It is assumed that the government has imposed a CET on DF to reduce emissions. Farms are catergorized into scattered mode, small-scale, medium-scale, and large-scale farms based on cow inventories.

Currently, there is a lack of consensus within the academic community regarding the most appropriate method for classifying high-carbon dairy farming (HCDF) and low-carbon dairy farming (LCDF) systems. However, scholars believe that the carbon footprint of dairy cows is positively correlated with milk yield (Huang, 2015). Furthermore, it has been demonstrated that, under a certain level of technology, an increase in farming scale is positively correlated with carbon emissions per cow (Shi et al., 2019). In summary, the mean carbon emissions of dairy cows from low to high are distributed across scattered mode farms, small-scale farms, medium-scale farms, and large-scale farms. This finding takes into account the “diseconomies of scale” phenomenon caused by an overly large farming scale (Liang and Wang, 2012; Hua, 2012), the trend toward appropriate large-scale farming, and the high pollution and emission reduction pressures of large-scale dairy farming. Given the prevailing circumstances in China, including the policy directives about large-scale farming and the withdrawal of scattered mode farms from the market, large-scale farming is designated as high-carbon dairy farming (HCDF). Conversely, scattered mode, small-scale farms, and medium-scale farms are categorized as low-carbon dairy farming (LCDF). The government levies CET according to emissions and only subsidizes LCDF.

Generally, a typical dairy farm consists of 70% adult cows, 10% young cows, and 20% heifer calves. The study regards 350 kg(w_nc) as the average weight of non-milking cows. There are ~80% and 60% milking cows in LCDF and HCDF, respectively. Previous studies have shown that the milk carbon footprint of cows is 1.19 ± 0.40 kgCO2-eq·kg-1. We assume it to be 0.79 kgCO2-eq·kg-1 and 1.59 kgCO2-eq·kg-1 in LCDF and HCDF, respectively. Beef cattle are regarded as non-milking cows, with a coefficient of 10.16 kgCO2-eq·kg-1 (Huang, 2015). The CEs of milking and non-milking cows are denoted as E_c and E_Nc, respectively. The emission coefficient (e) is calculated as

Therefore, the CE coefficient of LCDF(e₁) and HCDF(e₂) is 0.92 kgCO2-eq·kg-1 and 1.869 kgCO2-eq·kg-1, respectively.

The CET is a type of carbon price representing the minimum price that energy users pay for carbon emissions. An analysis of the implementation of CET levies in various countries reveals that, in the last century, the initial CET in some countries was less than CNY ¥10/ton. In the current century, the range of levies has varied from CNY ¥30/ton to CNY ¥1,060/ton. Drawing on the experience of formulating CET policies and practical operations for dairy farming in foreign countries, it is recommended that the CET rate for dairy farming should be set at a minimum of CNY ¥30/ton to achieve a significant emission reduction effect. In this study, a five-tier progressive tax structure is proposed, with rates ranging from CNY ¥30/ton to CNY ¥150/ton. This structure is complemented by four tax rebate rates (25%, 50%, 75%, and 100%), which are designed to provide financial incentives for low-carbon dairy farming practices.

To evaluate the effects of tax and subsidy in DF, there are two steps. First, we obtain the equilibrium price and yield in the market according to the econometric model. Second, the CET and subsidy are introduced into DF to evaluate their effects on the yield, milk price, and emissions in both HCDF and LCDF.

We assume that cow inventory is fixed and that CET and subsidies are applied to cow yields. There are n₁ and n₂ herds in LCDF and HCDF, respectively. Initially, yield per cow is q₀ for all farms, q₁ for LCDF, and q₂ for HCDF.

The total yield is as follows:

When computing abatement of CET and subsidy, we regard the CO_2−eq produced by cows as an indicator to evaluate CEs. Carbon footprint coefficients of milk and meat are used to calculate emissions of milking and non-milking cows, which are uniformly converted into emissions of milk per kilogram. Then, we obtain the CE coefficient e₁ and e₂. Therefore, total CE (E) is as follows:

The so-called “golden milk source belt” refers to the temperate grassland between ~40° and 50° north and south latitudes. The grasslands in this region are surrounded by a temperate climate all year round and are internationally recognized as a good dairy breeding zone. Heilongjiang Province, located in this category, is also the world-recognized black soil belt and the golden corn planting belt. Compared to the golden milk source belt of the Netherlands, New Zealand, and other countries, Heilongjiang Province of China does not have absolute advantages in the number of dairy cows and unit yield. If carbon tax and subsidy policies can achieve the double effect of emission reduction and economic growth in this region, it will have significant promotion value in the global golden milk source belt and even the global dairy farming industry.

