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Modeling the impact of product quality on dynamic pricing and advertising policies

https://doi.org/10.1016/j.ejor.2020.01.035Get rights and content

Highlights

  • Study the pricing–advertising–quality relationship.

  • Provide an optimal control application.

  • Generalize the condition of Dorfman–Steiner (1954).

Abstract

The marketing-mix of price–quality and advertising–quality relationship is well studied. Less understood is the price–advertising–quality relationship. This article fills the gap, investigating the interplay between price, advertising, and quality in an optimal control model. Our results generalize the condition of Dorfman–Steiner in a dynamic context. Also, they point to the impact of greater product quality on the dynamic policies of pricing and advertising. Furthermore, a phase diagram analysis shows 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. Our results spot the profitable opportunities of a firm managing a more complex marketing-mix.

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 t[0,) 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 ηpDppD be the price elasticity of demand, ηa

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 offersp˙[2Dp+(pC)Dpp]+a˙[Da+(pC)Dpa]=q˙[Dq(pC)Dpq+CqDp],p˙[Da+(pC)Dap]+a˙[(pC)Daa]=q˙[(pC)Daq+CqDa].

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

References (52)

  • S. Kalish

    Monopolist pricing with dynamic demand and production cost

    Marketing Science

    (1983)
  • Ö. Karaer et al.

    Quality and entry deterrence

    European Journal of Operational Research

    (2015)
  • S.K. Mukhopadhyay et al.

    A differential game theoretic model for duopolistic competition on design quality

    Operations Research

    (1997)
  • C. Nuttall

    The UK milestones for a driverless future

    (2019)
  • X. Pan et al.

    Dynamic optimal control of process–product innovation with learning by doing

    European Journal of Operational Research

    (2016)
  • J.-T. Teng et al.

    Optimal strategies for general price-quality decision models of new products with learning production costs

    European Journal of Operational Research

    (1996)
  • J. Vörös

    The dynamics of price, quality and productivity improvement decisions

    European Journal of Operational Research

    (2006)
  • J. Vörös

    Multi-period models for analyzing the dynamics of process improvement activities

    European Journal of Operational Research

    (2013)
  • M. Xue et al.

    Quality improvement and pricing with reference quality effect

    Journal of Systems Science and Systems Engineering

    (2017)
  • N. Amrouche et al.

    Pricing and advertising of private and national brands in a dynamic marketing channel

    Journal of Optimization Theory and Applications

    (2008)
  • E. Board

    The murky world of Madagascar’s roaring vanilla trade

    (2019)
  • J. Caulkins et al.

    Optimal pricing of a conspicuous product during a recession that freezes capital markets

    Journal of Economic Dynamics and Control

    (2011)
  • J. Chen et al.

    Price and quality decisions in dual-channel supply chains

    European Journal of Operational Research

    (2017)
  • M. Chen et al.

    Recent developments in dynamic pricing research: Multiple products, competition, and limited demand information

    Production and Operations Management

    (2015)
  • R. Chenavaz

    Dynamic pricing, product and process innovation

    European Journal of Operational Research

    (2012)
  • R. Chenavaz

    Better product quality may lead to lower product price

    The BE Journal of Theoretical Economics

    (2017)
  • Cited by (0)

    The authors like to thank three anonymous referees for their valuable comments and suggestions, which helped to improve the paper significantly.

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