Nonlinear pricing in multidimensional context: An empirical analysis of energy consumption
用中国家庭用电面板数据，估计了递增阶梯电价和分时电价下的消费者偏好，发现价格每涨1%用电量降0.7%，但多维定价的优化空间有限。
Modern business practices frequently employ a blend of pricing strategies to segment markets effectively. As a result, consumers may encounter pricing schedules that are nonlinear and multidimensional. This paper presents a structural approach for estimating multidimensional nonlinear pricing models involving multiple decision variables in an energy market. Using a unique, rich panel dataset of Chinese household electricity consumption, we structurally estimate consumer preferences under the influence of an Increasing Block Price (IBP) and a Time-of-Use (ToU) system. Our structural approach allows us to distinguish and evaluate household-level price elasticities of demand, presenting a novel explanation for consumers' feedback on marginal price changes. Through model-based simulations, we demonstrate that a 1% increase in price corresponds to a 0.7% reduction in total electricity demand. However, our analysis indicates that practical opportunities for optimization within multi-dimensional pricing systems are limited. Our findings offer distinct insights into the complex interplay between intricate pricing structures and energy consumption behavior, thereby providing valuable guidance for policymakers and regulators.