Decision Support
Warranty pricing with consumer learning

https://doi.org/10.1016/j.ejor.2017.06.024Get rights and content

Highlights

  • The dynamic warranty pricing with consumer learning is studied.

  • Warranty sales do not generate profit directly though are profitable overall.

  • Both consumers’ beliefs and the firm’s warranty policy are stable in the long run.

  • The firm only induces consumer learning when the true failure rate is high.

Abstract

We consider a problem in which a firm dynamically prices a product and its warranty service over time. Consumers can learn about the reliability of products based on warranty prices. A firm’s optimal product and warranty pricing policies are characterized. We find that a warranty should be priced lower than the marginal warranty service cost, which implies that warranty sales will not generate profits directly. However, offering a modest warranty still benefits the firm’s overall profits. We also show that consumers’ beliefs and the firm’s warranty policy converge in the long run. In a steady state, either a fraction of consumers will purchase a warranty or no consumer will purchase a warranty. Comparative statics analysis is conducted to show how factors such as a firm’s warranty service cost, consumers’ learning speed, and the heterogeneity of consumers’ handling costs determine consumers’ beliefs, the firm’s warranty policy and profitability in a steady state. Lastly, we note that a firm benefits from consumer learning by hiding the information about the true product reliability only when the true product failure rate is relatively high.

Introduction

Firms change warranty provisions for their products from time to time. For example, in October 2011, before formally introducing the iPhone 4S, Apple introduced a new Applecare+ service plan for iPhones at $99 to replace the previous $69 Applecare program (Slivka, 2011). In September 2013, before formally introducing the iPhone 5C and iPhone 5S, Apple increased the accidental damage service fee from $49 to $79 per incident, but the price for Applecare+ remained at $99 (Allen, 2013). The most recent change took place in September 2015. Before formally introducing the iPhone 6S and iPhone 6S Plus, Apple increased the price of Applecare+ for the iPhone 6S and iPhone 6S Plus from $99 to $129. Apple also increased the service fee from $79 to $99 for the new iPhone 6S and iPhone 6S Plus (Whitney, 2015).1

Apple is not the only example in practice of a firm changing its warranty provision. In the automobile industry, for example, Ford increased its powertrain warranty from 3 years or 36,000 miles to 5 years or 60,000 miles on its 2007 Ford Lincoln and Mercury models in 2006, and Kia and General Motors made similar moves in 2001 and 2006, respectively (see, Guajardo, Cohen, Netessine, 2016, Krisher, Warranty Week). In contrast, Chrysler dropped its lifetime warranty in 2009 two years after its introduction (Wernle, 2009).

Changing the warranty policy can drive a company’s profit in opposite ways. On one hand, offering a more generous warranty policy increases the cost to the firm due to a higher cost of honouring the warranty. On the other hand, a more generous warranty usually means that the warranty coverage is better or the warranty price will be lower. Thus, it increases the demand for the product by directly reducing consumers’ cost of owning it.

A more subtle yet important impact is that the warranty terms, such as the service length, price and service coverage, are considered important indicators influencing consumers’ beliefs about product reliability. As noted by extensive empirical studies, including Wiener (1985), Boulding and Kirmani (1993), Pilon (2009) and Jindal (2015), consumers tend to perceive warranty terms as an accurate and informative reflection of product reliability, and hence rely on the warranty terms and scope to make inferences about product reliability. This is also consistent with the beliefs of practitioners. As mentioned in Warranty Week (2006) and Krisher (2006), Ford and General Motors increased their warranties “in an effort to help it sell more autos by boosting its reputation for quality”, which indicates the consumers are treating the warranty as a reliable indicator of a firm’s product reliability.

In this paper, we study a dynamic model of a firm selling a single product with an optional warranty. The firm dynamically optimizes the price of the product and the price of the optional warranty. Consumers perceive the warranty price as an indicator of product reliability, and in particular, consumers perceive the product as more reliable when the warranty price is lower. Consumers have heterogeneous handling costs in case of product failures. Each consumer decides whether to buy both the product and warranty, the product only, or neither the product nor the warranty. Our goal is to consider how a firm should dynamically manage its warranty provision when warranty provision affects consumers’ beliefs about the product reliability. For example, how should a firm price its warranty policy? What is the optimal warranty policy in the long run? How does it depend on different factors, such as warranty cost and customer heterogeneity?

