Optimal advertising and pricing in a class of general new-product adoption models

Kurt Helmes, Rainer Schlosser and Martin Weber

European Journal of Operational Research, 2013, vol. 229, issue 2, 433-443

Abstract: In [21], Sethi et al. introduced a particular new-product adoption model. They determine optimal advertising and pricing policies of an associated deterministic infinite horizon discounted control problem. Their analysis is based on the fact that the corresponding Hamilton–Jacobi–Bellman (HJB) equation is an ordinary non-linear differential equation which has an analytical solution. In this paper, generalizations of their model are considered. We take arbitrary adoption and saturation effects into account, and solve finite and infinite horizon discounted variations of associated control problems. If the horizon is finite, the HJB-equation is a 1st order non-linear partial differential equation with specific boundary conditions. For a fairly general class of models we show that these partial differential equations have analytical solutions. Explicit formulas of the value function and the optimal policies are derived. The controlled Bass model with isoelastic demand is a special example of the class of controlled adoption models to be examined and will be analyzed in some detail.

Keywords: Optimal control; Dynamic programming; OR in marketing; Pricing; Sethi/Bass model (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (18)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:229:y:2013:i:2:p:433-443

DOI: 10.1016/j.ejor.2013.02.035

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