The mathematical treatment for effect of income and urban-rural income gap on indirect carbon emissions from household consumption.

Climate change and income inequality are global problems with a huge impact on the environment, society, and economic development. Many studies have shown a correlation among income, the income gap, and carbon emissions, but the influence mechanism remains unclear of income and the income gap on carbon emissions. Using the input-output method, we introduce residents' consumption tendency to construct a mathematical model to discuss the mechanism of the influence of income and the income gap on indirect carbon emissions from household consumption (ICEH). Data at the national and provincial levels are used to conduct empirical research based on the model. Our model indicates four scenarios in which income and the income gap affect ICEH through residents' consumption tendency. When richer urban residents have a greater consumption tendency, a decrease in the income gap would reduce carbon emissions. The empirical results show that a decrease in the income gap is correlated with an increase in ICEH in China from 2002 to 2012. Therefore, the win-win situation of "increased income and narrowed income gap-reduced carbon emissions" is hard to achieve in China. Policymakers must urgently explore other ways to reduce carbon emissions.