Design for the environment: Impact of regulatory policies on product development

Accepted Manuscript

Design for the Environment: Impact of Regulatory Policies on Product Development Sirish Kumar Gouda, Sreelata Jonnalagedda, Haritha Saranga PII: DOI: Reference:

S0377-2217(15)00677-3 10.1016/j.ejor.2015.07.043 EOR 13132

To appear in:

European Journal of Operational Research

Received date: Revised date: Accepted date:

14 January 2015 10 July 2015 17 July 2015

Please cite this article as: Sirish Kumar Gouda, Sreelata Jonnalagedda, Haritha Saranga, Design for the Environment: Impact of Regulatory Policies on Product Development, European Journal of Operational Research (2015), doi: 10.1016/j.ejor.2015.07.043

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Highlights • We address an automaker’s product quality choice problem under different regulatory constraints • We propose an alternate regulatory mechanism based on traditional and environmental quality • We discuss the role of economies of scale and synergies on the quality levels provided by the automaker

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• We find that composite regulation can provide higher triple bottom line performance

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• We also analyze the triple bottom line performance of automaker under different market settings

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Design for the Environment: Impact of Regulatory Policies on Product Development

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Sirish Kumar Gouda E-317, Hostel Blocks, IIM Bangalore, Bannerghatta Road, Bangalore-560076, Karnataka 560076 India. Dr. Sreelata Jonnalagedda Indian Institute of Management Bangalore E-208, Academic block IIM Bangalore, Bannerghatta Road Bangalore, Karnataka 560076 India.

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Corresponding Author: Dr. Haritha Saranga D-105 Academic block IIM Bangalore, Bannerghatta Road Bangalore, Karnataka 560076 India. Phone: +918026993130 Fax: +918026584050 E-mail: [email protected]

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Abstract

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Globally automakers are facing pressure from their stakeholders to follow sustainable business practices and produce products that are less harmful to the environment. The introduction of gas guzzling automobiles in the US market despite the increasingly stringent emission norms highlights the widening gap between the goals of the regulators and the automakers, demanding a fresh outlook at the regulatory framework. In this paper, we therefore propose a composite regulatory standard that not only allows the regulators to control various environmental standards, but also provides automakers with an opportunity to exploit scale economies and synergies in product development. Our results show that under the composite regulations, sufficiently high economies of scale will ensure higher traditional and environmental qualities as well as higher profits for the automaker while operating in two markets as opposed to a single market. We also find under the composite regulations that, when more demanding norms are in place, despite positive synergies between traditional and environmental quality attributes, higher environmental quality is not guaranteed unless the scale economies are sufficiently high. Our work has implications for regulatory authorities in evaluating alternative policy design under heterogeneous market characteristics Preprint submitted to Elsevier

25th July 2015

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and technological synergies. Keywords: OR in environment and climate change, New Product Development (NPD), Environmental Regulations, Synergies, Economies of scale 1. Introduction

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The US automobile emission norms have become progressively stricter over the last decade, yet it is unclear whether they resulted in providing “a cleaner, healthier environment for the American people” (DiPeso, 2007, Hassett and Metcalf, 2008). The implementation of CAFE standards1 a few years ago has resulted in improvement of adjusted average fuel economy and CO2 emissions. However, the introduction of a considerable number of gas guzzlers in the market over the past few decades2 has caused setbacks, as automakers made the most of the loopholes in the gas guzzler tax scheme3 , leading to higher consumption of gasoline and subsequent increase in air pollution4 . One of the fundamental reasons for this widening gap between the goals of regulators and the automakers is the significant costs involved in developing technologies that can meet the progressively stringent norms. Given this conflict between environmental sustainability (for the regulators) and economic sustainability (for the automakers), a fresh outlook towards the regulatory framework is needed. For economic sustainability, automakers need to take cognizance of the needs of consumers in various markets. While most developed market customers focus on speed, power, comfort and safety related features in an automobile, fuel economy is one of the most important driving factors in emerging markets. In fact, the ever increasing volatility in oil prices coupled with global recession have begun to drive consumer preferences in the developed markets also towards more fuel efficient vehicles, bringing in some convergence in customer preferences between developed and developing worlds. Despite the convergence in consumer interest, the differences in regulatory norms of different countries make it difficult for automakers to provide the same products in all the markets they operate in. Ford Fiesta ECOnetic Diesel, for example, regarded amongst the most fuel efficient (85 miles per gallon) and lowest CO2 emitting (at 87 grams per km) cars5 , was not introduced in United States owing to comparatively stricter emission norms for diesel operated vehicles in the US (Spital and Wesley, 2010).

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standards are fuel efficiency norms imposed by the Environmental Protection Agency (EPA) for automobiles at the fleet level. 2 CAFE has separate standards for "passenger cars" and "light trucks", despite the majority of "light trucks" actually being used as passenger cars. As a result, the market share of "light trucks" grew steadily from 9.7% in 1979 to 47% in 2001 and remained in 50% numbers up to 2011. "CAFE 2011 SUMMARY OF FUEL ECONOMY PERFORMANCE". NHTSA. Last accessed on 2014-05-27. http://theenergycollective.com/jemillerep/104841/can-new-cafe-standards-deliver-promised-benefits 3 The Gas Guzzler Tax is imposed on new passenger cars (not trucks, minivans, and sport utility vehicles) that do not meet the required fuel economy standards. Last accessed on 2014-06-18. http://www.epa.gov/fueleconomy/guzzler/ 4 http://www.electrifyingtimes.com/gasguzzlerloophole.html According to an estimate by an NGO, Friends of the Earth, the savings in the amount of gasoline consumed would have been an astounding 490 million gallons, if the gas guzzler tax was applied to light trucks and SUVs. Last accessed on 2014-06-06. 5 http://www.ford.co.uk/Hidden/FordECOneticTechnology/tabid=tab2. Last accessed on 2014-10-18.

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While stricter emission standards are desirable from the environmental point of view, to ensure longterm sustainability of the industry and cooperation from the automakers, an effective regulation would have to allow firms to operate profitably along with ensuring lower carbon footprint (through lower consumption of fuel) and lesser emissions. A well designed set of environmental regulations can result in a better triple bottom-line performance, that is, better economic, social, and environmental performance for the firm (Elkington, 1998). In this paper we propose a composite regulatory constraint, wherein the automaker at the least has to meet a weighted sum of fuel efficiency and emission related quality levels. Such a composite standard is akin to energy star ratings in consumer durable industries such as refrigerators and washing machines. We first model a multinational automaker’s choice of traditional and environmental qualities under composite and conventional regulatory regimes. We next study the impact of (i) synergies6 between traditional and environmental qualities, (ii) production scale economies and (iii) heterogeneity in consumer valuations, on traditional and environmental quality levels provided by the automakers in different markets. In particular we look at automakers operating in both developed and emerging markets. The contrast between the two markets is that in the developed market there is consumer willingness to pay as well as stricter regulatory standards for environmental attributes compared to emerging markets. We evaluate the merits and demerits of composite regulation compared to the existing individual regulations in the presence of diverse market and regulatory conditions. Our results show that under a composite regulation, even though the emerging market consumers may not value environmental quality, sufficiently high economies of scale will ensure higher traditional and environmental qualities, as well as higher profits for the automaker while operating in two markets as opposed to a single market. If the developed country consumers have sufficiently high valuation for the environmental quality, we find that the level of environmental quality that the automaker provides increases with the economies of scale. Our results also indicate that under a composite regulation with stringent norms, higher environmental quality is not guaranteed despite synergies, unless the scale economies are sufficiently high. We believe that this paper is highly relevant to the automakers operating in both the developed and emerging markets as well as to the regulatory authorities, as it provides a fresh perspective on the way automobile emission regulations can be framed to benefit all the three stakeholders namely the customer, the environment, and the automaker. The rest of the paper is organised as follows: In section 2, we review the relevant literature. We develop the model and discuss the results in section 3 and conclude in section 4 by providing some important managerial implications. All proofs and derivations of various expressions are presented in the appendix. We provide the results, intuition behind the results and discuss the implications in the main body. 6 We

use the concept of synergy to model the relationship between traditional and environmental quality.

