The production of enterprises can be roughly divided into the input stage of production factors, the production stage of intermediate products and the output stage of finished products. The input stage of production factors includes the input of clean production equipment to reduce carbon emissions from the source; if carbon is discharged during the intermediate product production stage and the finished product output stage, it can be reduced by end-of-pipe treatment equipment. Based on these carbon emission control links, carbon emission reduction technologies can be divided into two categories: cleaner production technology in the production factor input stage and end-of-pipe technology in the latter two production stages.
Carbon abatement cost is the main constraint for each enterprise to choose cleaner production technology or end-of-pipe technology in the low-carbon city pilot policy and smart city pilot policy. The main goal of the enterprise is profit maximization, let P be the commodity price and A(KA) be the enterprise production technology. Under environmental regulation, enterprises usually adopt the following two ways to improve their emission reduction performance: one is the "innovation compensation effect", i.e., realizing the reduction of carbon emissions by upgrading the level of cleantech innovation of enterprises; the other is the "end-of-pipe treatment effect", i.e., the reduction of carbon emissions through the existing pollution control technology of enterprises. Therefore, this technology includes cleaner production technology (TI) and end-of-pipe technology (TE). The production technology A depends on the enterprise's investment in technological progress (KA), and f(KP) is the maximum output under certain technological conditions, which depends on the amount of capital input by the enterprise (KP). Referring to the model constructed by Färe et al. (2007) based on Hicks neutral technology, the revenue function of the enterprise is shown in Eq. (1).
$$\pi =PA({K_A})f({K_P})$$
1
The output function of the enterprise is \(F=A({K_A})f({K_P})\). Under the condition of perfectly competitive market, based on the income function and output function, the choice mechanism of carbon emission reduction technology under different policies can be analyzed. The enterprise carbon emission C (F, I, E) depends on the enterprise output (F), cleaner production technology expenditure (I) and end-of-pipe technology expenditure (E). It can be obtained that, \(C^{\prime}(F, \cdot , \cdot )>0\), \(C^{\prime}( \cdot ,I, \cdot )<0\), \(C^{\prime}( \cdot , \cdot ,E)<0\), i.e., the larger the output, the more carbon emissions; the more investment in cleaner production technology or end-of-pipe technology, the less carbon emissions. The carbon emission reduction technology level of the enterprise T (I, E) depends on the level of cleaner production technology (TI) and the level of end-of-pipe technology (TE). From this, \(T^{\prime}(I, \cdot )>0\) and \(T^{\prime}( \cdot ,E)>0\).
The production set of the enterprise is \(F=A({K_A})f({K_P})\), and the production set of the end-of-production carbon emission disposal technology is \({F_E}=\rho F\) (\(0<\rho <1\)).\(\rho\) reflects the proportion of expenditure on end-of-production carbon emission disposal costs (E) of the enterprise to total output, and also reflects the intensity of environmental regulation M. From the above analysis, the enterprise profit maximization is shown in Eq. (2), and the constraints are in Eq. (3).
$$\begin{array}{*{20}{c}} {s.t.}&{C[A({K_A})f({K_P}),\rho ({K_A})f({K_P})]} \end{array}=M$$
3
Eqs. (2) and (3) lead to Eq. (4)
$${{\partial C} \mathord{\left/ {\vphantom {{\partial C} {\partial (I+E)}}} \right. \kern-0pt} {\partial (I+E)}}= - {{\partial C} \mathord{\left/ {\vphantom {{\partial C} {\partial F}}} \right. \kern-0pt} {\partial F}}$$
4
Equation (3) shows that C is the final carbon emission of the enterprise under certain environmental regulation, production technology and carbon reduction technology, so the environmental regulation variable can be replaced by the carbon emission of the enterprise. Eq. (4) shows that under a certain environmental regulation, the profit maximization of the enterprise is conditional on the increase of marginal carbon emissions from production being equal to the decrease of marginal carbon emissions from TI and TE
Equation (5) can be obtained from the enterprise's technology function \(T^{\prime}(A, \cdot )>0\). Both cleaner production technology and end-of-pipe technology progress can promote the total level of enterprise technology and reduce carbon emissions.
