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This paper introduces a framework for modeling innovation diffusion that includes price and advertising. The adoption of a new product is characterized by two steps: awareness and adoption. Awareness is the stage of being informed about the product search attributes. The process of becoming aware is modeled as a simple “epidemic” type model, where the information is spread by advertising and word of mouth. The second step, adoption, is conditional on awareness, and it occurs if the perceived risk adjusted value of the product exceeds its selling price. The population is heterogeneous with respect to valuation of the product. Individuals are risk averse, and therefore are willing to pay more for the product, on the average, as information from early adopters reduces uncertainty about the product. Optimal control of the diffusion process by pricing and advertising over time is analyzed, and a comparative estimation of the model in one application is reported.
Shlomo Kalish (Sun,) studied this question.