企业对企业市场中最优非线性定价的实证分析
An Empirical Analysis of Optimal Nonlinear Pricing in Business-to-Business Markets
AI总结：
本文提出一种在B2B多维消费者异质性下实证估计最优非线性定价表的方法，并利用含未成交交易的教育服务数据表明二级价格歧视比线性定价至少提升利润8.2%，但仅恢复与一级价格歧视差距的7.1%。
摘要：
在连续选择情境下，消费者不仅决定是否购买产品，还决定购买多少。因此，企业优化的是完整的价格表，而非单一价格点。本文提供了一种在多维消费者异质性下实证估计最优价格表的方法，重点关注B2B应用。我们将该方法应用于一家教育服务公司的新数据，该数据不仅包含已成交交易的购买量信息，还包含最终未成交的潜在交易信息。我们表明，这些数据结合识别假设，有助于推断价格敏感度如何随“客户规模”变化。利用我们估计的模型，我们表明最优二级价格歧视（即最优非线性收费表）相较于线性定价至少将企业利润提高了8.2%。尽管如此，该二级价格歧视方案仅恢复了线性定价盈利能力与不可行的一级价格歧视之间差距的7.1%。我们还进行了若干进一步的模拟分析：（i）实证量化激励相容约束对最优定价和利润的影响程度；（ii）比较需求侧因素与成本侧因素在塑造最优价格表中的作用；（iii）研究固定费用对最优合同和盈利能力的影响。
英文摘要：
In continuous-choice settings, consumers decide not only on whether to purchase a product, but also on how much to purchase. Thus, firms optimize a full price schedule rather than a single price point. This paper provides a methodology to empirically estimate the optimal schedule under multi-dimensional consumer heterogeneity with a focus on B2B applications. We apply our method to novel data from an educational-services firm that contains purchase-size information not only for deals that materialized, but also for potential deals that eventually failed. We show that this data, combined with identifying assumptions, helps infer how price sensitivity varies with "customer size". Using our estimated model, we show that the optimal second-degree price discrimination (i.e., optimal nonlinear tariff) improves the firm's profit upon linear pricing by at least 8.2%. That said, this second-degree price discrimination scheme only recovers 7.1% of the gap between the profitability of linear pricing and that of infeasible first degree price discrimination. We also conduct several further simulation analyses (i) empirically quantifying the magnitude by which incentive-compatibility constraints impact the optimal pricing and profits, (ii) comparing the role of demand- v.s. cost-side factors in shaping the optimal price schedule, and (iii) studying the implications of fixed fees for the optimal contract and profitability.
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