We propose an optimal pricing model for products with both positive and negative network effects. A closed-form expression of the optimal pricing policy is derived under the assumption that the demand function is linear. When there are two customer types with different attitudes towards congestion, the monotonicity of the optimal price differs according to the price sensitivity of each customer type. We show that even if the number of customers who are averse to congestion increases, if the negative-type price sensitivity is low and the positive network effect is weak, increasing the optimal price will increase total profit.

中文翻译：

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存在正负网络效应时的最优定价策略

我们为具有正向和负向网络效应的产品提出了最优定价模型。最优定价政策的封闭式表达式是在需求函数是线性的假设下导出的。当存在两种对拥堵态度不同的客户类型时，最优价格的单调性根据每种客户类型的价格敏感度而不同。我们表明，即使厌恶拥堵的顾客数量增加，如果负型价格敏感性较低且正网络效应较弱，则提高最优价格会增加总利润。