Strategic Remanufacturing under Competition

Zhongwen Ma; Ashutosh Prasad; Suresh P. Sethi

doi:10.1515/roms-2019-0019

Published by De Gruyter June 12, 2019

Strategic Remanufacturing under Competition

Zhongwen Ma , Ashutosh Prasad and Suresh P. Sethi

From the journal Review of Marketing Science

https://doi.org/10.1515/roms-2019-0019

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Abstract

We investigate firms’ remanufacturing strategies for the case of a duopoly. On the one hand, remanufactured products cannibalize sales of new products of the same firm thereby hurting its profits. On the other hand, they can be part of a profitable marketing strategy that targets different customer preferences by providing a larger number of alternatives to customers. This paper studies the tradeoff between these effects and how it is influenced by competition. We develop a model where demand functions for new and remanufactured products of each firm are derived from utility maximization by a representative consumer. This allows us to capture preference and substitution effects between all offered products in the market. We discuss how equilibrium strategies are affected by factors such as competition, substitutability, production cost as well as remanufacturing cost. For example, when competitive intensity between new and new products, and remanufactured and remanufactured products, is (high), both (neither) firms offer remanufactured products in a symmetric equilibrium. If substitution between new and remanufactured products of the same firm is low, but the remanufactured product has a lower margin than the new product, firms can be worse off from remanufacturing.

Keywords: pricing; remanufacturing; competition; operations-marketing interface

Acknowledgements

The authors thank Ernan Haruvy, Elena Katok, and seminar participants at the 2012 INFORMS International Conference in Beijing for helpful comments. Authors are listed alphabetically.

Appendix

Table 1:

Matrix of subgame equilibrium payoffs.

	Firm 2 does not remanufacture (n)	Firm 2 remanufactures (r)
Firm 1 does not remanufacture (n)	πin,n=mn2(2+β)2,∀i∈1,2.	π1n,r=mn2−β−γ2−1−βmrγ2(4−β2−5γ2+2βγ2)2,π2r,n=−F+14(4−β2−5γ2+2βγ2)2×6β−11γ4+4(β−2)2−γ2β−23β−2mn2+((β2−4)2+γ216+β22β−9)mr2+48+β4β−34γ3−224−16β+β3γ)mnmr.
Firm 1 remanufactures (r)	π1(r,n)=−F+14(4−β2−5γ2+2βγ2)2×{((6β−11)γ4+4(β−2)2−γ2(β−2)(3β−2))mn2+((β2−4)2+γ2(16+β2(2β−9))mr2+(48+β(4β−34))γ3−2(24−16β+β3)γ)mnmr}.	πir,r=mn2+2γmnmr+mr22+β −3γ 2((2+β)2−9γ2)2+62+βγ 1−γmn−mr2((2+β)2−9γ2)2,∀i∈1,2.

Proof of Lemma 1

Examining each of the demand functions, the first term in each demand function when the prices are all zero (i.e. market potentials) are positive if and only if,

αn+αnβ−2αrγ1+β2−4γ2>0 and αr+αrβ−2αnγ1+β2−4γ2>0.

This occurs if and only if αr1+β>2αnγ. This gives the condition in Lemma 1 because the other conditions are implied.

The demands are decreasing in own price, and increasing in the rival product price if and only if,

1+β−2γ21−β1+β2−4γ2>0, β+β2−2γ21−β1+β2−4γ2>0, and γ1+β2−4γ2>0.

Simplifying these, we have the requirements

β+β2−2γ2>0, αn1+β−2αrγ>0, and 1+β−2γ>0.

The last inequality is always satisfied since 1>β>γ. The first inequality is implied from the third. Finally, the middle inequality holds because αn>αr.

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Proof of Theorem 1

Because 1>β>γ, we can show that 2(1+β)3−81+βγ2≥0. Furthermore, in πr,r−πn,n=(2γαn−cn−1+βαr−cr)22(1+β)3−81+βγ2, the numerator is a square and hence nonnegative. Thus, the entire expression is nonnegative. Moreover, πr,r=πn,n if the numerator is zero, i.e. if 2γαn−cn=1+βαr−cr.

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Proof of Theorem 2

Firms are indifferent between adopting remanufacturing strategy and not adopting it iff πr,rβ−πn,nβ=0. Therefore, we have,

0=(β−−2cr+2αr+3cnγ−3αnγcr−αr)αr−cr((2+β)3−9(2+β)γ2)2×[(2+β)2(2β−5)γ(αn−cn)+(2+β)3(αr−cr)−3(2+β)(1+2β)γ2(αr−cr)+27γ3(αn−cn)].

The first term yields the root β1=−2cr+2αr+3cnγ−3αnγcr−αr. The second term αr−cr((2+β)3−92+βγ2)2 is always positive. The third term yields all the other possible roots of β. Substituting root β1 into the third term, we have,

54γ3αn−cnαn−cn+αr−cr(αr−cr)3αn−cn−αr−crγαn−cn−αr−cr.

The above term is positive if αn−cn<αr−cr or γαn−cn>αr−cr. Therefore, for β<β1, firms will be better off, while for β>β1 and β not too large, firms will be worse off. By contrast, if we have γαn−cn<αr−cr<αn−cn then for β<β1, firms will be worse off, while for β>β1 with β not too large, firms will be better off.

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Published Online: 2019-06-12

Published in Print: 2019-06-26

Strategic Remanufacturing under Competition

Abstract

Acknowledgements

Appendix

Proof of Lemma 1

Proof of Theorem 1

Proof of Theorem 2

References

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