Dynamic advertising and pricing with constant demand elasticities

Kurt L. Helmes and Rainer Schlosser

Journal of Economic Dynamics and Control, 2013, vol. 37, issue 12, 2814-2832

Abstract: In this paper we analyze a stochastic dynamic advertising and pricing model with isoelastic demand. The state space is discrete, time is continuous and the planing horizon is allowed to be finite or infinite. A dynamic version of the Dorfman–Steiner identity will be derived. Explicit expressions of the optimal advertising and pricing policies, of the value function and of the optimal advertising expenditures will be given. The general results will be used to analyze the case of impatient customers. Furthermore, particular time inhomogeneous models and homogeneous ones with and without discounting will be examined. We will study the social efficiency of a monopolist's optimal policies and the consequences of specific subsidies. From a buyer's perspective, our analysis reveals that waiting – when looking at (immediate) expected prices – is never profitable should two or more units be available. But we will also prove that the sequence of average sales prices is monotone decreasing. Moreover, the techniques applied to solve the discrete stochastic advertising and pricing problem will be used to solve a related deterministic control problem with continuous state space.

Keywords: Dynamic advertising and pricing; Optimal deterministic and stochastic control; Dorfman–Steiner identity; Constant demand elasticities (search for similar items in EconPapers)
JEL-codes: C61 D42 M37 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:dyncon:v:37:y:2013:i:12:p:2814-2832

DOI: 10.1016/j.jedc.2013.08.004

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