Research on the Dynamic Analysis Application of Calculus in Product Pricing Strategies an Empirical Study Based on Yiwu Small Commodities Market

To address the dilemma that traditional static pricing fails to adapt to the dynamic market changes, this study constructs a product dynamic pricing analysis system based on calculus theory. By employing core tools including derivatives, differential equations, and integrals, it quantifies the correlation mechanism between dynamic variables (such as cost fluctuations, demand elasticity, and competitive dynamics) and product pricing. Taking 18 typical products across 6 categories in the Yiwu Small Commodities Market as the research objects, combined with the market's historical transaction data from 2021 to 2024, this study establishes three models: a marginal cost pricing model, a dynamic demand elasticity adjustment model, and an integral-based product lifecycle pricing model. The model accuracy is verified using three metrics: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). The results indicate that the prediction accuracy of the calculus-based dynamic pricing model is significantly superior to that of the traditional static pricing model, with an average MAPE of only 6.8%, a reduction of 13.2 percentage points compared with static pricing. After the application of this model, the average gross profit margin of the 18 products increased by 8.3%, among which products with high demand elasticity (e.g., disposable toothbrushes and non-woven shopping bags) achieved a profit growth rate of over 18%. This study confirms that calculus provides a precise quantitative analysis tool for dynamic pricing, and its core value lies in transforming pricing from an "experience-based judgment" to a "data-driven" approach. It offers theoretical support and practical paradigms for Yiwu small commodity enterprises to formulate flexible and efficient pricing strategies.