喆学（152）：精读博士论文考虑产品使用成本的定价优化（2）

摘要：This post will introduce the pricing optimization that considers the product usage cost from the intensive reading doctoral thesis

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“喆学（152）：精读博士论文

《基于消费者学习的免费增值信息产品

定价优化与运营研究》

考虑产品使用成本的定价优化（2）”

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"Zhexue (152): Intensive reading of doctoral dissertation

"Pricing optimization and operation research of free value-added information products based on consumer learning"

Pricing optimization considering product usage costs (2)"

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本期推文将从思维导图、精读内容、知识补充三个方面介绍精读博士论文《基于消费者学习的免费增值信息产品定价优化与运营研究》的考虑产品使用成本的定价优化。

This post will introduce the pricing optimization that considers the product usage cost from the intensive reading doctoral thesis "Research on Pricing Optimization and Operation of Free Value-added Information Products Based on Consumer Learning" from three aspects: mind mapping, intensive reading content, and knowledge supplement.

一、思维导图（Mind Maps）

二、精读内容（Intensive reading content）

(1)同时发布两个版本的条件(Conditions for publishing two versions simultaneously)

本文讨论了企业在市场中同时发布免费版和付费版产品的策略。通过分析收益差值，得出在网络外部性强度适中时，企业同时发布两个版本能获得更高收益。研究还发现，当网络外部性强度超过一定值时，收益增量为正，表明企业有动机同时发布两个版本。本文为理解Freemium策略在不同市场条件下的效果提供了理论依据。

This paper discusses the strategy of enterprises releasing free and paid versions of products in the market at the same time. By analyzing the difference in revenue, it is concluded that when the intensity of network externalities is moderate, enterprises can obtain higher revenue by releasing two versions at the same time. The study also found that when the intensity of network externalities exceeds a certain value, the incremental revenue is positive, indicating that enterprises have the motivation to release two versions at the same time. This paper provides a theoretical basis for understanding the effect of Freemium strategy under different market conditions.

本文探讨了企业在网络外部性影响下，同时发布免费版和付费版产品的策略。研究表明，在网络外部性较强时，企业通过免费增值模式可以获得更高收益。具体来说，当网络外部性强度γ在两个实根之外时，企业同时发布两个版本能获得更高的收益。文章通过数学推导分析了免费版使用成本、付费版使用成本、网络外部性强度以及免费版质量对最优收益的影响，指出在某些条件下，增加付费版质量或降低免费版质量可以提高收益。这为企业在不同市场条件下选择适当的产品策略提供了理论依据。

This paper explores the strategy of enterprises to release both free and paid versions of products under the influence of network externalities. The study shows that when network externalities are strong, enterprises can obtain higher returns through the free value-added model. Specifically, when the network externality intensity γ is outside the two real roots, enterprises can obtain higher returns by releasing two versions at the same time. The article analyzes the impact of the cost of using the free version, the cost of using the paid version, the intensity of network externalities, and the quality of the free version on the optimal return through mathematical derivation, and points out that under certain conditions, increasing the quality of the paid version or reducing the quality of the free version can increase the return. This provides a theoretical basis for enterprises to choose appropriate product strategies under different market conditions.

(2)数值分析(Numerical analysis)

1.网络外部性强度取值范围(Range of network externality intensity)

在网络外部性影响下，企业通过降低免费版使用成本、增加付费版质量或增强网络外部性来提高收益。研究表明，当网络外部性强度γ在两个实根之外时，企业同时发布免费版和付费版能获得更高收益。此外，企业可以通过数值分析方法探讨免费版质量设计，以优化收益。当阈值2sHcL/(sH+cH)时，网络外部性强度γ的适应范围最大，企业同时向市场发布两个版本的可能性最高。这为企业在不同市场条件下选择适当的产品策略提供了理论依据。

Under the influence of network externalities, enterprises can improve their revenue by reducing the cost of using the free version, increasing the quality of the paid version, or enhancing network externalities. Studies have shown that when the network externality intensity γ is outside the two real roots, enterprises can obtain higher revenue by releasing both the free version and the paid version. In addition, enterprises can explore the quality design of the free version through numerical analysis methods to optimize revenue. When the threshold is 2sHcL/(sH+cH), the adaptability range of the network externality intensity γ is the largest, and the possibility of enterprises releasing two versions to the market at the same time is the highest. This provides a theoretical basis for enterprises to choose appropriate product strategies under different market conditions.

