慧学（45）：精读博士论文考虑消费者情绪的平台裂变营销（2）

摘要：In this issue, the editor will introduce the platform fission marketing that considers consumer emotions (2) of the doctoral disse

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“慧学（45）：精读博士论文《考虑消费者行为的平台供应链销售策略优化研究》考虑消费者情绪的平台裂变营销（2）”

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"Hui Xue (45): Intensive reading of doctoral dissertation 'Optimization of platform Supply Chain Sales Strategies Based on Consumer Behavior' platform fission marketing that considers consumer emotions (2)"

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本期推文小编将从思维导图、精读内容、知识补充三个方面为大家介绍博士论文《考虑消费者行为的平台供应链销售策略优化研究》考虑消费者情绪的平台裂变营销（2）。

In this issue, the editor will introduce the platform fission marketing that considers consumer emotions (2) of the doctoral dissertation "Optimization of Platform Supply Chain Sales Strategies Based on Consumer Behavior" from three aspects: mind mapping, intensive reading content, and knowledge supplement.

一、思维导图（Mind mapping）

二、精读内容（Intensive reading content）

1、裂变营销程度（Degree of fission marketing）

（1）均衡解和需求比较（Equilibrium solution and demand comparison）

依据定理5.1，在口碑裂变营销情境下，深度裂变的最优努力水平高于适度裂变，同时其总体需求量始终保持在适度裂变之上。虽然深度裂变会导致部分对其反感的消费者流失，但由于投入的裂变努力更大，使得整体需求仍然超过适度裂变，因此深度裂变在推动需求增长方面展现出更明显的优势。

According to Theorem 5.1, in the context of word-of-mouth fission marketing, the optimal effort level for deep fission is higher than that for moderate fission, while its overall demand remains above that of moderate fission. Although deep fission may lead to the loss of some consumers who dislike it, the greater fission effort invested means that overall demand still exceeds that of moderate fission. Therefore, deep fission demonstrates a clear advantage in driving demand growth.

定理5.2表明，在折扣裂变营销中，深度裂变的最优努力水平与补贴水平均高于适度裂变，但其需求受多方面因素共同作用，包括消费者的偏好与厌恶情绪、产品价格、偏好型消费者比例以及裂变成本系数。当厌恶情绪更强时，只有在价格较高且成本较低的情况下，深度裂变需求才会超过适度裂变；而当偏好占优势时，则在偏好型消费者比例较高或中等、价格较高且成本较低时，深度裂变的需求才会更大，否则适度裂变更具竞争力。因此，在折扣裂变营销中，深度裂变并不必然优于适度裂变，其效果取决于市场环境与消费者情绪的匹配。

Theorem 5.2 shows that in discount fission marketing, the optimal effort and subsidy levels for deep fission are higher than those for moderate fission, but its demand is influenced by multiple factors, including consumer preferences and aversions, product price, the proportion of preferred consumers, and the fission cost coefficient. When aversion is stronger, demand for deep fission will exceed that for moderate fission only when prices are high and costs are low. When preferences prevail, demand for deep fission will only be greater when the proportion of preferred consumers is high or moderate, prices are high, and costs are low; otherwise, moderate fission is more competitive. Therefore, in discount fission marketing, deep fission is not necessarily superior to moderate fission; its effectiveness depends on the alignment between the market environment and consumer sentiment.

推论5.4表明，在口碑裂变营销下，深度裂变能够带来更高的需求，但在折扣裂变营销中却可能导致需求下降。结合定理5.2与推论5.4可见，深度裂变并非始终优于适度裂变，在某些情况下甚至会因厌恶型消费者的流失而造成需求减少。同时，为实现利润最大化，深度裂变所对应的价格折扣应低于适度裂变，但拼多多在实践中却采取了深度裂变并设置更高折扣的做法，最终引发了严重亏损。因此，本研究建议资金有限的中小企业在应用折扣裂变营销时，应充分评估深度裂变的适用条件，以降低利润受损的风险。

Corollary 5.4 shows that deep fission can lead to higher demand under word-of-mouth fission marketing, but it may lead to lower demand under discount fission marketing. Combining Theorem 5.2 with Corollary 5.4, we can see that deep fission is not always superior to moderate fission. In some cases, it can even lead to a decrease in demand due to the loss of aversion consumers. At the same time, to maximize profits, the price discount corresponding to deep fission should be lower than that of moderate fission. However, Pinduoduo actually adopted deep fission and set higher discounts, ultimately resulting in serious losses. Therefore, this study recommends that small and medium-sized enterprises with limited funds should fully evaluate the applicable conditions for deep fission when applying discount fission marketing to reduce the risk of profit loss.

