# The total CO emissions can

The total CO2 emissions can be calculated by multiplyingC¯ by X:equation(9)C=C¯X=C¯(I−Ad)−1Yd=BYdwhere C is the total CO2 emissions of the economy; B=C¯(I−Ad)−1 andB = (bij) are the direct and indirect CO2 emission intensity matrices to produce the per-unit final demand, respectively; and bij is the total CO2 emissions required from sector j to i to produce the per unit output in sector j.

3.2. Linkage analysis of CO2 emissions by HEM

For simplicity, we assume that the economy is divided into two blocks, namely, Bs and B-s. Bs represents a block of sectors with similar characteristics (sectors with similar CGP 3466B intensity or industries with similar energy consumption structure) or a single sector, and B-s represents the remaining blocks. The economy B can be described as follows:equation(10)B=[Bs,sBs,−sB−s,sB−s,−s]

The total CO2 emissions of the economy C can be described as:equation(11)[CsC−s]=[C¯s00C¯−s][XsX−s]=[C¯s00C¯−s]([As,sAs,−sA−s,sA−s,−s][XsX−s]+[YsY−s])=[C¯s00C¯−s][Δs,sΔs,−sΔ−s,sΔ−s,−s][YsY−s]whereC=[CsC−s] is sexual reproduction the vector of the total CO2 emissions, X=[XsX−s] is the vector of the total output, Y=[YsY−s] is the vector of the final demands, A=[As,sAs,−sA−s,sA−s,−s] is the matrix of the direct consumption coefficients, and (I−A)−1=[Δs,sΔs,−sΔ−s,sΔ−s,−s] is the Leontief inverse matrix.