Our results suggest that the warranty should not be priced higher than its marginal cost; hence warranty sales by themselves should not make a profit for the firm. While this contradicts the results of some analytic models (e.g., Lutz, Padmanabhan, 1995, Padmanabhan, 1995, Padmanabhan, Rao, 1993) that state the warranties are a highly profitable service, there is no consensus among practitioners on the profitability of warranties due to some accounting issues. For example, Warranty Week (2014) questions the profitability of Applecare and Applecare+. Moreover, our results are consistent with the findings of the empirical study of Jindal (2015) that warranties should not be priced higher than its marginal costs when the warranty is sold simultaneously with the product. Thus, to some extent, our paper complements the results of this empirical study by providing support from a theoretical modeling perspective.

Our steady state analysis shows that consumers’ beliefs and the firm’s warranty policies converge. In the long run, it is possible that a fraction of consumers will purchase a warranty or no consumer purchases warranty depending on the firm’s warranty cost, consumers’ learning speed and heterogeneity of consumers’ handling costs. The long-run warranty policy and consumers’ beliefs depend on these parameters.

Lastly, we further find that the firm prefers to hide the true product reliability and manipulate consumers’ perceived beliefs about the product failure rate through learning rather than disclosing information about the true product reliability to the consumers only when the true product failure rate is relatively high.

The remainder of the paper is organized as follows. Section 2 reviews the relevant literature. Section 3 introduces the base model, and Section 4 studies the firm’s optimal dynamic product and warranty pricing problem. Section 5 compares the results with when information about true product failure rate is disclosed to the consumers to illustrate the impact of consumer learning. Section 6 extends our model to the case when there is some uncertainty in consumers’ belief updating about the product failure rate in order to validate the model robustness. Finally, Section 7 provides concluding remarks, a discussion of the limitations of this paper, and possible future research.

Section snippets

Literature review

As pointed by Emons (1989), it is generally recognized that warranties have four economic roles: insurance, screening, signaling, and incentive. For example, Heal (1977) shows that warranties provide consumers with insurance and build up a risk-sharing mechanism based on the assumption that consumers are risk averse. Chun and Tang (1995) and Zhou, Li, and Tang (2009) further examine how consumers’ risk preferences affect the optimal warranty price. Based on the idea that a firm with less

Model

A monopolist firm sells a product over repeated sales periods in an infinite horizon. At the beginning of each period, say period t, the firm sells the product at price pt and offers an optional warranty with price wt to consumers. The product and warranty prices, pt and wt, are the firm’s decisions made at the beginning of period t. The firm’s unit procurement cost of the product is c and the discounted expected warranty service cost on each unit of product is cw. Notice that cw is simply

Model analysis

In Section 4.1, we study the properties of a firm’s optimal product and warranty pricing decisions when consumers learn about the product failure rate through warranty prices. We then focus on characterizing the steady state in Section 4.2 and conduct comparative statics of the steady state in Section 4.3.

Comparison to full information about reliability

We have studied how consumers’ behavior and a firm’s pricing policies are affected by the learning mechanism in the previous sections. In this section, we are going to study the impact of consumer learning by comparing it with the case of when consumers know the true reliability.

All else is the same as before. The only difference is that the firm discloses the true reliability information and consumers have full information about the true failure rate λa. In this case, the consumer’s surplus of

Extension: uncertainty in consumers’ belief updating

In our basic model, we assume that consumers’ belief updating process about product failure rate, as given by (1), is deterministic. In reality, there are stochastic factors that can affect consumers’ beliefs on product reliability. For example, a firm may face uncertainties in online reviews, which also affect consumers’ perception on reliability and their purchasing decisions. We model this type of effect, on an abstract level, by a stochastic factor Xt, t=1,2,. We assume that {Xt} is a

Conclusion

In this paper, we consider the problem of a firm dynamically pricing a product and its warranty service in a multi-period setting when the warranty price affects consumers’ beliefs about product reliability. We show that the warranty should not be priced higher than its marginal cost, which is consistent with the findings of some empirical studies. In the long run, both a firm’s optimal warranty price and consumers’ beliefs about product failure rate converge. In particular, when the firm’s

Acknowledgments

The authors thank two anonymous reviewers for their comments and suggestions that helped to improve the paper.