（2）裂变营销程度选择（Fission marketing degree selection）

引理5.3表明，平台在口碑裂变营销中的决策主要取决于价格水平、偏好型消费者比例和裂变成本。当价格过低时，平台不会选择裂变；当价格较高而偏好型消费者比例偏低时，可能在深度裂变与不裂变之间权衡；而在偏好型消费者比例较高且成本适中的情况下，平台可在不同裂变方式中进行选择，其中适度裂变更具优势。

Lemma 5.3 shows that a platform's decision in word-of-mouth fission marketing depends primarily on price, the proportion of preferred consumers, and the cost of fission. When the price is too low, the platform will not choose fission. When the price is high and the proportion of preferred consumers is low, it may choose to trade off between deep fission and no fission. When the proportion of preferred consumers is high and the cost is moderate, the platform can choose between different fission methods, with moderate fission being more advantageous.

定理5.3说明，在口碑裂变营销中，适度裂变相较于无裂变始终能提升利润，是较为稳妥的策略。深度裂变只有在价格较高且成本较低时才优于适度裂变，否则适度裂变更具优势。总体而言，深度裂变的有效性依赖于高价格、低成本和较大比例的偏好型消费者，否则其利润提升难以实现。

Theorem 5.3 shows that in word-of-mouth fission marketing, moderate fission consistently increases profits compared to no fission, making it a more reliable strategy. Deep fission is superior to moderate fission only when prices are high and costs are low; otherwise, moderate fission is more advantageous. Overall, the effectiveness of deep fission depends on high prices, low costs, and a large proportion of preferred consumers; otherwise, profit increases are difficult to achieve.

引理5.4指出，在口碑裂变营销中，当偏好型消费者比例较小，如果销售价格过低，或价格与裂变成本系数同时处于高位，深度裂变不仅不能提升利润，反而可能因利润率不足或成本过高而导致利润下降。因此，平台在采用口碑裂变营销时，需要谨慎考虑是否实施深度裂变，以防在不利条件下产生负面效果。

Lemma 5.4 states that in word-of-mouth fission marketing, when the proportion of preferred consumers is small, if the sales price is too low, or if both the price and the fission cost coefficient are high, deep fission will not only fail to increase profits, but may even lead to a decline in profits due to insufficient profit margins or excessive costs. Therefore, when platforms adopt word-of-mouth fission marketing, they need to carefully consider whether to implement deep fission to prevent negative effects under unfavorable conditions.

引理5.5表明，在折扣裂变营销下，平台的裂变选择受价格、偏好型消费者比例和成本条件影响：价格较低时不实施裂变；价格适中时，比例较低选择不裂变，比例较高可在适度裂变与不裂变间选择；价格较高时，比例较低可能采取深度裂变或不裂变，否则在一定成本区间三种方式均可出现。定理5.4进一步指出，适度裂变始终优于不裂变，但与深度裂变的比较取决于价格、成本、偏好比例和消费者情绪。当成本较低且偏好比例或价格较高时，深度裂变更具优势，否则可能因厌恶型消费者流失而导致利润下降。

Lemma 5.5 shows that under discount fission marketing, the platform's fission choice is influenced by price, the proportion of preferred consumers, and cost conditions: when the price is low, no fission is implemented; when the price is moderate and the proportion is low, no fission is chosen; when the proportion is high, a choice between moderate fission and no fission is possible; when the price is high and the proportion is low, deep fission or no fission may be adopted; otherwise, within a certain cost range, all three options may be adopted. Theorem 5.4 further states that moderate fission is always better than no fission, but the comparison with deep fission depends on price, cost, preference ratio, and consumer sentiment. When cost is low and the preference ratio or price is high, deep fission is more advantageous; otherwise, profits may decline due to the loss of averse consumers.

推论5.5表明，在口碑裂变营销中，消费者情绪不会影响平台对裂变深度的选择；但在折扣裂变营销中，消费者情绪却会对平台决策产生显著作用。进一步来看，引理5.6指出，当偏好型消费者占比不足且裂变成本较高时，深度裂变不仅无法增加利润，反而可能导致收益下降。由引理5.4与引理5.6可推得，深度裂变并不是一种可持续的策略，这也解释了多数平台未普遍采用该模式的原因。

Corollary 5.5 shows that in word-of-mouth fission marketing, consumer sentiment does not influence the platform's choice of fission depth; however, in discount fission marketing, consumer sentiment does have a significant impact on the platform's decision. Furthermore, Lemma 5.6 states that when the proportion of preferred consumers is insufficient and the fission cost is high, deep fission not only fails to increase profits but may actually lead to a decrease in revenue. Lemmas 5.4 and 5.6 indicate that deep fission is not a sustainable strategy, which explains why most platforms have not widely adopted this model.