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2. Literature Review

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There has been a surge in the research work related to sustainable operations management in recent years (Tang and Zhou, 2012, Govindan et al., 2014). While a lot of work has been done in the areas of remanufacturing and reuse (Van der Laan and Salomon, 1997, Debo et al., 2005, Atasu et al., 2009, Wu, 2012), environmental impact on inventory decisions (Chen and Monahan, 2010, Bouchery et al., 2012, Chen et al., 2013) and green manufacturing processes and strategies (Florida, 1996, King and Lenox, 2001, Bergenwall et al., 2012, Dekker et al., 2012), very few researchers have looked at the impact of green product development on the environment(Chen, 2001, Su et al., 2011, Wang et al., 2015). The anecdotal evidence supports the wider belief that investments in sustainable operations would only lead to higher costs. Porter and Van der Linde (1995) on the other hand showcase examples from several companies which have realised higher profits, improvements in products and processes through investment in environmental aspects. They also emphasise on the role of regulatory authorities in promoting environmentally sustainable products through creation of favourable operating conditions for firms. Parry and Bento (2000) discuss the concept of a double dividend which claims that environmental taxes could simultaneously reduce the environmental impact as well as the costs of the tax reform under specific taxation schemes. In our work, we too discuss the role of regulation in promoting development of environmentally friendly products. The literature in environmental economics and sustainable operations management is replete with research on various emission regulations (such as cap and trade, taxes and subsidies) and their impact on the firms, consumers and the environment (Dobilas and MacPherson, 1997, Parry and Bento, 2000, Jaffe et al., 2004, Kroes et al., 2012, Gong and Zhou, 2013). While most of the aforementioned studies have focused on the effect of these regulations under general business conditions, very few have explored the impact of regulations on new product development in the automobile sector (Chen, 2001, Su et al., 2011, Zhang et al., 2012). Our work focuses primarily on the quality choices available to automakers during the design and product development stages and proposes a composite regulation to achieve a better triple bottom line performance. Our analytical model is similar to the micro-economic models which look at customer willingness to pay (WTP), economies of scale and product line design (Moorthy and Png, 1992, Chen, 2001, Kim and Chhajed, 2002, Krishnan and Zhu, 2006). Even though we consider customer willingness to pay and economies of scale similar to the aforementioned studies, our study deals with geographically separated markets without cannibalisation as the automaker operates independently in these markets. In his study, Chen (2001) investigates a monopolist’s decision in providing environmental and traditional qualities to different markets and the effect of government regulations on these quality levels. He finds that the monopolist will provide the same amount of total environmental quality in mass market and market segmentation strategies. He also finds that stricter environmental regulations might not benefit the environment. As mentioned in the above section, we develop our model using the concept of synergies and do not restrict our model to technological trade-offs. Su et al. (2011) is an extension of Chen’s 5

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Figure 1: Relative priority of features

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work which considers Zero-sum technology and Synergy technology for various scenarios discussed in Chen (2001). They find that the total green quality can be improved by investing in the synergy technology. While Su et al. (2011) incorporate synergies in terms of marginal costs, we consider the effect of synergies directly on the quality levels. We also incorporate and investigate the effects of composite regulations in our model as opposed to the individual regulations in the above papers. Zhang et al. (2012) extend the work of Chen (2001) by introducing subsidies given by the government into automaker’s decision making problem. They find that the subsidies result in higher total environmental quality and profits for the firm. While we use a different regulatory policy, we too investigate the impact of regulations on the triple bottom line of the firm.

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3. Model

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We model the product quality (traditional and environmental) choice of a multinational automaker in the presence of economic and regulatory constraints. We consider a scenario where the automaker is operating in both developed and emerging markets of size ni , where i = {D, E}, D and E represent developed and emerging markets respectively. For convenience in notation, we use nE = n = 1 (size of emerging market normalized to 1) and nD = N. Due to the significant investments in product development and production tooling, we assume that the automaker introduces a single product in both markets with traditional quality qt and environmental quality qe . We define the quality attributes which are highly valued by the customers as traditional qualities and those quality attributes which are provided to decrease the environmental impact as environmental qualities. Consumers, especially in the emerging markets have very low valuations for attributes with lower emissions. Our survey of dealers of a leading automaker in India revealed that customers value fuel efficiency the most and have very low valuations for lower emissions (see Figure 1). As the consumers in the emerging market value fuel efficiency as a primary quality attribute, and as consumers 6

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in the developed nations are also increasingly demanding cars with higher fuel efficiency, we consider fuel efficiency as a traditional quality. On the other hand, emission related attributes, which have some valuation in developed markets, but exhibit very little or no value in emerging markets, are categorised as environmental quality variables. As we are interested in understanding the manufacturer trade-offs under regulatory constraints, we restrict our attention to product attributes that directly translate to either traditional quality (fuel efficiency) or environmental quality (tail pipe emissions). We assume that consumer willingness to pay for the product is linear in both the traditional quality as well as the environmental quality. We also assume that consumers in a given market (developed or emerging) are homogenous in their valuation for environmental and traditional qualities. Further, we assume that consumers vary in their willingness to pay for traditional and environmental quality, and that the willingness to pay varies for developed and emerging market consumers. Specifically, consumer valuation for the product in a given market i is Ui (vti , vie , qt , qe ) = vti qt + vie qe where, vti and vie represent the valuations of a customer in market i for unit traditional and environmental quality respectively. Consistent with observations from the dealer survey in the Indian market, we assume that the emerging market consumers do not value environmental quality attributes, that is vEe = 0. For a given price pi , the automaker serves the market consumers in market i only if vti qt + vie qe − pi ≥ 0. E D For the sake of simplicity, we assume that vtE = 1, vtD = vt , vD e = ve , p = p and p = P. While automakers introduce multiple models in various markets, we only consider a single product, as our focus is primarily on the impact of an alternative regulatory policy on design decisions and not on the product line design. Another reason for focusing on a single product, is the increasing trend of introducing the same product in various markets by automakers such as GM, Ford, Toyota etc. Ford, for example, is working towards designing a global product, which can meet the needs of customers in most parts of the world under the "One Ford Strategy" 7 . While automakers independently invest in improving traditional as well as environmental quality, they are cognizant of the synergies that exist between the traditional quality attributes (such as mileage, horsepower and speed) and environmental qualities (such as lower carbon dioxide emissions). For example, ’turbocharger’ used in automobiles to provide higher power, also helps reduce the emissions through effective consumption of fuel. Another example of positive synergies is Honda’s next-generation technology, AVTEC (Advanced Variable Valve Timing and Lift Electronic Control), which improves fuel consumption and at the same time reduces emissions at both medium and high loads through internal exhaust gas recirculation and improved charging efficiency and performance (Duleep, 2011). However, inherently there can also be negative synergies between these two quality attributes. An increased vehicle size, for example, is relatively harmful to the environment given the increased emissions resulting from it. We therefore explicitly account for the interaction between traditional and environmental attributes using a synergy factor α (−1 ≤ α ≤ 1). Specifically, we assume that the manufacturer invests in input 7 http://wardsauto.com/management-amp-strategy/one-ford-strategy-key-global-challenge-executives-say. Last accessed on 2014-11-09.

