Infinite-horizon optimal advertising in a market for durable goods

Abstract

SUMMARYIn 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 NerloveArrow (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.

A dynamic model for tuberculosis transmission and optimal treatment strategies in South Korea

“…Since the number of incidence after the jump at 2001 yr is not decreasing, we apply OC theory to our model for proposing optimal treatment strategies of TB in South Korea. OC theory has been applied in many areas including economics (Dorfman, 1969;Kamien and Schwartz, 1992;Weber, 2005), engineering , biology (Fister et al, 1998;Joshi, 2003;Jung et al, 2002Jung et al, , 2009Kirschner et al, 1997;Lenhart and Workman, 2007) and medicine (Jung et al, , 2006(Jung et al, , 2008Lenhart et al, 2005). In our work, the control plans are associated with three control mechanisms: distancing, case finding and case holding efforts.…”

Advertising and production of a seasonal good for a heterogeneous market

“…Although the infinite horizon formulation is the natural setting for the analysis of some dynamic optimization problems in advertising, as for instance in the recent papers (Jørgensen et al, 2001), (Weber, 2005), (Grosset and Viscolani, 2008), there are special situations for which a finite horizon formulation is obviously needed. Examples of this case are advertising for an event, as in (Jørgensen et al, 2006), introducing a new product, as in (Buratto et al, 2006a), and advertising for a seasonal product, as in (Favaretto and Viscolani, 2004).…”

Optimal double control problem for a PDE model of goodwill dynamics

“…Moreover, since the empirical studies summarized by Bagwell in [4]) indicate the existence of decreasing returns to advertising efforts, we include this observation in the new model and we assume a non-linear relation between advertising and goodwill. A similar assumption was used by Weber in [41] and by Mosca and Viscolani in [29] in a goodwill model expressed by an ordinary differential equation. In addition, we have expanded the existing models by allowing the depreciation of goodwill to be non-constant, but rather heterogeneous with respect to the usage experience of the product.…”