References (51)

  • Warranty Week (2014). Apple’s warranty & applecare programs. Warranty Week. October...
  • G.A. Akerlof

    The market for “lemons”: Quality uncertainty and the market mechanism

    The Quarterly Journal of Economics

    (1970)
  • G. Allen

    Apple’s accountants have spotted applecare’s weaknesses

    Forbes

    (2013)
  • S. Balachander

    Warranty signalling and reputation

    Management Science

    (2001)
  • W. Blischke

    Mathematical models for analysis of warranty policies

    Mathematical and Computer Modelling

    (1990)
  • ChunY.H. et al.

    Determining the optimal warranty price based on the producer’s and customers’ risk preferences

    European Journal of Operational Research

    (1995)
  • G.A. DeCroix

    Optimal warranties, reliabilities and prices for durable goods in an oligopoly

    European Journal of Operational Research

    (1999)
  • G. Gallego et al.

    Flexible-duration extended warranties with dynamic reliability learning

    Production and Operations Management

    (2014)
  • G. Gallego et al.

    No claim? Your gain: Design of residual value extended warranties under risk aversion and strategic claim behavior

    Manufacturing & Service Operations Management

    (2014)
  • J.A. Guajardo et al.

    Service competition and product quality in the US automobile industry

    Management Science

    (2016)
  • G. Heal

    Guarantees and risk-sharing

    The Review of Economic Studies

    (1977)
  • P. Jindal

    Risk preferences and demand drivers of extended warranties

    Marketing Science

    (2015)
  • A. Kalra et al.

    Signaling quality through specialization

    Marketing Science

    (2008)
  • U.S. Karmarkar

    Future costs of service contracts for consumer durable goods

    AIIE Transactions

    (1978)
  • C.A. Kelley

    An investigation of consumer product warranties as market signals of product reliability

    Journal of the Academy of Marketing Science

    (1988)
  • Cited by (27)

    • A systematic warranty-reliability-price decision model for two-dimensional warranted products with heterogeneous usage rates

      2022, Computers and Industrial Engineering
      Citation Excerpt :

      Under different repair options, Matis, Jayaraman, and Rangan (2008) presented the optimal price and pro-rate warranty period. Lei, Liu, and Shum (2017) considered the problem of warranty price affecting customers’ beliefs on product reliability, and the multi-period optimal dynamic product’s sale price and warranty period were investigated. Shang, Si, Sun, and Jin (2018) proposed a condition-based renewable replacement warranty policy, and the optimal warranty period, sale price, and replacement threshold were optimized in a monopoly market.

    • Dynamic pricing of two-dimensional extended warranty considering the impacts of product price fluctuations and repair learning

      2021, Reliability Engineering and System Safety
      Citation Excerpt :

      The acceleration of product technology innovation and product updates means that dealers have to dynamically adjust product prices to increase sales volume and maximize profits [4,22]. Lei et al. [23] determined that the cost of some components and product prices declined at a rate of 1% per week, for example in consumer communication products and computers. Yang et al. [24] showed that the price of the Apple MacBook trended downward, meaning that selling one week earlier or later at the same price resulted in a loss of approximately 1%.

    • A stochastic simulation-optimization model for base-warranty and extended-warranty decision-making of under- and out-of-warranty products

      2020, Reliability Engineering and System Safety
      Citation Excerpt :

      Yazdian et al. [52] proposed a mathematical model to jointly optimize the selling price of used products, degree of their remanufacturing process and the length of their warranty period. Lei et al. [28] proposed a model to determine the optimal price of the product (and its warranty) when customers have the choice whether or not to buy the warranty offered by the manufacturer. Giri et al. [14] considered a two-echelon closed-loop supply chain network and developed two game-theoretic models to analyze the pricing strategies, warranty period and greening strategy.

    View all citing articles on Scopus
    View full text