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environmental quality qei . However, the resulting environmental quality due to synergies is a function of both input environmental as well as traditional qualities, as shown below:

qe = qei + αqt

(3.1)

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Modeling output environmental quality in such a manner is not just for analytical tractability but also because automakers commonly invest in traditional quality, which may result in some amount of environmental quality as well, depending upon the synergies. The examples discussed above also indicate that the causality is in the direction assumed in the above equation. We assume that the marginal cost of providing traditional quality qt and input environmental quality qei are ct qt2 and ce q2ei respectively. For convenience in notation and computation, we assume ct = c and ce = β c (β > 0). The automobile industry, since the introduction of moving assembly line by Henry Ford in the early 19th century, is known for high economies of scale as it requires capital intensive investments into plant and machinery. The tagline, the customer can have any color, so long as it is Black for Ford’s ModelT cars exemplifies these scale economies and the resultant need for higher volumes in order to reduce marginal cost of production. To account for such volume-based cost advantages we assume that the marginal cost reduces to f (θ , η) ∗ (cqt2 + β cq2ei ) where 0 θ 0 (0 < θ ≤ 1) is production economies of scale parameter, η is the total size of the market served by the automaker, and f (θ , η) = θ η . For example, if the automaker is serving only the developed market, f (θ , η) = θ N and when the automaker is serving both developed and emerging markets, f (θ , η) = θ N+1 . The automaker maximizes his profits below by choosing appropriate quality level qt and qei .

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Maximize p,P,qt ,qei N[P − θ N+1 (cqt2 + β cq2ei )] + [p − θ N+1 (cqt2 + β cq2ei )] subject to qt − p ≥ 0 vt qt + ve qe − P ≥ 0 qe = qei + αqt

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In addition to consumer choice constraint, the automaker is also subjected to regulatory constraints. We model two variants of the regulatory constrains. The first one is the individual regulations, which represents the existing set of rules in developed economies such as the US. In this case, the automaker has to comply with the regulations imposed on both the traditional qualities (e.g., fuel efficiency) as well as the environmental qualities (e.g., emission values) separately. Thus, to operate in a market where regulations are imposed upon the automaker to provide at least rt levels of traditional quality and re levels of environmental quality, we need qt ≥ rt and qe ≥ re . Similar to the customers, the regulatory bodies can only observe the output environmental quality (and not the input environmental quality because of synergies). 8

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wqt + (1 − w)qe ≥ K

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The second variant of regulatory constraint is a proposed composite regulatory constraint, which considers a weighted average of the traditional quality and the output environmental quality. Washing machine manufacturers/regulators, for example, use a formula involving the energy consumption and the water extraction index8 . Anderson et al. (1997) use a composite measure to evaluate the consumer satisfaction based on standardisation quality and customisation quality. Inspired by the use of composite measures in practice and in literature, we propose a regulatory constraint of the following nature

(3.2)

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where, w is the weight associated with traditional quality in the developed market and (1-w) is the weight associated with output environmental quality in the developed market. Here, K represents the lower bound on the weighted average of quality levels which is the minimum quality value the regulator demands from the automakers. As the emission norms in the emerging markets are at least few years behind the emission norms in the developed markets, we assume, without loss of generality, that no regulation exists in the emerging market and that the automaker has to meet only the developed market standards. Also, the customer and the government will only be able to observe the output quality levels (qe ) and hence the above constraints related to the regulations and customer valuations have the output environment quality levels, while the costs incurred by the automaker have the input quality level (qei ) in the objective function.

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4. Results and Discussion

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The automaker’s problem is discussed for the case in which he is operating in both markets and the other relevant cases can be derived from the same. The quality levels provided by the automaker under the two regulatory mechanisms are explored in the presence of synergies and economies of scale.

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Lemma 1. The optimal quality levels under the Individual Regulations (IR) case are

qt∗

 N(vt +αve )+1   N+1   2θ N+1 c(N+1) 2θ α β c(N+1)re +Nvt +1 = 2θ N+1 (N+1)c(α 2 β +1)     rt

i f rt < r¯t and re < r¯e i f rt < r¯t and re > r¯e otherwise

8 https://www.energystar.gov/index.cfm?c=clotheswash.pr_crit_clothes_washers.

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Last accessed on 2014-11-06.

(4.1)

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q∗ei

q∗e =

 Nve +αβ [N(vt +αve )+1]     2θ N+1 β c(N+1) Nve

2θ N+1 β c(N+1)    r e

+ αrt

i f rt < r¯t and re < r¯e i f rt < r¯t and re > r¯e

(4.2)

i f rt > r¯t and re < r¯e otherwise

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 Nve    2θ n+N β  c(N+1)      2θ N+1 α β c(N+1)re +Nvt +1  re − α 2θ N+1 (N+1)c(α 2 β +1) =  Nve    2θ N+1 β c(N+1)    r − αr e t

i f rt < r¯t and re < r¯e

i f rt > r¯t and re > r¯e

(4.3)

otherwise

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Nve +αβ (Nvt +αNve +1) Nvt +αNve +1 where 2θ = r¯e . Here, r¯t and r¯e represent the optimal quality N+1 c(N+1) = r¯t and 2θ N+1 β c(N+1) levels the automaker will provide when no constraints are imposed.

qt∗ =

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2θ c(N+1)  2θ N+1 β cK(N+1)(w+α−wα)+(Nvt +1)(1−w)2 −w(1−w)Nve 2θ N+1 (N+1)c[(1−w)2 +β (w+α−wα)2 ]

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Nve 2θ N+1 β c(N+1)  2θ N+1 cK(N+1)(1−w)+(w+α−wα)[Nwve −(1−w)(Nvt +1)] 2θ N+1 (N+1)c[(1−w)2 +β (w+α−wα)2 ]

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q∗e =

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Lemma 2. The optimal quality levels under the Composite Regulation (CR) case are given by,

 (N(vt +αve )+1)  Nve +αβN+1 2θ

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i f KVCQ > K otherwise

i f KVCQ > K otherwise

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β c(N+1)

2θ N+1 K(N+1)c[(1−w)+αβ (w+α−αw)]+w2 Nv

where KVCQ = [w + α(1 − w)]

e −w(1−w)(Nvt +1)] 2θ N+1 (N+1)c[(1−w)2 +β (w+α−wα)2 ]

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(4.4)

(4.5)

(4.6)

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Here, KVCQ represents the voluntary composite quality (VCQ) provided by the automaker, when no regulations are in place. The optimal quality levels under various business conditions are provided in Table 1 for individual regulations and in Table 2 for composite regulations. We next present the results under the composite regulatory regime, followed by a comparison of the individual and the composite 10

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regulatory regimes. We provide the optimal pricing levels in appendix (Tables A.1 and A.2). We also draw insights from the relevant results for the three stakeholders, namely, the automaker, regulator, and the customer. Conditions

Quality levels qt ∗ =

qei ∗ = 0

Emerging market only

vt +αβ (vt +αve ) 2θ N β c

q∗e =

= r¯e

qt∗

Nve +αβ [N(vt +αve )+1] 2θ N+1 β c(N+1)

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N(vt +αve )+1 2cθ N+1 (N+1)

i f rt > r¯t and re < r¯e otherwise

i f rt < r¯t and re < r¯e

N+1 r +Nv +1 e t = 2αβ c(N+1)θ N+1 c(α 2 β +1) 2(N+1)θ 

i f rt < r¯t and re > r¯e   rt otherwise  Nve i f rt < r¯t and re < r¯e  2θ N+1 β  c(N+1)      r − α 2αβ ct (N+1)θ N+1 re +Nvt +1 i f rt < r¯t and re > r¯e e 2(N+1)θ N+1 c(α 2 β +1) q∗ei =  Nv e  i f rt > r¯t and re < r¯e  N+1    2θ β c(N+1) r − αrt otherwise  e Nv +αβ [N(v +αv )+1] e t e  i f rt < r¯t and re < r¯e  2θ N+1 β c(N+1)  Nv ∗ e qe = 2θ N+1 β c(N+1) + αrt i f rt > r¯t and re < r¯e   r otherwise