By 2022, Heilongjiang will have 1.1 million dairy cows and 5.01 million tons of raw milk. The number of dairy cattle and milk production are among the top in China. According to the Statistical Yearbook of Heilongjiang Province, there are ~1.02 and 0.34 million cows in LCDF and HCDF on average. According to previous dairy surveys in this area, the proportions of milking cows in the two types of farms are 80% and 65%. Therefore, there are ~82,000 herds (n₁) and 220,000 herds (n₂) of milking cows, respectively.

Without considering the import of dairy products, this study collects data from the China Dairy Industry Yearbook, China Statistical Yearbook, and China Dairy Industry Statistical Data. These data include the per capita consumption of dairy products in urban and rural areas of the region in the past 10 years, the urban and rural population, the total output and purchase price of raw milk, the costs of dairy cow farming at various scales, and the output of main products (per cow). Based on these data, the demand function and cost function of raw milk are constructed (shown in Table 1). The function fitting yields a satisfactory outcome, with the capacity to reflect the overall characteristics of the data, thus facilitating model analysis.

After the implementation of the carbon tax, the changes in CE, output, and economic growth rate of HCDF and LCDF are illustrated in Figures 1, 2.

First, it is evident that the imposition of a CET leads to changes in the market shares of LCDF and HCDF. Specifically, the market share of LCDF will increase, while that of HCDF will decline (see Figure 1). When the tax rates are set at CNY¥ 30/ton and CNY¥ 150/ton, the market share of LCDF increases by 0.08% and 0.42%, respectively, while the market share of HCDF decreases by 0.15% and 0.78%, respectively. It is evident that, as the tax rate increases, the rate of withdrawl from the market for HCDF is greater than that of LCDF. This finding suggests that the implementation of a CET may facilitate the low-carbon transformation of dairy farming.

Second, an analysis of the data reveals a decline in average milk yield per dairy cow in both the HCDF and LCDF systems as the tax rate increases. When the tax rate ranges from CNY¥ 30/ton to CNY¥ 150/ton, the change rates of milk yield per cow in LCDF and HCDF are (−0.35%, −1.75%) and (−0.58%, −2.93%), respectively. HCDF exhibits a heightened sensitivity to alterations in the tax rate, resulting in a more pronounced decline in milk yield and a more substantial rate of emission reduction when compared to LCDF. This finding suggests that the CET exerts a more pronounced inhibitory effect on HCDF.

Third, the CET can effectively reduce the industry's carbon emissions. However, it is important to note that this finding will result in a reduction in raw milk production and economic growth rate (Figure 2). This potential outcome could be considered a “double dividend”. When the tax rate is set at CNY¥ 30–150/ton, the growth rate of industrial carbon emissions is reduced by −0.459%, while the growth rate of raw milk production is decreased by −0.432%. Concurrently, the economic growth rate is diminished by −0.31%, resulting in a net economic effect that is −1.54% lower. For a constant tax rate, the magnitude of the carbon reduction is greater than the magnitude of the production reduction and the magnitude of the economic recession. As the carbon tax increases, production and the economy are less affected. The impact of the tax on the production and the economy is much smaller than the impact of the carbon reduction, suggesting that an appropriate carbon tax has the potential to deliver a “double dividend”. However, a reduction in raw milk production could potentially lead to a disparity between supply and demand in the market. Therefore, a binding carbon tax could be employed in conjunction with incentive-based subsidies to leverage a market-based environmental regulatory instrument and achieve the dual objectives of reducing carbon emissions from industry, promoting low-carbon agriculture, and stabilizing the supply of raw milk.

When a unified CET is levied and subsidies are provided in the form of different CET rebate ratios, the growth rate of yield, CE, and economy is shown in Figure 3. There are five tax rates and four rebate ratios, as mentioned before.

First, CE reductions increase across all tax rebate scenarios, and the share of tax rebates is inversely proportional to CE reductions at the same tax rate. This finding suggests that CE reductions can still be achieved with a combination of carbon tax and subsidies, but the amount of emission reductions from a tax rebate is lower compared to a carbon tax alone. With a fixed tax rebate rate, CE increases as the tax rate increases.

