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.marketing, new products, diffusion of innovation

This paper deals with pricing of a new product over time by a monopolist who maximizes the discounted profit stream. The interdependency of cost and demand on cumulative production makes the problem inherently dynamic. Cost is assumed to be declining with cumulative production (learning curve effect), while demand is a function of price and cumulative sales, representing word-of-mouth and saturation effects. The paper addresses this problem in a general framework that includes several previous results as special cases, and provides new insights in other situations. While the learning curve and word-of-mouth effect cause prices to be lower than the price that maximizes immediate revenues, the saturation factor has the opposite effect. The price path over time is affected by these factors and the interest rate. We characterize the price path under several different situations and interpret the results for policy guidelines.pricing, dynamic pricing, learning curve, diffusion of innovations

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A central problem in marketing is: how should the firm position (reposition) and price a line of related (substitute) products in order to maximize profits (or welfare). We formulate this problem faced by a monopolist as a mathematical program, outline how to obtain the market data from a sample of customers, discuss what cost data are relevant, and suggest a heuristic algorithm to solve the problem. The output of the process is a list of products to offer, their prices, and the customer segments which purchase each product. While additional real world complexities, e.g., uncertainty about customer wants, product performance, and competitive response, are not modeled, we believe the system developed can serve as an important input into the decision process when new products are designed and priced. The methodology can be used as a part of a decision support system, where management specifies the number of products desired. The system suggests a few good solutions, together with the prices and customer segments served by each product. We use the standard assumption that the market is composed of different customer segments of various sizes, each containing homogeneous customers. Customers choose one brand only, the one that provides them with maximum value for the money. The firm faces both fixed and variable production and marketing costs for each product. Competition is either nonexistent, or assumed not to respond to the firm's moves. The information available to the firm is the sizes and preferences of the segments, based on a sample of customers, and the cost data. As an alternative to the traditional approach of estimating a parametric utility function, and aggregating customers into segments, we can also use the raw data as input, where each customer in the sample represents a segment. This, we believe, allows us to reduce the errors introduced in the process. Heuristics for solving the problem are suggested. The heuristics are evaluated on a set of simulated problems, and compared to the optimal solutions. The heuristics perform well when compared to all feasible solutions on a set of small simulated problems. We also discuss the application of the procedure to a ‘real life' sized problem.product line, product positioning pricing, decision support, heuristics