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Both markets

ve + αrt 2θ N β c   re  N(v +αv )+1 t e   2cθ N+1 (N+1) 

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qe ∗ = 2θα c  (vt +αve )  i f rt < r¯t and re < r¯e   2θN N c 2θ αβ cre +vt ∗ qt = 2θ N c(α 2 β +1) i f rt < r¯t and re > r¯e    rt otherwise  ve i f rt < r¯t and re < r¯e   2θ N β c     N  r − α 2θ αβ cre +vt i f rt < r¯t and r > r¯e e 2θ N c(α 2 β +1) q∗ei =  ve  i f rt > r¯t and re < r¯e  N    2θ β c re − αrt otherwise  ve +αβ (vt +αve ) i f rt < r¯t and re < r¯e   2θ N β c

Developed market only

(vt +αve ) 2θ N c

1 2θ c

= r¯e

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Table 1: Optimal quality levels under various business conditions in the presence of individual regulations

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Conditions

Quality levels qt ∗ =

Emerging market only

1 2θ c

qei ∗ = 0

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qe ∗ = 2θα c    e)  (vt +αv i f K¯VCQ > K 2θ N c ∗ qt =  N 2 v −v (1−w)w]  t e  2θ Kβ c(w+α−αw)+[(1−w) otherwise 2θ N c[β (w+α−αw)2 +(1−w)2 ]     vNe i f K¯VCQ > K 2θ β c ∗ Developed market only qei =  N +(w+α−αw)[wv −v (1−w)]  e t  2K(1−w)cθ otherwise 2θ N c[β (w+α−αw)2 +(1−w)2 ]    t +αve ))  (ve +αβ (v i f K¯VCQ > K 2θ N β c ∗ qe =  N 2 v −(1−w)wv  e t  2θ Kc[αβ (w+α−αw)+(1−w)]+w otherwise 2θ N c[β (w+α−αw)2 +(1−w)2 ]    t +αve )+1  N(vN+1 i f KVCQ > K 2cθ (N+1) qt∗ =  N+1 2  t +1)(1−w) −Nve w(1−w)  2θ β cK(N+1)(w+α−αw)+(Nv otherwise 2θ N+1 (N+1)c[β (w+α−αw)2 +(1−w)2 ]     N+1Nve i f KVCQ > K 2θ β c(N+1) ∗ Both markets qei =  N+1  e −(Nvt +1)(1−w)]  2θ cK(N+1)(1−w)+(w+α−αw)[Nwv otherwise 2θ N+1 (N+1)c[β (w+α−αw)2 +(1−w)2 ]   [N(vt +αve )+1]   Nve +αβ i f KVCQ > K 2θ N+1 β c(N+1) ∗ qe =  N+1 (w+α−αw)]+Nve w2 −(Nvt +1)w(1−w)   2θ K(N+1)c[(1−w)+αβ otherwise 2θ N+1 (N+1)c[β (w+α−αw)2 +(1−w)2 ] h i h i +αve ) Note: Where K¯VCQ = [w + α(1 − w)] (vt2θ +(1 − w) 2θvNeβ c and Nc h

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Table 2: Optimal quality levels under various business conditions in the presence of composite regulations

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Recent technological advancements in the automobile industry have made possible higher fuel efficiency along with lower tailpipe emissions. Similarly, scale economies from serving larger markets enable automakers to recoup their investments into expensive product technologies. It is therefore important for automakers to understand the role of synergies and scale economies in meeting the regulatory standards as well as increasing profits. For ease of discussion, we will consider the case when the automaker is operating in the developed market (in the presence of composite standards) to understand the economic and environmental impact of various parameters, such as synergies and scale economies. However, we extend this discussion to other cases, involving only emerging market and both emerging and developed markets, as and when relevant. 12

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Proposition 1. Under the composite regulatory regime, if the regulatory constraint is not stringent enough, (i.e., K¯VCQ > K), then both quality levels (traditional and environmental quality) increase with an increase in synergy (as α increases) as well as an increase in economies of scale (as θ decreases). i

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e) + (1 − w) 2θvNeβ c , the customer valuations for the When K¯VCQ > K, where K¯VCQ = [w + α(1 − w)] (vt2θ+αv Nc respective qualities are sufficiently high and the cost of providing these qualities is sufficiently low such that the automaker is able to meet the regulatory constraint with relative ease. Under this context, an increasing value of α essentially means that as traditional quality increases, the output environmental quality also increases. Therefore, the automaker will end up providing increasing levels of environmental quality with increasing levels of α through the traditional route. Similarly, as the degree of scale economies increase, the per unit cost of producing the same quality level decreases. Therefore, to exploit the higher valuations of customers, automakers will increase the quality levels with increasing economies of scale.

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Proposition 2. If the regulatory constraint is sufficiently stringent, (i.e., K¯VCQ ≤ K), then the environmental quality will increase with increasing levels of synergy only if the economies of scale are sufficiently high i.e. if i1/N h (1−w)(w+α−αw)(vt w(1−w)−ve w2 ) ¯ θ <θ = 3 3 Kc{α(1−w) +β (w+α−αw) −(1−w)(w+α−αw)((1−w)+αβ (w+α−αw))}

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Intuitively one would expect that as synergies increase, the environmental quality will improve. However, the above proposition shows that it is not the case always. In the absence of a regulatory constraint, the optimal qualities provided by the automaker are dictated by consumer valuations and marginal costs. If the economies of scale is sufficiently high then, the automaker will take the most profitable route (traditional or environmental) that will allow him to meet the regulatory constraint. As a result, the environmental quality increases either through improved environmental input quality or through synergy effects of traditional quality. For example, BMW’s plug-in hybrid i8 sports car boasts an emission of 49 g/km because of the low-weight carbon-fiber body and efficient dynamics. However, BMW’s ability to achieve such high levels of environmental quality can be partly attributed to the high economies of scale owing to sizeable demand for these cars in the US and in China9 . On the other hand if the economies of scale are relatively low, then an increase in either traditional or environmental qualities to meet the regulatory constraint will also increase costs of providing higher quality. Without high economies of scale, the consumer valuation for environmental quality does not offset the corresponding cost of providing it. Therefore the automaker is forced to increase one of them at the expense of the other even if synergies increase. Therefore, we find that when the regulatory constraint is sufficiently stringent (that is K¯VCQ ≤ K ), the automaker provides higher levels of output environmental qualities only when there are sufficiently high economies of scale. 9 http://www.ft.com/cms/s/0/d023e0b2-067d-11e4-ba32-00144feab7de.html#axzz38MYpZojJ.

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To illustrate why environmental quality provided by the automaker decreases with increasing levels of synergy when economies of scale is low, we take a numerical example. In this example, we have assumed w= 0.65, vt = 400, ve = 200, β = 0.25, c = 2, θ = 0.98, N = 10, and K = 1000. To meet the regulatory constraint, the automaker can either increase traditional quality (qt ) or increase the input environmental environmental quality (qei ). As the level of synergy (α) increases, the automaker tends to invest more in traditional quality (qt ) and less in input environmental quality (qei ) to meet the regulatory constraint. From Figure 2, we can see that the reduction in input environmental quality with increasing levels of synergy is more than the increment in the traditional quality thus decreasing the total environmental quality (qe ) when θ > θ¯ .

