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Infinite‐horizon optimal advertising in a market for durable goods
Author(s) -
Weber Thomas A.
Publication year - 2005
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.765
Subject(s) - convergence (economics) , durable good , mathematical economics , arrow , economics , regular polygon , horizon , trajectory , state (computer science) , set (abstract data type) , mathematical optimization , microeconomics , mathematics , computer science , physics , geometry , algorithm , astronomy , programming language , economic growth
In this paper we analyse the optimal infinite‐horizon advertising policy of a monopolist firm in a market for durable goods, based on classic models by Vidale–Wolfe ( Oper. Res . 1957; 5 (3):370–381) and Nerlove–Arrow ( Economica 1962; 29 (114):129–142). A set of necessary conditions for optimality generalizing previous results is provided for the resulting non‐convex system. In addition, we establish local (and in some cases global) asymptotic convergence of an optimal trajectory towards the unique optimal steady state. Copyright © 2005 John Wiley & Sons, Ltd.