Second, at the same tax rate, production and economic activity increase with higher rebate rates. If all carbon tax revenues are used to subsidize LCDF, a “double dividend” is achieved in terms of CE reductions from dairy farming. With a fixed tax rebate, CE increases with it, but the yield and economic changes are uncertain. When the rebate rate is 25%, 50%, and 75%, compared to the carbon tax alone, the yield and economic growth rate increase significantly, but they remain negative. When the rebate rate is 100%, the yield and economic growth rate are positive, indicating that the subsidy's role in promoting yield and economic growth is greater than the carbon tax's inhibiting role. We also find the tax rebate ratio boundary is 92%. When it is higher than it, the promoting effect of subsidy on yield is greater than inhibiting effect.

Third, subsidies increase LCDF yields and are positively correlated with tax rates. In other words, as the tax increase, the amount rebated to LCDF is higher, which promotes a significant increase in yields. For example, in the case of the full tax rebate scenario, compared to the carbon tax alone, yields for LCDF turn from negative to positive, and yields for HCDF decrease even more (Figure 4), with yields increasing by 0.6 to 3.4% for LCDF and decreasing by 0.047 to 0.24% for HCDF. At the same time, market share increased by 0.34–1.73% for LCDF and decreased by 0.64–3.21% for HCDF. This finding suggests that carbon tax and subsidies together can significantly promote LCDF and discourage HCDF, both of which have a stronger effect in discouraging HCDF than the carbon tax alone.

In conclusion, the carbon tax exerts a substantial inhibitory influence on CE, production, and the economy. Although the subsidy does serve to attenuate the abatement capacity of the carbon tax to a certain extent, it concomitantly promotes the production of raw milk and the economic degree of improvement while concomitantly promoting the synergistic development of carbon abatement, the supply of raw milk, and economic growth. When considering the impact of low-carbon subsidies on fiscal pressure and total social welfare, it is evident that carbon tax revenues are generally highlighted to promote the development of LCDF in the form of tax rebates.

Many scholars associate CE with economic development. Li (2012); Li et al. (2013) and Chen and Shang (2014), found that economic factors are the main reason for CE in China's animal husbandry. If prices of agricultural products are stable, changes in yield can reflect economic trends. Therefore, we study the decoupling relationship between the yield and CE with the equation below. Let e(E, Q) represent the decoupling elasticity index (shown in Table 2).

Weak decoupling, growth connection, and expansion negative decoupling all represent both an increase in yield and CE. Weak negative decoupling, strong negative decoupling, recessive decoupling, and recessive connection result in increased yield growth. It is only through the implementation of strong decoupling strategies that the overall yield can be enhanced while concurrently reducing CE. We will discuss different decoupling intervals in detail.

Considering ε′/θ should be non-negative, decoupling results of the actual model can be obtained in Figure 5.

When 1.311 < ε′/θ < 2.045, strong decoupling occurs, with yield growth being most closely aligned with CE. This optimal range represents the condition for implementing the CET-subsidy policy. When ε′/θ = 2.045, a strong decoupling persists, but with the least negative impact. If the subsidies are higher than taxes with the goal of maximizing yield while reducing emissions, the government could also choose this point. When ε′/θ = 1.311, emission reductions are more pronounced. If the subsidies are not higher than taxes with the goal of maximal abatement and stable yield, the government could choose this point.

When ε′/θ equals 1.311, 1.550, and 2.045 with a tax rate ranging from CNY¥ 30/ton to CNY¥ 150/ton, the economic growth rates are shown in Figure 6. For the same tax rate, a small ratio represents a lower subsidy and a higher economic growth rate. When ε′/θ equals 2.045, the economy decreases. When ε′/θ equals 1.311 and 1.55, the economy increases with an increase in tax.

In summary, strong decoupling represents the optimal harmonization between dairy farming production growth and CE, making this interval the preferred range for the government to implement carbon tax and subsidy regulation. Among them, if the government carries out subsidies only to the limit of carbon tax revenue, the tax-subsidy ratio can be chosen, and the double dividend effect of carbon tax can also be realized. The carbon tax and subsidy regulation have the least negative impact on output and the most obvious emission reduction effect under the strong decoupling effect. However, in the latter case, government expenditure on subsidies is greater than the revenue from carbon tax. Therefore, under carbon tax and subsidy regulation, if the government's objective is raw milk production growth while achieving optimal emission reduction—without allowing fiscal expenditure to exceed tax revenue—it may choose to formulate a policy accordingly. Alternatively, if the government allows subsidy expenditure for CE reduction to be greater than carbon tax revenue and aims to balance emission reduction with maximizing raw milk production, it may formulate a policy accordingly.