Figure 2: Traditional and Environmental qualities vs Level of synergy(α)

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Proposition 3. If the regulatory constraint is sufficiently stringent, (i.e., K¯VCQ ≤ K), the automaker will provide higher environmental quality with increasing degree of economies of scale (decreasing value of t θ ), only if customer valuation for environmental quality is above a threshold value i.e. if ve > (1−w)v w

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When the regulatory constraint is not stringent, the automaker will provide optimal qualities as dictated by valuations and costs. As the stringency of the regulatory constraint increases, he is forced to make a trade-off between the two qualities in order to meet the constraint. As economies of scale increase, the marginal cost of providing both traditional and the environmental quality decreases. Therefore the trade-off will depend upon the valuations as well as the weights associated with the two qualities. The automaker will choose to increase the quality for which the regulator has assigned higher weight at the expense of the other. This results in higher environmental quality as   economies of scale increases, (1−w)vt unless the valuation for environmental quality is very low ve < w . Proposition 4. The automaker will provide higher environmental quality while operating in multiple 14

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markets than when he is operating only in the developed market, only if economies of scale are above a critical threshold, i.e., i h Nve +αβ (N(vt +αve )+1) (a) If K¯VCQ > K and KVCQ > K, then θ < (N+1)(v e +αβ (vt +αve )) (b) If K¯VCQ < K and KVCQ < K, then θ <

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i +(1 − w)

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Given that the emerging market consumers do not have any valuation for environmental quality, one would expect lower levels of environmental quality when operating in both the markets when the regulatory constraint is not too stringent. Even under a more stringent regulatory environment, the automaker can choose to provide higher traditional quality in order to extract higher prices from emerging market. Proposition 4(a) however suggests that, even in a non-stringent regulatory environment, high scale economies enable the automaker to provide higher environmental quality while operating in two markets versus a single market. Operating in two markets bring in more scale economies compared to operating in one market. On the other hand, when the regulation is stringent, the automaker is forced to trade-off between the two qualities in meeting the constraint. While the stringency does not guarantee an automatic increase in environmental quality, Proposition 4(b) shows that, if economies of scale are sufficiently high, then operating in two markets results in better environmental performance in comparison to operating in developed market only. This threshold on economies of scale clearly depends on the size of the developed market relative to emerging market. That is, if the size of the developed market is relatively large then the automaker will always provide higher environmental quality in multiple markets than when he is operating only in developed market. When one of the markets is disproportionately high, that market dictates the quality choices made by the automaker. For example, if the size of the developed market is very large, then the automaker’s presence in multiple markets will result in higher environmental quality relative to operating in the developed market. On the other hand if the emerging market size is large, then the level of environmental quality is always inferior when operating in two markets compared to developed market only.

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4.1. Economic and Environmental impact of Composite regulation In this section, we present a comparison between the impact of individual regulations and composite regulations on the triple bottom line performance of a firm as measured by its economic, environmental and social performance. The automaker’s profits reflect his economic performance, the traditional quality offered represents the social performance (from the customers standpoint) and the amount of environmental quality represents environmental performance of the firm. In the case of individual regulations, the constraints facing the automaker are such that he has to provide quality levels that are greater than the level set by the regulatory authorities for each of the two qualities separately, i.e., if the regulatory authorities impose a minimum traditional quality standard to be rt and the minimum environmental 15

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quality standard to be re , then the automaker has to ensure qt ≥ rt and qe ≥ re . A corresponding composite regulation, which considers a weighted average of the two qualities would on the other hand require the automaker to ensure wqt + (1 − w)qe ≥ wrt + (1 − w)re . Figure 3 illustrates the relationship between the composite regulation and individual regulation.

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Figure 3: Composite constraint vs Individual constraint

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Proposition 5. If α < 0 and (a) If r¯t < rt , r¯e > re and wr¯t + (1 − w)r¯e > wrt + (1 − w)re (i.e., region 3 in Figure 3), the automaker exhibits higher economic and environmental performance in the presence of composite standards than in the presence of individual standards. (b) If r¯t > rt , r¯e < re and wr¯t + (1 − w)r¯e > wrt + (1 − w)re (i.e., region 5 in Figure 3), the automaker exhibits higher economic and social performance in the presence of composite standards than in the presence of individual standards. +αve ) (vt +αve ) where, r¯t = (vt2θ and r¯e = vt +αβ Nc 2θ N β c Note that r¯t and r¯e represent the optimal quality levels the automaker will provide when no regulations are imposed. If we consider Proposition 5(a), while one would intuitively expect the automaker to provide higher environmental performance in the presence of individual regulations (as compared with composite regulations case), when there are negative synergies, our result suggests the contrary. We find that the automaker provides lower environmental quality in the presence of individual standards. When 16

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the regulatory constraint on traditional quality is very stringent, the negative synergies result in lower environmental quality under the individual regulations. However, the compensatory nature of the composite regulation allows the manufacturer to make up for the lower traditional quality with the higher levels of environmental quality. In this case, we also find that the profits of the automaker are higher in the presence of composite regulations as compared to when individual regulations are enforced, irrespective of whether the synergies are positive or negative. To understand how this plays out in practice, let us consider the example of an automaker, who is using a petrol based engine technology in one of their models (petrol based engines are known to produce lesser NOX and PM emissions but suffer from lower fuel efficiency levels than diesel based engines that produce relatively higher NOX and PM emissions). Suppose the vehicle is able to just meet the emission standards; however, the fuel efficiency standards for this type of vehicle are very high. With individual constraints, the automaker is forced to make significant investments to upgrade this specific model. However, with composite regulations in place, the automaker may work on further reduction in emissions (if it is less expensive than fuel efficiency improvement), which will allow him to compensate for the lower fuel efficiency, ultimately resulting in higher performance on the environmental front as well as cost savings for the automaker. Similarly, for Proposition 5(b), in which the regulator imposes high levels of environmental quality regulation in the presence of negative synergies, the automaker chooses to provide lower levels of traditional quality in the individual regulation case than in the case of composite standard. Also the profits under composite standard are higher than the ones the automaker earns under the individual regulations. The Ford Fiesta (ECOnetic model) exemplifies our intuition from this proposition.

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Proposition 6. In the presence of composite standards and if KVCQ > K¯VCQ > K, the automaker will provide better triple bottom line performance while operating in both markets than when he is operating only in the developed market above a critical level of economies of scale.

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Firms which have better environmental, social and economic performances are said to have a better triple bottom line performance. The above proposition implies that the automaker can provide better environmental quality and traditional quality and at the same time have higher profitability under the composite standard above a threshold level of economies of scale. Unless the cost savings from economies of scale are sufficiently high, simply being in multiple markets will not result in higher profitability or ensure better quality of the products. When KVCQ > K¯VCQ (voluntary composite quality provided by automaker in both markets is more than the voluntary composite quality provided in developed market only), both the environmental quality and traditional quality provided by the automaker while operating in both markets are greater than the quality levels provided while operating only in the developed market. Whereas, lower cost of providing traditional quality (ct ) and a larger size of the emerging market (relative to the size of developed market) help the automaker provide higher traditional quality when he is operating in both markets compared to operating in the developed market alone; higher economies of scale (lower value of θ ) help the automaker 17

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provide higher environmental quality as well (Proposition 4(a)). Thus, if the triple bottom line performance (environmental, social and economic performances) is considered, not all automakers would benefit from being present in multiple markets. Automakers like Ford, Toyota, GM etc, enjoy significant economies of scale and therefore it is not only profitable for them but also beneficial for the environment (better environmental quality) as well as the consumers (better traditional quality) when they operate in multiple markets. For example, Toyota saved more than $1000 per vehicle in material costs, by using common parts across various models (Hoffman, 2012). However, automakers like Vauxhall, Smart and Citroen who target niche segments with very little or no scale economies, are better off operating in the developed markets, where customers value both traditional as well as environmental aspects of the product. 4.2. Regulator’s toolbox

