Decision SupportModeling the impact of product quality on dynamic pricing and advertising policies☆
Introduction
The marketing-mix of the price–quality and advertising–quality relationships have been extensively studied. Surveys in dynamic pricing (Chen, Chen, 2015, Den Boer, 2015, Elmaghraby, Keskinocak, 2003) and in dynamic advertising (Erickson, 1995, Feichtinger, Hartl, Sethi, 1994, Huang, Leng, Liang, 2012, Jørgensen, Zaccour, 2014, Sethi, 1977) reveal the separate analysis of both relationships in prior research. In practice though, recent media claims recall that firms need to manage altogether (opposing two-by-two) price, advertising, and quality. For instance, this marketing-mix concern arises for the American telecom industry with AT&T (Flint, 2019, The Wall Street Journal) and also in the vanilla industry of Madagascar (Board, 2019, The Economist). Even for the hypothetical market of driverless car, which interests classical automotive groups such as PSA – program Autonomous Vehicle for All – and new entrants like Google – program Waymo, there is a discussion about the simultaneous setting of price, advertising, and quality (Nuttall, 2019, Financial Times). Despite its practical relevance, the price–advertising–quality relationship has received little attention by scholars so far, as attested by the influential textbooks of Dockner, Jorgenssen, Long, and Gerhard (2000) and Jørgensen and Zaccour (2012). This article bridges the gap, offering a theoretical foundation of the price–advertising–quality relationship and of the impact of quality on dynamic pricing and advertising policies.
In this article, we investigate the joint dynamic pricing, advertising, and quality investment policies, focusing on the conditions under which greater quality drives higher or lower price and advertisement. We propose an optimal control model coping with the following elements: a firm sets pricing, advertising, and quality investment policies over time. Consumers are sensitive to price, advertisement and product quality; quality is costly to produce for the firm. The preferences of consumers and the organization of the firm are tied to the dynamics of demand and supply, which, in turn, are linked to the dynamic pricing, advertising, and quality investment policies. Literature on marketing-mix with dynamic pricing, advertising, and quality thus informs this research.
The closest articles to our research are Chenavaz (2017a) and Chenavaz and Jasimuddin (2017), which consider the impact of quality on price and on advertising, respectively. Considering jointly the price–quality and advertising–quality relationships, we show how advertisement affects the price–quality relationship and how price changes the advertising–quality relationship. In their vein, we offer structural (opposing parametric) results, enabling to solve the monopolist’s dynamic behavior problem under the most general demand formulation, which accounts for nonlinearities and dynamics in response to quality changes.
Our main results are as follows. First, we generalize the condition of Dorfman and Steiner (1954) in a dynamic context, stressing the profit-maximizing conditions for the price–advertising, price–quality, and advertising–quality relationships. Second, we develop the pricing–advertising–quality relationship, examining the conditions under which better quality triggers higher or lower price and advertisement. Third, a phase diagram analysis learns that quality develops monotonically in time and converges to a unique steady state. We also show that quality investment could either decrease or increase over time but this depends on its effectiveness. Such results foster the understanding of more complex marketing-mix opportunities, enhancing the profitability of the firm.
The paper is organized as follows. Section 2 presents the related contributions. Section 3 develops the model, whereas Section 4 generalized the rules of Dorfman–Steiner to a dynamic context. Section 5 studies the impact of quality on dynamic pricing and advertising. Section 6 computes the optimal trajectories using a phase plane analysis, and Section 7 concludes.
Section snippets
Related contributions
Dynamic marketing-mix research provide numerous related contributions. Such contributions focusing on dynamic pricing, advertising, and product quality, are regularly surveyed. Some of these surveys focus on pricing (Dockner, Jorgenssen, Long, Gerhard, 2000, Jørgensen, Zaccour, 2012, Den Boer, 2015) and others on advertising (Feichtinger, Hartl, Sethi, 1994, Bagwell, 2007, Huang, Leng, Liang, 2012, Jørgensen, Zaccour, 2014). More specific literature pointers have been provided recently for the
Model development
The intertemporal behavior of a monopolist is modeled in an optimal control setting. The planning horizon is infinite and the time is continuous.
Generalizing the rules of Dorfman–Steiner
In this section, we generalize the static rules of Dorfman and Steiner (1954) in a dynamic context, looking at the dynamic price–advertising–quality relationship. The rules of Dorfman and Steiner (1954) have to be verified for levels of price and advertising to be candidate as optimal values. As such, these rules provide a useful benchmark against which potential price and advertising levels can be evaluated.
We first posit elasticity notations. Let be the price elasticity of demand,
Quality impact on dynamic pricing and advertising
In this section we examine the impact of better quality on price and advertising policies, when the rules of Dorfman and Steiner (1954) studied in the previous section apply. The optimal pricing and advertising policies have to hold at any time of the planning period. Thus, we consider the time derivative of (10a) and (10b). Rearranging terms offers
Recall Hpp, Haa, and Hpa from (12a), (12b),
Computation of the optimal trajectories
We start out with analyzing our deterministic model. Afterwards, we provide an extension where the horizon date, T, is finite and stochastic.
Conclusion
In this research, we proposed a comprehensive, dynamic modeling of price, advertising, and quality. The model is comprehensive, yet with no sacrifice of generality, as it permits general (structural) functional forms for the cost and the relationships between the marketing-mix variables at the demand level. On the basis of an optimal control model, we offer analytic results. First, we generalize the classical condition of Dorfman and Steiner (1954) to a dynamic context. Second, we provide the
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The authors like to thank three anonymous referees for their valuable comments and suggestions, which helped to improve the paper significantly.