（3）消费者剩余（Consumer surplus）

定理5.5表明，口碑裂变营销中，深度裂变可通过提升需求和营销投入增加消费者剩余；而在折扣裂变营销下，结合定理5.2可知，当偏好型消费者比例低且裂变成本高时，适度裂变更有助于提升消费者剩余，显示出不同裂变模式下最优裂变程度对消费者剩余的显著差异。

Theorem 5.5 shows that in word-of-mouth fission marketing, deep fission can increase consumer surplus by increasing demand and marketing investment; while in discount fission marketing, combined with Theorem 5.2, it can be seen that when the proportion of preference consumers is low and the fission cost is high, moderate fission is more conducive to improving consumer surplus, showing a significant difference in the optimal fission degree on consumer surplus under different fission modes.

2、内生的销售价格（Endogenous sales price）

本节将销售价格视为内生决策变量，平台结合电子商务与社交平台利润确定价格与裂变力度。引理5.7表明，无裂变、适度裂变与深度裂变的最优选择取决于偏好型消费者比例、裂变成本及努力成本，仅在特定条件下选择适度或深度裂变。引理5.8进一步指出，当偏好型消费者比例较高且折扣幅度较小时，适度裂变与深度裂变的最优价格均高于无裂变，可能引发“先抬价再折扣”的欺骗性营销，但一旦被识破，将削弱分享动机。

This section treats the sales price as an endogenous decision variable, and the platform determines the price and fission intensity based on the profits of both e-commerce and social platforms. Lemma 5.7 shows that the optimal choice between no fission, moderate fission, and deep fission depends on the proportion of preferred consumers, fission costs, and effort costs. Moderate or deep fission is only chosen under specific conditions. Lemma 5.8 further indicates that when the proportion of preferred consumers is high and the discount is small, the optimal price for both moderate fission and deep fission is higher than no fission. This may lead to deceptive marketing tactics such as "raising prices first, then discounting." However, once detected, this weakens the motivation to share.

数值分析结果表明，口碑裂变营销中，低成本系数倾向深度裂变，高成本系数倾向适度裂变；折扣裂变营销中，积极情绪下适度裂变优于深度裂变，而负面情绪占多数时，仅低成本条件下深度裂变具有优势。这进一步验证了本章前几节的核心结论：深度裂变适用于高价且低成本情境，折扣裂变的效果则显著依赖消费者情绪。

Numerical analysis results show that in word-of-mouth fission marketing, low-cost coefficients favor deep fission, while high-cost coefficients favor moderate fission. In discount fission marketing, moderate fission outperforms deep fission under positive sentiment, while deep fission only has an advantage under low-cost conditions when negative sentiment predominates. This further confirms the core conclusions of the previous sections of this chapter: deep fission is suitable for high-price and low-cost scenarios, while the effectiveness of discount fission is significantly dependent on consumer sentiment.

三、知识补充（Knowledge supplementation）

1、均衡利润概述（Overview of equilibrium profit）

利润均衡指消费者与生产者在价格、产量和利润上实现匹配，从而达到双方利益的平衡与最大化。在市场经济中，供求双方通过价格调整，最终趋向于这种均衡状态。拓展来看，利润均衡属于一种静态结果，市场条件变化（如需求上升）会在短期内打破这一平衡。此时，生产者可参考长期利润均衡的原则制定定价策略，以实现经济效益的最优化。

Profit equilibrium refers to the matching of prices, output, and profits between consumers and producers, thereby balancing and maximizing the interests of both parties. In a market economy, supply and demand ultimately converge towards this equilibrium through price adjustments. More broadly, profit equilibrium is a static outcome; changes in market conditions (such as increased demand) can disrupt this equilibrium in the short term. In these situations, producers can formulate pricing strategies based on the principles of long-term profit equilibrium to optimize economic efficiency.

2、消费者剩余概述（Overview of consumer surplus）

消费者剩余指消费者为购买一定数量商品所愿支付的最高价格与实际市场价格之间的差额。马歇尔基于边际效用价值论提出了消费者剩余的概念，范里安则提出了若干计算方法。作为衡量消费者福利的重要指标，消费者剩余被广泛用于经济分析。产业的社会福利可表示为消费者剩余与生产者剩余之和，或等于总消费效用减去生产成本。1977年，A.K.迪克西特和斯蒂格利茨将内在规模经济引入一般均衡模型，得出市场应追求最适度边际利润而社会应关注消费者剩余的结论。通常认为，消费者剩余最大化的条件是边际效用等于边际支出。

Consumer surplus refers to the difference between the maximum price a consumer is willing to pay for a given quantity of goods and the actual market price. Marshall proposed the concept of consumer surplus based on the marginal utility theory of value, and Varian developed several calculation methods. As a key indicator of consumer welfare, consumer surplus is widely used in economic analysis. The social welfare of an industry can be expressed as the sum of consumer surplus and producer surplus, or as total consumption utility minus production costs. In 1977, A.K. Dixit and Stiglitz introduced inherent economies of scale into the general equilibrium model, concluding that the market should pursue optimal marginal profits while society should focus on consumer surplus. It is generally believed that maximizing consumer surplus requires marginal utility equal to marginal expenditure.

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翻译：Google翻译

参考资料：百度、Chatgpt