Models of new product diffusion : current status and research agenda

Diffusion models, mathematical attempts to describe the growth patterns of new products and relate them to variables such as price and population characteristics, have seen major development trends in the past few years. This paper reviews that progress in order to isolate those areas most likely to be fruitful for further development. The paper first reviews some of the behavioral underpinnings of diffusion models: the phenomena being modeled. Next, the major explicit form models are reviewed and classified according to whether they have market-controls or not and according to the number of stages they explicitly consider. These models are related to larger-scale simulation models (especially in the solar energy area) that use explicit-form models as building blocks. The paper concludes with a discussion of some important advances that still need to be made in this important and rapidly-growing area

A New Product Adoption Model with Price, Advertising, and Uncertainty

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

Monopolist Pricing with Dynamic Demand and Production Cost

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

Optimal Price Subsidy Policy for Accelerating the Diffusion Of Innovation

Due to the risk inherent in dependence on foreign oil, there is a social benefit in aiding the introduction of alternative energy sources into the market place. The Federal government has initiated a number of programs, including price subsidies, to help accelerate the market diffusion of new, alternative energy systems. We develop a model to investigate analytically the effects of a price subsidy over time on the rate of market diffusion. The model considers word-of-mouth effects and learning curve cost declines. Under a set of conditions that a new technology should be expected to meet before commercialization, the optimal subsidy level is shown to be nonincreasing in time. The related market price is shown to be closely related to the diffusion effect. If there is no such effect, the price to the customer is constant. If there is positive diffusion effect, price increases in time, while if market saturation causes demand to decline over time price decreases in time.price subsidy, diffusion of innovations

Closed-Loop Advertising Strategies in a Duopoly

Using the Lanchester model to describe the dynamics of the market where two firms compete for customers by advertising, we solve the problem of determining an optimal advertising strategy for maximum discounted profits. We develop both open- and closed-loop strategies and explain the relationship between them. Using a new mathematical approach, we prove that our closed-loop solution is a global Nash equilibrium. The closed-loop strategy is time-variant and depends linearly on the actual market share. The time-variant coefficient incorporates the discount factor, its computation requires the solution of a backward differential equation and a set of two nonlinear differential equations for an initial value problem. The closed-loop advertising expenditures are proportional to the open-loop advertising expenditures and to the square of the competitor's actual market share. This provides a very practical adaptive control rule that allows the manager to adjust the actual advertising expenditure and to deviate from budget. We illustrate the use of our control rule, using data for the period 1968--1984 of the Cola War Marketing implications of the results are provided.marketing, competitive strategy, Nash equilibrium, bilinear-quadratic differential game, noncooperative

A Market Entry Timing Model for New Technologies

A central issue in new product development and planning is the market timing/entry decision. An entry too early may risk pushing an under-developed product into the marketplace, with possible negative results; however, a product/technology may sacrifice sales if entry is delayed too long. A market diffusion model is developed that incorporates negative word-of-mouth associated with new product failure, resulting from premature introduction. Our analysis suggests that, when introducing a new technology, significant penalties may be associated with mistiming introduction. The analysis was applied to a problem facing the photovoltaic program of the Department of Energy. A proposal to construct a 100-home demonstration program for photovoltaics (PV) in the Southwest was being evaluated. The analysis of this case showed that an argument can be made to delay the demonstration program for several years and that significant risks (in terms of lowered ultimate market penetration) exist when starting this PV demonstration program prematurely.marketing, new products, diffusion models

A repeat purchase diffusion model : Bayesian estimation and control

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