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It is highly desirable for automobile regulations to play the dual role of enforcing stricter regulations to benefit the environment and the common man; and simultaneously provide enough leeway to the automakers to expand their offerings to meet the customer needs. As discussed earlier, the current US regulations did not allow Ford Fiesta Diesel, the most fuel efficient car in the world, into the US market despite consumer interest. One of the bloggers at treehugger.com for example expressed his disappointment as follows: “Granted, diesels are more popular in Europe than in North-America, and while they tend to emit less CO2 than gasoline engines, they have their downsides too ... But they do much better than a few years ago, and the nastiest diesel emissions come from large trucks, not modern passenger vehicles...So please Ford, bring your most fuel-efficient models to this side of the Atlantic...”10 . In August 2012, the Obama administration announced that, passenger cars need to achieve, on average, 54.5 miles per gallon at the fleet level, which is almost double the standards set for 2011, at 27.3 miles per gallon. Although these CAFE standards seem stringent, they still allow the automakers to introduce environmentally unfriendly vehicles through exploitation of loopholes in the regulations. In fact, with the existing standards, it seems the regulators are unable to achieve the environmental and social targets set by the government11 . On the other hand, even though the composite regulation appears to favor the automaker, it can be constructed in such a way that regulators can create performance targets on social or environmental fronts at various points in time by altering the parameters w, rt and re . Thus the composite index approach provides sufficient flexibility to regulators to steer the automakers in a direction that is beneficial to both the society and the environment, simultaneously ensuring industry profitability. To illustrate this, we take a numerical example where we have r¯t < rt , r¯e < re which implies K¯VCQ ≤ 10 http://www.treehugger.com/cars/please-ford-bring-fiesta-econetic-71-mpg-us-north-america.html. Last accessed on 2014-09-06. 11 http://www.usnews.com/news/articles/2012/08/29/545-miles-per-gallon-for-all-cars-by-2025-not-exactly. Last accessed on 2014-10-09.

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(a) qt vs w

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K. As discussed above, r¯t and r¯e represent the optimal quality levels the automaker will provide when no regulations are imposed. In this example, we have assumed α= 0.5, vt = 400, ve = 200, β = 0.25, c = 2, θ = 0.98, N = 10, rt = 200 and re = 500. Figure 4 represents the social (traditional quality) and environmental performance of the automaker with respect to w values set by the regulator. Note that, qCR t IR and qt in figure 4(a) represent the traditional quality provided by the automaker under the composite IR constraint and individual constraint cases respectively. Similarly, qCR e and qe in figure 4(b) represent the environmental quality under composite and individual constraints. As demonstrated by the figures 4(a) & 4(b), by tweaking the values of w, the regulator can achieve higher social and environmental performance using composite regulations compared to the individual regulations. Similar observations can be made by changing the values of rt and re .

(b) qe vs w

Figure 4: Traditional and Environmental qualities vs Composite Regulatory Weight (w)

5. Managerial Implications and Conclusions We conclude based on our model and analysis that the effectiveness of introducing a green product into the market depends on the regulatory policies, firm’s economic constraints, as well as the consumer 19

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willingness to pay for environmental performance. Contrary to Chen (2001) who found that profit maximizing decisions made by a firm might not result in better environmental performance, we find that the sustainability of environmental, social and economic performance to a large extent depends on the how the regulatory framework is designed. Our results show that under the composite regulations, even though the emerging market consumers may not value environmental quality, sufficiently high economies of scale will ensure higher traditional and environmental qualities as well as higher profits for the automaker when operating in two markets compared to a single market. We also find under the composite regulation with stringent norms, higher environmental quality is not guaranteed despite positive synergies, unless the scale economies are sufficiently high. If the developed country consumers have sufficiently high valuation for the environmental quality, we find that the level of environmental quality that the automaker provides is positively correlated to the economies of scale. Our model will help the automobile manufacturers in deciding the quality levels to be provided given a specific regulatory constraint. It also helps automakers in deciding if and when to operate in markets with varying levels of regulations and customer valuations for environmental quality. Another unique feature of our model is the concept of synergy between qualities and its impact on quality level decisions. Our results show that the automakers as well as the environment will be better off when there are higher synergies. The Ford Fiesta (ECOnetic model) further exemplifies the benefits of a composite regulation versus individual regulation. Even though the ECOnetic outperformed all other cars from across the world on fuel efficiency (traditional quality) parameter, it failed to meet the emission regulations in the US, due to its diesel based engine. In order to introduce the ECOnetic in the US, Ford would have had to invest close to $350 million and tweak the engine to meet the US emission standards. The huge investment which required the sale of a minimum of 350,000 vehicles to break-even, coupled with the negative sentiment about diesel cars in the US, made it an unviable option for the automaker (Spital and Wesley, 2010). Therefore, Ford instead decided to introduce a petrol based (ECO-boost) Ford Fiesta in the US market, which, while meeting the emission standards, has much lower fuel efficiency than the ECOnetic model. We conjecture based on our model that, the use of a composite regulation in the US would have allowed ECOnetic model to make up for its higher emissions through higher fuel efficiency performance, which is valued by customers and therefore would have resulted in better performance by the automaker on the social front. For the regulatory bodies, this model provides a framework for evaluating alternative policy design, based on market characteristics and technological path dependencies. Firms will be motivated to take up greener product development when they perceive an economic benefit from the same. While regulatory policies help maintain some environmental standards, stringent regulations might lead to a case where the overall environmental quality provided will be lower, if the industry’s economic incentives are not taken into account during the policy design. While the significant investments required for product development, production tooling and the as20

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sociated scale economies drive automakers towards introducing the same products across the world, the inflexible norms as exemplified by Ford Fiesta make it difficult to exploit these scale economies. Therefore, there is a need for the regulatory authorities to recognise the fact that technological innovation in the auto sector in general is incremental and path dependent rather than disruptive in nature. Considering this, our proposed composite regulation allows the regulatory bodies to push for innovation in both the traditional and environmental qualities by tweaking the weights in the regulatory constraint. One of the limitations of our model is the assumption that the valuations for the traditional and environmental qualities are quantifiable and the customer can evaluate them clearly while making purchase decisions. It might be difficult for the consumers to quantify some of these valuations and make choices based on them. Also, we have assumed that the traditional and environmental qualities can be expressed in some equivalent terms to make comparisons with the constraints imposed by the governmental regulations. Future research can look at the impact of various policy decisions on the introduction of multiple products which are vertically differentiated. Quality decisions will then depend on various factors such as possible cannibalisation, different levels of synergy in the products and different consumer valuations for these products. Future studies can also look at the impact of various regulations on quality decisions when two or more firms are competing in a market.

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Appendix A. Tables Quality levels

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p∗ = qt ∗ = 2θ1 c  v2e (vt +αve )2  i f rt < r¯t and re < r¯e   2θ N c + 2θ N βc    2θ N αβ cre +vt  vt 2θ N c α 2 β +1 + ve re i f rt < r¯t and re > r¯e ( ) P∗ = 2    i f rt > r¯t and re < r¯e (vt + αve )rt + 2θvNeβ c     vt rt + ve re otherwise  N(v +αv )+1 t e  i f rt < r¯t and re < r¯e   2cθ N+1 (N+1)N+1 2αβ c(N+1)θ re +Nvt +1 p∗ = i f rt > r¯t and re < r¯e 2(N+1)θ N+1 c(α 2 β +1)    rt otherwise  2 2 +(v +αv ) N(v +αv ) t e t e e  + 2θ N+1Nv i f rt < r¯t and re < r¯e  N+1 (N+1) 2cθ β c(N+1)      N+!  v 2αβ c(N+1)θ re +Nvt +1 + v r i f rt < r¯t and re > r¯e t e e 2(N+1)θ N+1 c(α 2 β +1) P∗ = 2  Nve   i f rt > r¯t and re < r¯e (vt + αve )rt + 2θ N+1 β c(N+1)    vt rt + ve re otherwise

