Budget Constraints, Price Shocks and Urban Rural Consumption Allocation: Cobb-Douglas Utility Framing for Food, Tobacco, Alcohol and Apparel

There is an obvious income gap between urban and rural residents in China; changes in income levels and commodity prices will jointly affect the distribution of household consumption budget and consumption structure. This paper takes food, tobacco, alcohol, and clothing as the research objects, constructs a Cobb-Douglas two-commodity consumption model based on utility maximization, and uses the statistical data of income and consumption expenditure of urban and rural residents from 2021 to 2025 to calibrate the preference parameters of the model, and sets up three scenarios of benchmark, income increase, and food price rise for analysis. The results show that both urban rural income and target category consumption generally grow. Rural residents witness faster consumption growth yet remain at lower absolute consumption levels. Rural households persistently allocate a larger budget share to food tobacco alcohol, with these two basic goods accounting for a higher proportion of their disposable income. Simulation suggests that income growth expands the consumption budget proportionally and lifts real consumption of both goods without changing budget shares. Given a fixed total budget, rising food tobacco alcohol prices reduce real consumption while leaving clothing consumption unaffected. This paper provides modeling insights for interpreting urban rural consumption disparities.