive analysis of local residents’ consumption. The lower the ecological footprint of ¥10,000 of GDP, the higher the efficiency of resource use, and vice versa.

$$ WEF = frac{Ecological, footprint ,per ,capita}{{GDP, per ,capita}} times $10,000

(8)

In eq. (8), *WEF*is an ecological footprint of ¥10,000 GDP.