The original C-CAPM encounters a risk-free rate puzzle, making it difficult for the capital and consumer markets to achieve equilibrium. This problem can be addressed by solving this risk-free rate puzzle. In this paper, we propose that a representative consumer in the C-CAPM does not reflect the reality of China's social development. Second, we introduce three kinds of typical consumers, low-, middle- and high-income consumers, to embody the heterogeneity of risk attitudes. From the perspective of the consumer Pareto optimum, we derive the new C-CAPM and risk-free rate equation. Third, we compare the new model with the original C-CAPM and risk-free rate equation and theoretically explain this equation. Using monthly data on social consumption in China from 2011 to 2019, we find that the income gap in China is the underlying reason for this risk-free rate puzzle.