In a competitive market, the study introduces the CET and subsidy as exogenous variables in the cost-benefit analysis of DF and constructs theoretical models in both HCDF and LCDF. With five CET rates and four rebate ratios, it analyzes the responses of carbon abatement, milk yield, and economic growth in Heilongjiang Province, located in the golden milk source belt. We have made the following conclusions:

First, in the scenario of CET only, five tax rates ranging from CNY¥ 30/ton to CNY¥ 150/ton lead to abatement of 0.067%−0.335%, a yield decrease of 0.06%−0.28%, and an economic growth of 0.16%−0.79%. This finding validates the “double dividend” effect of CET on both abatement and economic growth. It effectively reduces the high-carbon share and increases the low-carbon share in the market. A higher tax rate results in more abatement but lower milk yield, which may result in insufficient supply. Therefore, the introduction of a subsidy policy should also be considered.

Second, in the scenario of tax-subsidy policy, if the subsidy works in the form of a tax rebate, four ratios from 25% to 100% will weaken the abatement and promote an increase in milk yield. With the same tax rate, the growth rate of yield increases with the tax rebate ratio, but the abatement reduces. When the tax rebate ratio is 92%, the milk yield is equal to the initial level. If all tax revenue is used for subsidies, the ratio of subsidy to tax is ε′/θ = 1.55, where yield and abatement increase by 0.01–0.052% and 0.02–0.11%, respectively. The market share of LCDF increases and high carbon decreases, indicating that the tax-subsidy policy is more effective in promoting low-carbon development than the tax-only policy.

Finally, decoupling analysis shows that, when 1.311 < ε′/θ < 2.045, strong decoupling and yield growth is most coordinated with CE. When ε′/θ =1.311, there is maximal abatement with less yield growth. When ε′/θ =2.045, there is maximal yield growth with less abatement. If the subsidy is less than tax revenue, the optimal ratio ranges from 1.311 to 1.550, where the government could determine the specific point according to policy targets.

First, a unified framework and standards for CET and subsidies in dairy farming must be formulated. International organizations should assume the leading role in formulating a unified framework and standards for global livestock CET and subsidies. This framework should include clarifying the scope of CE collection, the principles of tax rate setting, and the objects and methods of subsidies for dairy farming. The aim of this study should be to ensure that all countries have a unified reference standard during implementation and to avoid “carbon leakage” and trade unfairness caused by differences in rules. Recognizing the heterogeneity in economic levels, energy structures, and emission reduction capabilities across countries along the golden milk source belt, countries are permitted to devise specific CE and subsidy policies that align with their respective national contexts, operating within the overarching unified framework. This approach will establish an incentive mechanism that promotes the harmonized advancement of dairy production, CE reduction, and economic growth, thereby fully leveraging the “double dividend” potential inherent in CET.

Second, an international coordination mechanism for CET and subsidies in dairy farming should be established, along with an international CET coordination agency for the dairy farming industry. This mechanism would address potential trade disputes and policy conflicts over dairy products caused by CET and subsidies. Regular meetings should be held to facilitate the exchange of experiences regarding CET subsidies among countries, using the golden milk source belt as an example. In addition, it is recommended that all countries establish a CET information-sharing platform to exchange CE data, CET collection status, subsidy distribution information, and other relevant information. At the same time, there is a necessity to strengthen the supervision of CET collection and subsidy utilization to prevent enterprises from gaining improper benefits through the false reporting of CE or the misuse of subsidies. This will help ensure the fairness and effectiveness of the policies.

Third, the revenues from a CET should be allocated to the research and innovation of low-carbon technologies in dairy farming, the promotion of energy transformation and industrial upgrading, and the support of developing countries and small-scale farming entities. The abatement from dairy farming can be achieved through the implementation of strategies such as the optimization of feed formulas, the improvement of manure management, and the enhancement of energy efficiency. The establishment of special scientific research funds is recommended, to provide subsidies and tax incentives for the research and development of low-carbon dairy farming technologies. Enterprises and scientific research institutions should be encouraged to conduct research, development, and promotion of low-carbon technologies. Concurrently, the funds can be utilized to assist countries with less advanced dairy farming in the development of low-carbon infrastructure and the enhancement of their capacity to respond to climate change. It is also crucial to direct attention toward the vulnerable groups in the dairy farming sector, who are particularly affected by CET. To mitigate the adverse effects of CET, tax exemptions should be considered.

The sample size is relatively small, which may limit the generalization of the results. Future studies with larger sample sizes are needed to further validate our findings. Besides, we have not considered the cost of low-carbon technology and CE reduction by farms, which will be improved in the future.