Since carbon emission depends on F, TI and TE, the degree of influence between I and C under the constraint of environmental regulation is shown in Eq. (6). Eq. (6) shows that the carbon emission reduction effect of TI depends on F and E.
$$\frac{{\partial C}}{{\partial I}}=\frac{{\partial C}}{{\partial F}} \cdot f+\frac{{\partial C}}{{\partial E}} \cdot \rho f$$
6
Equation (7) can be obtained from Eq. (6), Eq. (4) and the technology function.
$$\frac{{\partial T}}{{\partial A}}=(\frac{{\partial {T_I}}}{{\partial C}}+\frac{{\partial {T_E}}}{{\partial C}}) \cdot [\frac{{\partial C}}{{\partial F}}(1 - 2\rho )]f>0$$
7
The goal of low carbon cities is to minimize carbon emissions. According to Eq. (7), with the strengthening of environmental regulations, the enterprises invest in carbon emission reduction End-of-pipe technology increases, and carbon emissions decrease, i.e., \({{\partial C} \mathord{\left/ {\vphantom {{\partial C} {\partial \rho }}} \right. \kern-0pt} {\partial \rho }}<0\). When \(\rho \in (0,0.5)\), because \([\frac{{\partial C}}{{\partial F}}(1 - 2\rho )]f>0\), so \(\frac{{\partial {T_I}}}{{\partial C}}+\frac{{\partial {T_E}}}{{\partial C}}>0\). Because TE is a decreasing function of carbon emissions, so \({{\partial {T_I}} \mathord{\left/ {\vphantom {{\partial {T_I}} {\partial C}}} \right. \kern-0pt} {\partial C}}>0\), i.e., TI is an increasing function of carbon emissions.
This suggests that the technology is effective in reducing carbon emissions when the ratio of TE inputs to outputs is high \(\rho \in (0,0.5)\), i.e. \({{\partial {T_E}} \mathord{\left/ {\vphantom {{\partial {T_E}} {\partial C}}} \right. \kern-0pt} {\partial C}}<0\), as the inputs to the technology increase, carbon emissions decrease. At the same time, i.e. \({{\partial {T_I}} \mathord{\left/ {\vphantom {{\partial {T_I}} {\partial C}}} \right. \kern-0pt} {\partial C}}>0\), the decrease in carbon emissions correspondingly reduces the demand for cleaner production technologies. The reason for this result is that, compared with the two types of technology, the replacement cost of TI is higher, requiring enterprises to replace most of the production equipment, change the production process, and even the structure of the labor force has to be changed accordingly, which may not only lead to a significant increase in the enterprise's fixed costs and the number of layoffs, but also may result in a short period of time unable to recruit a labor force that matches the new technology, so that the enterprise falls into a production stoppage. On the contrary, the application of TE only requires enterprises to pay for carbon reduction equipment fees and related equipment maintenance, repair, and operation costs. This cost is significantly lower compared to the cost of TI rollout. Although TI can reduce carbon emissions from the root cause, the application cost is also lower, and at the same time, it is also the direction of the progress of carbon reduction technology. However, based on the profit maximization objective, due to the high replacement cost of TI, enterprises preferred the lower cost TE when they could meet the requirements of environmental regulation on carbon emissions. However, as TI continued to accumulate, improve, and mature, the replacement cost decreased (Santhakumar et al., 2022). At the same time, environmental regulations continue to increase, and the use of TE increases, and when the proportion of its expenditure exceeds 0.5, it leads to a significant increase in the input cost of end-of-pipe technology, and enterprises begin to apply TI. when \(\rho \in (0.5,1)\), because \([\frac{{\partial C}}{{\partial F}}(1 - 2\rho )]f<0\), so \(\frac{{\partial {T_I}}}{{\partial C}}+\frac{{\partial {T_E}}}{{\partial C}}<0\).
