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Strategic Remanufacturing under Competition

  • Zhongwen Ma EMAIL logo , Ashutosh Prasad and Suresh P. Sethi

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.

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

A
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,i1,2.π1n,r=mn2βγ21βmrγ2(4β25γ2+2βγ2)2,π2r,n=F+14(4β25γ2+2βγ2)2×6β11γ4+4(β2)2γ2β23β2mn2+((β24)2+γ216+β22β9)mr2+48+β4β34γ322416β+β3γ)mnmr.
Firm 1 remanufactures (r)π1(r,n)=F+14(4β25γ2+2βγ2)2×{((6β11)γ4+4(β2)2γ2(β2)(3β2))mn2+((β24)2+γ2(16+β2(2β9))mr2+(48+β(4β34))γ32(2416β+β3)γ)mnmr}.πir,r=mn2+2γmnmr+mr22+β 3γ 2((2+β)29γ2)2+62+βγ 1γmnmr2((2+β)29γ2)2,i1,2.
B

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+αnβ2αrγ1+β24γ2>0 and αr+αrβ2αnγ1+β24γ2>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+β2γ21β1+β24γ2>0, β+β22γ21β1+β24γ2>0, and γ1+β24γ2>0.

Simplifying these, we have the requirements

β+β22γ2>0, αn1+β2αrγ>0, and 1+β2γ>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.

Proof of Theorem 1

Because 1>β>γ, we can show that 2(1+β)381+βγ20. Furthermore, in πr,rπn,n=(2γαncn1+βαrcr)22(1+β)381+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 2γαncn=1+βαrcr.

Proof of Theorem 2

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

0=(β2cr+2αr+3cnγ3αnγcrαr)αrcr((2+β)39(2+β)γ2)2×[(2+β)2(2β5)γ(αncn)+(2+β)3(αrcr)3(2+β)(1+2β)γ2(αrcr)+27γ3(αncn)].

The first term yields the root β1=2cr+2αr+3cnγ3αnγcrαr. The second term αrcr((2+β)392+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,

54γ3αncnαncn+αrcr(αrcr)3αncnαrcrγαncnαrcr.

The above term is positive if αncn<αrcr or γαncn>αrcr. 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 γαncn<αrcr<αncn 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

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