Production, Manufacturing and Logistics
Interaction of pricing, advertising and experience quality: A dynamic analysis

https://doi.org/10.1016/j.ejor.2016.06.056Get rights and content

Highlights

  • Innovative marketing model involving experience quality is proposed.

  • Optimal marketing mix is determined.

  • Guidelines for subsidizing quality are derived.

  • History dependent equilibria (indifference threshold, Skiba point) are identified.

Abstract

For certain goods or services, the quality of the product can be assessed by customers only after consumption. We determine the optimal time paths for pricing, advertising and quality for a profit-maximizing firm facing demand that is influenced both by this experience quality as well as by advertising. In particular, there may exist two optimal trajectories separated by an indifference threshold in which the firm has the same utility of converging to either of the two long-run steady states. Or, to put it in a nutshell: the optimal mix of marketing instruments may lead to history-dependence. One implication is that there may be a market failure such that a government subsidy could help reach the steady state that is best for the Economy in the sense of having greater sales and a higher quality product.

Introduction

In a path-breaking paper on information and consumer behavior, Nelson (1970) distinguishes between qualities of a brand that consumers can determine by inspection prior to purchase, denoted as search qualities (sometimes also called ‘design quality’; Nelson (1974) exemplifies it by the style of a dress), and qualities which can be evaluated only after the purchase, so-called experience qualities. Experience goods or services include medical services, new vacation resorts, restaurant meals, repairs, and wine. Typically, experience goods are characterized by asymmetric information; firms know the quality of the goods and services they produce, but customers do not directly observe that quality prior to purchase. Hence, there can at times be gaps between actual and anticipated quality.

Kotowitz, Mathewson, 1979a, Kotowitz, Mathewson, 1979b incorporate this insight into a dynamic model in which a monopolist maximizes profit in the face of customers who are imperfectly informed about the quality of the monopolists’ product. Demand is driven by perceived, not just actual, product quality, and perceptions in turn evolve over time in response to both advertising and differences experienced between expected and actual quality. While the model adopts the perspective of the monopolist, the paper also considers social welfare implications. We do here as well, but with a richer model, and whereas Kotowitz–Mathewson were primarily concerned with the possibility of there being too much advertising, from a social welfare perspective, we focus on the possibility that potentially viable firms may need to be jump-started by outside assistance. For a dis-cussion of the socially optimal marketing instruments in the Ko-towitz–Mathewson model, see the excellent survey of Sethi (1977).

A series of subsequent papers extended this line of inquiry. Conrad (1985) considers dynamics of the expected quality in terms of goodwill: if goodwill has promised a lower (higher) quality than the consumer experiences after the purchase, the goodwill will increase (decrease). Using optimal control theory, Conrad derives the optimal paths of quality and advertising. Likewise Ringbeck (1985) considers a profit-maximizing monopolist whose stock of customers is increased by advertising, but decays by bad quality. Differential game approaches are considered in El Ouardighi, Jørgensen, and Pasin (2008); El Ouardighi, Jorgensen, and Pasin (2013); El Ouardighi and Kogan (2013); El Ouardighi and Pasin (2006), and El Ouardighi (2014).

The next major advance in this literature was recognizing that customers can also learn about quality by communicating with others who have already used the service or bought the product. Hence, the reputational adjustment dynamics should include a term reflecting sales volume, and we do so in our model. Spremann (1985) presents the first model of which we are aware that incorporated this idea. In particular, Spremann (1985) assumes the seller’s reputation depends on both the quality-price ratio as perceived by former customers and the quantity already sold. Spremann’s model leads to two optimal equilibria: the producer is either cheap or expensive. Both equilibria are remarkable departures from price-corresponds-to-quality mode, which turns out to be sub-optimal if reputation is being generated. Feichtinger, Luhmer, and Sorger (1988) extend Spremann’s model by studying the interaction between optimal advertising and price image in detail. Caulkins, Feichtinger, Haunschmied, and Tragler (2006) incorporate similar thinking but consider a two-state optimal control model. They consider non-durables which customers purchase on an ongoing basis, so one state variable measures the number of current customers, but the second state variables, denoted as reputation, reflects the expected quality of a good. Its dynamics are driven by the gap between expected and realized quality (relative to price), as in all papers in this genre, and also by sales volume. Numerical analysis with parameters based on the U.S. cocaine market show that there might exist multiple equilibria and even persistent cycles.