2.不同网络外部性强度下的最优收益(Optimal returns under different network externality intensities)

在不同网络外部性强度下，企业设计免费版质量的策略会有所不同。当网络外部性强度较弱（γ=0.1）时，免费版质量的可行域为空，企业仅销售付费版。当强度适中（γ=0.5），免费版质量的最佳值为0.5，企业同时销售免费版和付费版。当强度较强（γ=0.9），免费版质量的可行域为(0.9, 0.9)，企业可以更自由地设计免费版质量。这表明，随着网络外部性增强，企业在设计免费版质量时拥有更大的灵活性，以实现收益最大化。

Under different network externality strengths, the enterprise's strategy for designing the quality of the free version will be different. When the strength of network externalities is weak (γ=0.1), the feasible domain of the free version quality is empty, and the enterprise only sells the paid version. When the strength is moderate (γ=0.5), the optimal value of the free version quality is 0.5, and the enterprise sells both the free version and the paid version. When the strength is strong (γ=0.9), the feasible domain of the free version quality is (0.9, 0.9), and the enterprise can design the free version quality more freely. This shows that as network externalities increase, enterprises have greater flexibility in designing the quality of the free version to maximize their profits.

在网络外部性影响下，企业设计免费版质量的策略会随外部性强度γ的变化而调整。当γ

Under the influence of network externalities, the enterprise's strategy for designing the quality of the free version will adjust with the change of the externality intensity γ. When γ

3.外部参数联合影响下的收益增量(Incremental earnings under the combined influence of external parameters)

图3-7展示了企业在不同免费版质量sL和网络外部性强度γ下的收益增量Δ。颜色越明亮表示收益增量越大。企业可以通过优化免费版质量来最大化收益增量Δ。在网络外部性较强且免费版质量适中时，企业同时发布免费版和付费版可获得更高利润。这为企业在免费增值模式下如何设定免费版质量提供了指导。

Figure 3-7 shows the incremental revenue Δ of enterprises under different free version quality sL and network externality strength γ. Brighter colors indicate larger incremental revenue. Enterprises can maximize incremental revenue Δ by optimizing the quality of the free version. When network externalities are strong and the quality of the free version is moderate, enterprises can obtain higher profits by releasing both the free version and the paid version. This provides guidance for enterprises on how to set the quality of the free version under the free value-added model.

三、知识补充（Knowledge supplement）

网络外部性对消费者的购买决策有显著影响，具体体现在以下几个方面：

Network externalities have a significant impact on consumers' purchasing decisions, which is reflected in the following aspects:

1.增加产品吸引力：

1. Increase product attractiveness:

当越来越多的人使用某个产品或服务时，该产品对其他潜在用户的吸引力增加。例如，社交媒体平台的用户越多，对新用户的吸引力就越大，因为用户可以与更多的朋友和家人连接。

When more and more people use a product or service, the product's attractiveness to other potential users increases. For example, the more users a social media platform has, the more attractive it is to new users because users can connect with more friends and family.

2.提高产品价值：

2. Increase product value:

网络外部性可以提高产品的价值。例如，在通信网络中，网络中用户越多，每个用户能联系的人就越多，从而提高服务的价值。

Network externalities can increase the value of a product. For example, in a communication network, the more users there are in the network, the more people each user can contact, thereby increasing the value of the service.

3.影响消费者预期：

3. Influence consumer expectations:

消费者可能会基于对产品未来普及程度的预期来做出购买决策。如果他们预期某个产品会广泛被采用，他们可能更倾向于早期采用，以便在未来获得更好的兼容性和更多的功能。

Consumers may make purchasing decisions based on their expectations of the future popularity of a product. If they expect a product to be widely adopted, they may be more inclined to adopt it early in order to obtain better compatibility and more features in the future.

4.增加转换成本：

4. Increase switching costs:

对于已经拥有大量用户的网络产品，消费者可能会因为转换成本高而不愿意更换到其他产品。例如，用户可能不愿意从一个拥有大量联系人的社交网络迁移到另一个网络。

For network products that already have a large number of users, consumers may be reluctant to switch to other products due to high switching costs. For example, users may be reluctant to migrate from one social network with a large number of contacts to another network.

5.影响产品选择：

5. Influence on product selection:

在多个产品之间做出选择时，消费者可能会选择用户基础更大的产品，因为这样的产品更有可能继续存在并得到支持。

When choosing between multiple products, consumers may choose products with a larger user base because such products are more likely to continue to exist and be supported.

6.促进口碑传播：

6. Promote word-of-mouth communication:

网络外部性可以通过口碑效应加速产品的传播。当用户发现一个产品对他们有用，他们更可能推荐给其他人，从而增加产品的用户基础。

Network externalities can accelerate the spread of products through word-of-mouth effects. When users find a product useful to them, they are more likely to recommend it to others, thereby increasing the user base of the product.

7.影响价格敏感度：

7. Influence on price sensitivity:

在某些情况下，网络外部性可以降低消费者对价格的敏感度。如果一个产品提供了独特的网络价值，消费者可能愿意支付更高的价格。

In some cases, network externalities can reduce consumers' sensitivity to price. If a product provides unique network value, consumers may be willing to pay a higher price.

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翻译：谷歌翻译

参考资料：谷歌、Chat GPT

参考文献：陈小艳. 基于消费者学习的免费增值信息产品定价优化与运营研究[D]. 西南交通大学, 2021.