Gradual Transition Mathematical Economics: System Innovation and China's Practice

China, as a nation undergoing gradual transition toward a market economy, presents unique challenges when applying conventional mainstream models with institutional invariance assumptions to analyze its economic growth.Such approaches prove inadequate in capturing the institutional dynamics inherent to progressive transition economies.The endogenous integration and operationalization of institutional factors remains a critical theoretical challenge in economics.This study proposes a methodological framework that: (1) Quantifies the dual allocation ratios of key resources between administrative planning interference and market mechanisms, while evaluating their differential efficiency states across non-competitive and competitive sectors.(2) Analyzes institutional impacts through the real estate prism, particularly land transaction regimes characterized by binary valuation flow rates (0 or 1) under transaction prohibitions versus permissions, and price existence versus non-existence.By defining distortion indices for non- competitive sectors and benchmark indices for competitive sectors, we establish mathematical logic for dual-system transition economies and construct simultaneous equations to compute both institutional residuals in national economic output and growth effects from structural institutional reforms.Empirical analysis through historical data input not only interprets past growth trajectories but also simulates potential growth dividends from future institutional optimization.