Because \({{\partial {T_E}} \mathord{\left/ {\vphantom {{\partial {T_E}} {\partial C}}} \right. \kern-0pt} {\partial C}}<0\), so \({{0<\partial {T_I}} \mathord{\left/ {\vphantom {{0<\partial {T_I}} {\partial C}}} \right. \kern-0pt} {\partial C}}<{{\partial {T_E}} \mathord{\left/ {\vphantom {{\partial {T_E}} {\partial C}}} \right. \kern-0pt} {\partial C}}\) or \({{\partial {T_I}} \mathord{\left/ {\vphantom {{\partial {T_I}} {\partial C}}} \right. \kern-0pt} {\partial C}}<0\). Although the increase of TE input can still effectively reduce the number of pollutants, i.e. \({{\partial {T_E}} \mathord{\left/ {\vphantom {{\partial {T_E}} {\partial C}}} \right. \kern-0pt} {\partial C}}<0\), at this time\(\rho \in (0.5,1)\), i.e., the ratio of TE expenditure to output has exceeded half. This means that the focus of the company has shifted to reducing carbon emissions, and most of the revenue is taken up by the cost of carbon reduction treatment. Therefore, the selection of carbon reduction technologies is based on \(\rho \in (0,0.5)\)and \(\rho \in (0.5,1)\) has certain intuitive experience and practical significance. Although there are differences in the break-even point of different types of enterprises, for most enterprises, the cost of carbon emission reduction alone consumes half of the enterprise's production income, which is too high a cost for enterprises aiming at profit maximization to continue to use TE for production activities. In view of this, when \(\rho \in (0.5,1)\), it is time to reduce input of TE and increase input of TI, so as to know \({{\partial {T_I}} \mathord{\left/ {\vphantom {{\partial {T_I}} {\partial C}}} \right. \kern-0pt} {\partial C}}<0\), instead of \({{0<\partial {T_I}} \mathord{\left/ {\vphantom {{0<\partial {T_I}} {\partial C}}} \right. \kern-0pt} {\partial C}}<{{\partial {T_E}} \mathord{\left/ {\vphantom {{\partial {T_E}} {\partial C}}} \right. \kern-0pt} {\partial C}}\). At this point, TI has become more mature, with lower replacement costs than at the beginning of the technology's existence and is able to replace TE.
The goal of the smart city pilot policy is to stimulate disruptive technological innovation in various fields in the pilot city. Although technological innovation to reduce carbon emissions is also one of the goals of this pilot policy, carbon emission reduction is not the only goal of the smart city pilot policy compared to the low-carbon city pilot policy, which may ease strains on reduce carbon emissions in the pilot cities of this policy. Even the pilot policy of smart cities may also lead to an increase in carbon emissions in pilot cities (Acemoglu et al., 2012). This is because on the one hand, technological innovation brings about an increase in energy efficiency, and on the other hand, there is a lack of strict constraints similar to the pilot policy of low-carbon cities, so carbon emissions may increase instead (Chen et al., 2020). Eq. (5) also shows that this phenomenon exists. Smart cities are likely to decline due to the lower pressure of carbon emission reduction, so either \(\rho \in (0,0.5)\) or \(\rho \in (0.5,1)\),\(\frac{{\partial T}}{{\partial C}} \cdot \frac{{\partial C}}{{\partial E}} \cdot \rho f\) all likely to fall, i.e. the input of E is smaller, so the effect of TE on carbon emission reduction may not be significant. Accordingly, in Eq. (6), because \(\frac{{\partial C}}{{\partial E}}\) is smaller, \(\frac{{\partial C}}{{\partial F}}\) is determined by \(\frac{{\partial C}}{{\partial I}}\). When \(\rho \in (0,0.5)\), because \([\frac{{\partial C}}{{\partial F}}(1 - 2\rho )]f>0\), so \({{\partial {T_E}} \mathord{\left/ {\vphantom {{\partial {T_E}} {\partial C}}} \right. \kern-0pt} {\partial C}}{\text{=}}0\)and \({{\partial {T_I}} \mathord{\left/ {\vphantom {{\partial {T_I}} {\partial C}}} \right. \kern-0pt} {\partial C}}>0\), this implies that carbon emissions increase as production increases. Although this encourages TI improvement, i.e., it may be that TI does not play a role in carbon reduction due to excessively high technology replacement costs and loose carbon reduction constraints; when \(\rho \in (0,0.5)\), in Eq. (7) \([\frac{{\partial C}}{{\partial F}}(1 - 2\rho )]f<0\), so \({{\partial {T_E}} \mathord{\left/ {\vphantom {{\partial {T_E}} {\partial C}}} \right. \kern-0pt} {\partial C}}{\text{=}}0\)and \({{\partial {T_I}} \mathord{\left/ {\vphantom {{\partial {T_I}} {\partial C}}} \right. \kern-0pt} {\partial C}}<0\), which implies that with the increase in carbon emissions, it encourages TI to play a role in carbon reduction. Therefore, for smart cities, when \(\rho \in (0,0.5)\), TE and TI do not have a significant effect on carbon emission reduction; when \(\rho \in (0.5,1)\), TE does not have a significant effect on carbon emission reduction, but TI has a significant effect.
The dual-pilot policy cities have both carbon reduction and technological innovation objectives. Because of the purpose of carbon reduction, when \(\rho \in (0,0.5)\), TE can effectively reduce carbon emissions, i.e., \({{\partial C} \mathord{\left/ {\vphantom {{\partial C} {\partial E}}} \right. \kern-0pt} {\partial E}}<0\). According to Eq. (6), \(\frac{{\partial C}}{{\partial F}} \cdot f=\frac{{\partial C}}{{\partial E}} \cdot \rho f - \frac{{\partial C}}{{\partial I}}\) can be obtained. Because the increase in production leads to an increase in carbon emissions, i.e., \(\frac{{\partial C}}{{\partial F}}>0\),so \(\frac{{\partial C}}{{\partial I}}<0\). This means that when \(\rho \in (0,0.5)\), TI has been invested in production and is effective in reducing carbon emissions. When\(\rho \in (0.5,1)\), from the conclusion of the low-carbon city pilot policy, the input cost of TE is significantly increased, so the main use of TI to reduce carbon emissions. Therefore, for the dual-pilot policy city that implements the low-carbon city pilot policy and the smart city pilot policy, when \(\rho \in (0,0.5)\),both TE and TI have a significant impact on carbon emission reduction, and TE has a greater role in reducing carbon emissions; when \(\rho \in (0.5,1)\), only TI significantly reduces carbon emissions.
In summary, we can summarize the carbon reduction technology selection strategy of the low-carbon city pilot policy and the smart city pilot policy. For enterprises under the low-carbon city pilot policy, since carbon reduction is the main goal, so when \(\rho \in (0,0.5)\),they may choose TE to reduce carbon according to the principle of profit maximization; when \(\rho \in (0.5,1)\), companies can choose TI to reduce carbon emissions. For enterprises under the smart city pilot policy, although they are also subject to the constraints of environmental regulations, innovation is the main goal, when \(\rho \in (0,0.5)\), the replacement cost of TI is high, the enterprise may not have the initiative to use TI to reduce carbon emissions nor the motivation to reduce carbon emissions through TE because it will increase its production cost; when \(\rho \in (0.5,1)\), the carbon emissions of the enterprise have already exceeded the environmental regulation standard, the enterprise will take the initiative to use TI to achieve carbon emission reduction. For enterprises under the dual-pilot policy, there are both strict carbon emission standards and incentives for technological innovation, so when \(\rho \in (0,0.5)\), the enterprise reduces carbon emissions, it uses both TE and TI; however, when \(\rho \in (0.5,1)\), the cost of TE increases, only TI continues to play a role in reducing carbon emissions.