Developed market +αve ) = r¯t and only (vt2θ Nc vt +αβ (vt +αve ) 2θ N β c

= r¯e

N(vt +αve )+1 2cθ N+1 (N+1) Nve +αβ [N(vt +αve )+1] = r¯e 2θ N+1 β c(N+1)

= r¯t and

AN US

Both markets

CR IP T

Conditions

M

Table A.1: Optimal pricing under various business conditions in the presence of individual regulations

Quality levels

ED

Conditions

p∗ = qt ∗ = 2θ1 c   2 2  e)  (vt +αv + 2θvNeβ c i f K¯VCQ > K Nc 2θ Developed market only P∗ =  N 2  e w−(1−w)vt ]  2θ Kc[(vt +αve )βN (w+α−αw)+ve2(1−w)]+[v otherwise 2θ c[β (w+α−αw) +(1−w)2 ]    t +αve )+1  N(vN+1 i f KVCQ > K 2cθ (N+1) p∗ =  N+1 2  t +n)(1−w) −Nve w(1−w)  2θ β cK(N+1)(w+α−αw)+(Nv otherwise 2θ N+1 (N+1)c[β (w+α−αw)2 +(1−w)2 ]   2 N(vt +αve )2 +(vt +αve )  e  + 2θ N+1Nv i f KVCQ > K   2cθ N+1 (N+1) β c(N+1)   N+1 t +αve )β (w+α−αw)+ve (1−w)] Both markets P∗ = 2θ (N+1)Kc[(v otherwise  2θ N+1 (N+1)c[β (w+α−αw)2 +(1−w)2 ]      t (1−w)][Nw(vt +ve )−Nvt −(1−w)] + [vw−v 2θ N+1 (N+1)c[β (w+α−αw)2 +(1−w)2 ] h i h i +αve ) Note: Where K¯VCQ = [w + α(1 − w)] (vt2θ +(1 − w) 2θvNeβ c and Nc

AC

CE

PT

Emerging market only

KVCQ = [w + α(1 − w)]

h

N(vt +αve )+1 2cθ N+1 (N+1)

i h i e +(1 − w) 2θ N+1Nv β c(N+1)

Table A.2: Optimal pricing under various business conditions in the presence of composite regulations

24

ACCEPTED MANUSCRIPT

Proof of Lemma 1 Proof:The KKT simultaneous equations are given below L = N[P − θ N+1 (cqt2 + β cq2ei )] + [p − θ N+1 (cqt2 + β cq2ei )] + λ1 (qt − rt ) + λ2 (qe − re )

⇒ L = N[vt qt + ve qe − θ N+1 (cqt2 + β cq2ei )] + [qt − θ N+1 (cqt2 + β cq2ei )] + λ1 (qt − rt ) + λ2 (qe − re ) ∂L ∂ qei ∂L ∂ λ1 ∂L ∂ λ2

= N[vt + αve − θ N+1 (2cqt )] + [1 − θ N+1 (2cqt )] + λ1 + αλ2 = N[ve − θ N+1 (2β cqei )] + [0 − θ N+1 (2β cqei )] + λ2 = qt − rt

CR IP T

∂L ∂ qt

= qe − re = qei + αqt − re

Complementary slackness (CS) conditions: λ1 (qt − rt ) = 0 and λ2 (qe − re )

From CS conditions, we get λ1 > 0 and qt = rt (or) λ1 = 0 and qt > rt , and λ2 > 0 and qe = re (or) λ2 = 0 and qe > re

AN US

Using a combination of the above conditions and solving the first order conditions, we have the optimal quality levels as shown in Table 1. The optimal quality levels for other cases can be obtained in

M

a similar fashion.

Proof of Lemma 2

ED

Proof: The KKT simultaneous equations are given below L = N[P − θ N+1 (cqt2 + β cq2ei )] + [p − θ N+1 (cqt2 + β cq2ei )] + λ1 (wqt + (1 − w)qe − K)

∂L ∂ qei ∂L ∂ λ1

= N[vt + αve − θ N+1 (2cqt )] + [1 − θ N+1 (2cqt )] + λ1 (w + α(1 − w)) = N[ve − θ N+1 (2β cqei )] + [0 − θ N+1 (2β cqei )] + λ2 (1 − w) = wqt + (1 − w)(qei + αqt ) − K

CE

∂L ∂ qt

PT

⇒ L = N[vt qt + ve qe − θ N+1 (cqt2 + β cq2ei )] + [qt − θ N+1 (cqt2 + β cq2ei )] + λ1 (wqt + (1 − w)(qei + αqt ) − K)

Complementary slackness (CS) conditions: λ1 (wqt + (1 − w)qe − K) = 0

AC

⇒ λ1 > 0 and wqt + (1 − w)(qei + αqt ) = K (or) λ1 = 0 and wqt + (1 − w)(qei + αqt ) > K

Using a combination of the above conditions and solving the first order conditions, we have the

optimal quality levels as shown in Table 2. The optimal quality levels for other cases can be obtained in a similar fashion.

25

ACCEPTED MANUSCRIPT

Proof of Proposition 1 Proof: Under the composite regulatory regime, i f K¯VCQ > K, then +αve ) t +αve )) and qe ∗ = (ve +αβ2θc(v qt ∗ = (vt2θ Nc Nβc

It is easy to see that both quality levels increase with an increase in synergy (asα increases) and

CR IP T

increase in the economies of scale (asθD decreases)

Proof of Proposition 2

AN US

Proof: If K¯VCQ ≤ K , then h i ∂ qe ∂ 2θ N Kc[αβ (w+α−αw)+(1−w)]+w2 ve −(1−w)wvt = ∂α ∂α 2θ N c[β (w+α−αw)2 +(1−w)2 ]   β (1−w)(α+w−αw)[ve w2 −vt w(1−w)+2cKθ N ((1−w)+αβ (w+α−αw))] K[αβ (1−w)+β (w+α−αw)] ∂ qe ⇒ ∂α = − 2 (1−w)2 +β (w+α−αw)2 θ N c[(1−w)2 +β (w+α−αw)2 ] The output environmental quality provided will be higher with increasing levels of synergy if, ∂∂qαe > 0. Therefore,

θ N cK[αβ (1−w)+β (w+α−αw)][(1−w)2 +β (w+α−αw)2 ]−β (1−w)(α+w−αw)[ve w2 −vt w(1−w)+2cKθ N ((1−w)+αβ (w+α−αw))] 2

0 



M

θ N c[(1−w)2 +β (w+α−αw)2 ]

and as, θ N c (1 − w)2 + β (w + α − αw)2 2 > 0 



ED

⇒θ N cK αβ (1 − w)3 + β 2 (w + α − αw)3 − β (1 − w)(w + α − αw)((1 − w) + αβ (w + α − αw)) > β (1 − w)(w + α −

  αw) ve w2 − vt w(1 − w)

i1/N (1−w)(w+α−αw)(vt w(1−w)−ve w2 ) Kc{α(1−w)3 +β (w+α−αw)3 −(1−w)(w+α−αw)((1−w)+αβ (w+α−αw))}

PT

⇒θ <

h

To get a range of θ which lies between 0 and 1, we need α(1 − w)3 + β (w + α − αw)3 > (1 − w)(w + α −

CE

αw)((1 − w) + αβ (w + α − αw))

and vt (1 − w) > ve w (or) α(1 − w)3 + β (w + α − αw)3 < (1 − w)(w + α − αw)((1 − w) + αβ (w + α − αw)) and vt (1 −

