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Generalized Network Externality Function

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Arnut Paothong and G.S. Ladde

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With regards to the network externality function, the first derivative is commonly considered to be positive. However, the sign of its second derivative is based on the assumption about the marginal network value when the network grows. Three key assumptions are constant, decreasing, or increasing which generate a different functional form, linear, concave, convex function, respectively. There is an effort to mix these strict assumptions by combining them which generate the S-shaped function such as logistic, Gompertz or Sigmoid function. Unfortunately, to do so, the S-shaped function causes an inappropriate domain, negative network size. In this work, we develop a dynamic model to generalize a functional form of network externality function which not only keeps all good properties of the S-shaped function, but also has a desired domain.

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Network externality, S-shaped function, Sigmoid function JEL Classification: C51, D01, D11 >