Prices can independently shape perceptions of quality. Fruchter (2009) considers a model in which high prices, as well as advertising, can raise the consumers’ expectations concerning quality, and those expectations in turn have a positive effect on sales. Hence, price has both direct and indirect effects. High prices suppress sales today, for the usual reasons underpinning a downward sloping demand curve. However, charging high prices today could also have a salutary effect on demand in the long run by raising consumers’ perceptions of product quality or exclusivity. Conversely, cutting price today might temporarily boost sales but at the cost of undermining the brand’s reputation. We likewise allow for price to affect both long-run market potential and also current sales volume.

Kopalle and Winer (1996) employ the concept of reference pricing to make time-varying decisions regarding price and product quality. When the effect of a demand loss is greater or equal than that of a corresponding gain, constant optimal policies result, while otherwise it is optimal to have cyclical pricing and quality policies. Gavious and Lowengart (2012) extend Kopalle and Winer (1996) by incorporating the ability to separate the effects of reference quality and price on demand through reference quality formation. Their main result is that in the presence of reference quality effects the quality-price ratio is lower in steady state. In addition to these works, our paper considers advertising to be an additional instrument of the firm.

An apparently mostly independent line of work grew out of another observation concerning quality, and that is the interaction between quality, or at least perceived quality, and speed of service. In some settings (including health care and hair cutting), there is an inherent speed-quality tradeoff. Working faster will result in more sales and less customer waiting time but may also result in lower quality and dissatisfied customers. It would seem natural to study that tradeoff within queuing theory, but until Anand, Pac, and Veeraraghavan (2011), most queuing models implicitly assumed that the value the customer receives from the service is independent of the service duration. Recognizing the quality-speed tradeoff can produce striking results, such as the idea that intense competition can lead to firms operating competing queues to slow down, not speed up, their service.

Kostami and Rajagopalan (2014) advance that speed-quality tradeoff literature by placing it in within optimal (discrete) dynamic framework. In particular, they find the optimal balance between price and speed for the customers revenue and the congestion costs due to quality.

The two streams were not unrelated. Anand et al. (2011) had already introduced the notion of a benchmark speed, a speed at which the server is able to deliver a benchmark quality. And Kostami and Rajagopalan (2014) then make demand potential adjust over time in response to whether the actual delivered speed (and hence quality) compares favorably or unfavorably to that benchmark.

The present paper seeks to blend favorable aspects of both of these streams of research. It was motivated by Kostami and Rajagopalan (2014) but also considers advertising as another means to increase demand potential, as in the stream of papers following Kotowitz and Mathewson (1979a); 1979b), and we also think more explicitly about the gaps between customer expectations and realized quality.

We find history dependent optimal trajectories in the sense that it takes an initially large demand potential for it to be optimal to keep demand potential – and hence actual sales – high in the long run. The intuition is that investment in quality pays off especially when a large number of customers benefits from it. When the initial demand potential is too weak, the firm chooses a time path that invests less in quality and ends at a steady state where demand potential is relatively low.

This history dependent part of the solution leading to a low quality equilibrium has an outcome which is similar to Akerlof (1970). However, the big difference is that in our framework the quality of the product has a direct effect on the firm’s reputation. This is in contrast with Akerlof (1970), which focuses on markets where buyers use some market statistic. Akerlof (1970) argues that in such a scenario firms have an incentive to sell poor quality products. This is because if the quality were good, this would just add to the market statistic, so that in this way all firms benefit instead of just the individual seller.

The dynamics are more interesting than in a classic capital investment problem, however, because price is an additional control variable. On these latter trajectories the firm first increases and then decreases price. Thus the controls are not simply monotonic in the state. The price increase reduces the number of customers so that not too many of them suffer from the quality decrease, which prevents a too fast reduction of the demand potential.

Recall that the original (Kotowitz, Mathewson, 1979a, Kotowitz, Mathewson, 1979b) was motivated in part by the idea of market failure, specifically the possibility that a monopolist might over-invest in advertising experience goods. Our solution suggests that possibility of a different sort of market failure. If the higher-quality, higher-demand steady state were better from the point of view of the whole economy, it may be sensible for the government to intervene to stimulate the firm to choose the path towards this “better” steady state by subsidizing quality investments. This is an alternative to Leland (1979) and Shapiro (1983), in which the introduction of quality standards is proposed and analyzed.

The paper is organized as follows. Section 2 presents the model in an optimal control setting. Section 3 discusses the optimal policies regarding pricing, quality investment and advertising, including the existence of multiple long-run steady states. In that context, the indifference point separating the basins of attraction is discussed. Section 4 briefly considers a model variant where quality costs are linearly dependent on sales, and it is shown that history dependence survives this model change. The final Section 5 discusses conclusions and possible extensions.