AC

w) < ve w

Proof of Proposition 3 Proof: If K¯VCQ ≤ K , then h i ∂ qe ∂ 2θ N Kc[αβ (w+α−αw)+(1−w)]+w2 ve −(1−w)wvt N 2 2 ∂θ =∂θ h N 2θ c[β (w+α−αw) +(1−w) i ] h i w2 ve −(1−w)wvt ∂ t [αβ (w+α−αw)+(1−w)] ⇒ ∂∂qθe = ∂∂θ 2θ2θ NKc + ∂ θ 2θ N c[β (w+α−αw)2 +(1−w)2 ] c[β (w+α−αw)2 +(1−w)2 ]

e −(1−w)vt ) ⇒ ∂∂qθe =0 − 2θ N+1 N∗w(wv c[β (w+α−αw)2 +(1−w)2 ]

26

>

ACCEPTED MANUSCRIPT

The output environmental quality will increase with increasing levels of economy of scale if

∂ qe ∂θ

<0

(Higher θD implies lower economies of scale). Therefore, e −(1−w)vt ) − 2θ N+1 N∗w(wv <0 c[β (w+α−αw)2 +(1−w)2 ]

⇒

vD e 1−w

>

vtD w

CR IP T

Proof of Proposition 4: Proof: Part (a) h

i

h

i

h

i

N(vt +αve )+1 (vt +αve ) Nve ¯ +(1−w) Here KVCQ = [w+α(1−w)] 2cθ N+1 (N+1) +(1−w) 2θ N+1 β c(N+1) and KVCQ = [w+α(1−w)] 2θ N c If K¯VCQ > K and KVCQ > K, then the environmental quality in both the cases are given by

and

M

D If qDE e > qe , then Nve +αβ [N(vt +αve )+1] (vt +αve )) > (ve +αβ 2θ N β c 2θ N+1 β c(N+1) h i Nve +αβ (N(vt +αve )+1) ⇒ θ < (N+1)(v e +αβ (vt +αve ))

ve 2θ N β c

AN US

Nve +αβ [N(vt +αve )+1] 2θ N+1 β c(N+1) (ve +αβ (vt +αve )) qD e = 2θ N β c

qDE e =

h

Above this threshold value of θ (lower degree of economies of scale), the automaker chooses to

ED

provide lower value of environmental quality in the multiple markets case.

qD e =

PT

Part (b): When K¯VCQ < K and KVCQ < K, then the environmental quality in both the cases are given by 2θ N+1 K(N+1)c[(1−w)+αβ (w+α−αw)]+Nve w2 −(Nvt +1)w(1−w) qDE and e = 2θ N+1 (N+1)c[β (w+α−αw)2 +(1−w)2 ] 2θ N Kc[αβ (w+α−αw)+(1−w)]+w2 ve −(1−w)wvt 2θ N c[β (w+α−αw)2 +(1−w)2 ]

CE

D If qDE e > qe , then

>

2θ N Kc[αβ (w+α−αw)+(1−w)]+w2 ve −(1−w)wvt 2θ N c[β (w+α−αw)2 +(1−w)2 ]

AC

2θ N+1 K(N+1)c[(1−w)+αβ (w+α−αw)]+Nve w2 −(Nvt +1)w(1−w) 2θ N+1 (N+1)c[β (w+α−αw)2 +(1−w)2 ] 2 e w −(Nvt +1)w(1−w) ⇒ θ < Nv (N+1)[w2 ve −(1−w)wvt ]

Proof of Proposition 5: Proof: We will denote the parameters under individual regulations case with superscript IR and parameters under the composite regulations case with superscript CR. 1. If

vt +αve 2θ N c

+αve ve < rt and α( vt2θ N c ) + ( 2θ N β c ) >> re then,

27

i .

ACCEPTED MANUSCRIPT

vt +αve 2θ N c

qtIR = rt and qCR t =

ve CR qIR ei = qei = ( 2θ N β c ) ve vt +αve ve CR qIR e = ( 2θ N β c ) + αrt and qe = α( 2θ N c ) + ( 2θ N β c )

As

vt +αve 2θ N c

< rt ,

+αve ⇒ α( vt2θ N c ) > αrt , if α < 0

+αve ve ⇒ ( 2θvNeβ c ) + α( vt2θ N c ) > ( 2θ N β c ) + αrt

2

π IR = N[(vt + αve )rt + 2θ(vNe )β c − θ N (crt2 + β c( 2θvNeβ c )2 )] 2

As we have



vt +αve 2θ N c



AN US

⇒π IR = N[(vt + αve )rt + 4θ(vNe )β c − θ N crt2 ]    2    vt +αve vt +αve N 2 N IR CR − θ crt + θ c 2θ N c ⇒ π − π = N (vt + αve ) rt − 2θ N c       2 vt +αve vt +αve IR CR N 2 +θ c − rt ⇒ π − π = N (vt + αve ) rt − 2θ N c 2θ N c

CR IP T

CR ⇒ qIR e <qe      2  2   ve ve +αve N c vt +αve + v ∗ − θ + β c π CR = N (vt + αve ) vt2θ e Nc 2θ N β c 2θ N c 2θ N β c

< rt , we can prove that π IR − π CR < 0.

The second result in proposition 5 can be proved in a similar way as above.

M

Proof of Proposition 6:

ED

Proof: Triple bottom line performance is represented by traditional quality, environmental quality and profits the firm achieves under a business condition. h

N(vt +αve )+1 2cθ N+1 (N+1)

PT

Here KVCQ = [w+α(1−w)]

i h i h i h i ve e) e ¯VCQ = [w+α(1−w)] (vt +αv +(1−w) 2θ N+1Nv and K +(1−w) . N N 2θ c 2θ β c β c(N+1)

If KVCQ > K¯VCQ > K, then the environmental quality in both the cases are given by

CE

Nve +αβ [N(vt +αve )+1] 2θ N+1 β c(N+1) (ve +αβ (vt +αve )) qD e = 2θ N β c

qDE e =

and

AC

D If qDE e > qe , then

Nve +αβ [N(vt +αve )+1] (vt +αve )) > (ve +αβ 2θ N β c 2θ N+1 β c(N+1) h i Nve +αβ (N(vt +αve )+1) ⇒ θ < (N+1)(v e +αβ (vt +αve ))

Similarly,

If qtDE > qtD , then N(vt +αve )+1 +αve ) > (vt2θ Nc 2cθ N+1 (N+1) h i N(vt +αve )+1 ⇒ θ < (N+1)(vt +αve )

28

ACCEPTED MANUSCRIPT

DE > π D , then and If π 

(N + 1) (vt + αve )



N(vt +αve )+1 2cθ N+1 (N+1)



+ ve ∗



Nve 2θ N+1 β c(N+1)



    2  N(vt +αve )+1 2 Nve − θ N+1 c 2cθ + β c N+1 (N+1) 2θ N+1 β c(N+1)

       2  2  vt +αve vt +αve ve ve N > N (vt + αve ) 2θ N c + ve ∗ 2θ N β c − θ c 2θ N c + β c 2θ N β c 1 4β c(N+1)θ N+1

>

1 4β cθ N

⇒θ <

  N(N + 2)v2e + β (N(αve + vt ) + 1)(N(αve + vt ) + (2vt + 2αve − 1))

  2 ve (1 + α 2 β ) + 2αβ ve vt + β vt2 h 2

N(N+2)ve +β (N(αve +vt )+1)(N(αve +vt )+(2vt +2αve −1)) N(N+1)(v2e (1+α 2 β )+2αβ ve vt +β vt2 )

If θ < min

nh

N(N+2)v2e +β (N(αve +vt )+1)(N(αve +vt )+(2vt +2αve −1)) N(N+1)(v2e (1+α 2 β )+2αβ ve vt +β vt2 )

i

CR IP T

⇒

i h i h io N(vt +αve )+n Nve +αβ (N(vt +αve )+n) , (n+N)(v , , (n+N)(ve +αβ (vt +αve )) t +αve )

AC

CE

PT

ED

M

AN US

then the automaker has a better triple bottom line performance while operating in multiple markets.

29