Section snippets

The model

Dorfman and Steiner (1954) is the first paper offering a quantitative approach to firm behavior simultaneously dealing with price, quantity, advertising and quality, albeit in a static setting. Standing on the shoulders of so many others (see, e.g., the survey by Feichtinger, Hartl, & Sethi, 1994), we design a dynamic framework to derive optimal pricing, advertising, and quality policies.

Denote by p the price of a good, a the advertising rate, q the quality of the product, and K is the maximum

Numerical results

We numerically determine the optimal solution, using the toolbox OCMat; see http://orcos.tuwien.ac.at/research/ocmat_software/. The underlying boundary value approach is described in Grass, Caulkins, Feichtinger, Tragler, and Behrens (2008) and Grass (2012).

The parameters used are δ=0.05,α=0.5,κ=2,q¯=100,γ=0.05,r=0.03,β=0.01,θ=1.

The (K, λ)-phase portrait (Fig. 1) shows that there are two stable steady states, K1 and K2. Note that the Legendre Clebsch condition is fulfilled on the optimal

Quality costs linearly increasing in production

As mentioned above, one can also consider the case in which the cost of producing greater quality c(q) applies to each unit produced, e.g., because producing quality goods requires the firm to spend more on better materials, devote more labor hours per unit produced, etc. Broadly speaking, the earlier model which associated quality with design may be more applicable to invention and to information goods, whereas this variant may be more applicable to quality for traditional physical goods. In

Conclusions

We investigated a model in which demand potential for a product evolves over time in a manner that depends on advertising, price and quality. In particular, demand potential can be increased through advertising and undercut if the quality of goods or services sold does not live up to consumers’ notion of the desired target quality.

We find history dependent behavior, where a so-called Skiba point defines a threshold level of demand potential that divides the state space into two regions. This

Acknowledgments

The present work was supported by the Austrian Science Fund (FWF): P25979-N25 and FWO Project G.0809.12N. We would like to thank Fouad El Ouardighi and Stefan Wrzaczek for their valuable comments.

References (30)

  • F. El Ouardighi et al.

    A dynamic game with monopolist manufacturer and price-competing duopolist retailers

    OR Spectrum

    (2013)
  • F. El Ouardighi et al.

    Dynamic conformance and design quality in a supply chain: an assessment of contracts’ coordinating power

    Annals of Operations Research

    (2013)
  • G. Feichtinger et al.

    Dynamic optimal control models in advertising: recent developments

    Management Science

    (1994)
  • G. Feichtinger et al.

    Optimal price and advertising policy for a convenience goods retailer

    Marketing Science

    (1988)
  • G.E. Fruchter

    Signaling quality: dynamic price-advertising model

    Journal of Optimization Theory and Applications

    (2009)
  • Cited by (32)

    • A survey of dynamic models of product quality

      2023, European Journal of Operational Research
    • Integration of development and advertising strategies for multi-attribute products under competition

      2022, European Journal of Operational Research
      Citation Excerpt :

      Liu, Zhang, & Tang (2015) extend the work by assuming that the operations department can determine the product quality and propose the firm’s optimal transfer pricing strategy between the two departments. Caulkins et al. (2017) explore the optimal time paths for pricing, advertising, and quality for the experience products such as services where the market demand is influenced both by the experience quality and advertising. Wang, Hu, & Liu (2017) study the price and quality strategies in a market that is price-sensitive or quality-sensitive.

    • Advertising and quality improving strategies in a supply chain when facing potential crises

      2021, European Journal of Operational Research
      Citation Excerpt :

      There have been various game theoretic attempts to incorporate quality control into management activities. One common way to achieve this is to consider quality investment as a control variable contributing to goodwill build-up, customer retention, demand, potential market size and so on (see,e.g.,De Giovanni, 2011; Nair & Narasimhan, 2006; Ringbeck, 1985Bsemi He, Xu, Xu, & Wu, 2016Bsemi Buratto et al., 2019; Caulkins et al., 2017Bsemi Guan, Ye, & Yin, 2020). The marketing implications of quality are well-supported in the business literature.

    • Decisions and coordination in a capacity sharing supply chain under fixed and quality-based transaction fee strategies

      2020, Computers and Industrial Engineering
      Citation Excerpt :

      Zhu (2016) studies the pricing, quality, and timely decisions in outsourcing contracts under symmetric and asymmetric information. Caulkins et al. (2017) design a dynamic framework to derive the optimal policies of pricing, quality investment, and advertising, considering the historical dependence of demand potential. Chen, Liang, Yao, and Sun (2017) investigate the price and quality decisions in dual-channel SCs.

    View all citing articles on Scopus
    View full text