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Managerial Delegation Contracts, “Green” R&D and Emissions Taxation

Joanna Poyago-Theotoky and Soo Keong Yong

Abstract

We introduce an explicit environmental incentive into a managerial compensation contract in the context of a Cournot duopoly with pollution externalities under an emissions tax regime. We show that, depending on the effectiveness of “green” R&D, compared to a standard sales compensation contract, the explicit environmental focused contract results in more abatement. As a consequence, the regulator sets a lower emissions tax, and social welfare is higher. Moreover, in general, firm owners earn higher profits when adopting the environmental delegation contract.

JEL Classification: H23; L1; M5; Q58

Acknowledgements

We wish to thank Paul Dobson, Simona Fabrizi, John Hillas, Michael Kopel, Steffen Lippert, Shravan Luckraz, Ralf Martin, Mirabelle Muuls, Partha Sen, Charles Vanmarrewijk, the Editor Burkhard C. Schipper, three anonymous referees and participants at the 2017 European Association of Environmental and Resource Economists Conference (Athens), the 2017 Singapore Economic Review Conference (Singapore) and the 2017 East Asian Association of Environmental and Resource Economics (Singapore) for helpful comments and suggestions. The earlier draft of the paper has also benefitted from the comments and suggestions from seminar participants at the Imperial College Business School and the Grantham Institute for Climate Change and the Environment.

A Appendix

A.1 Proof of Lemma 1

Proof Part (i): From (9) the first-partial derivative with respect to αi gives t(αi,αj)αi=3Aαj2γ[3(αi+αj)+4αiαjγ]2>0forij. Part (ii): From (10), xi(αi,αj)αi=Aαj(3+4αjγ)[3(αi+αj)+4αiαjγ]2<0 and xi(αi,αj)αj=3Aαi[3(αi+αj)+4αiαjγ]2>0. Part (iii): From (11), qi(αi,αj)αi=Aαi2γ[3(αi+αj)+4αiαjγ]2<0forij.

A.2 Proof of Propositions 1–3

Proposition 1 The difference in profits, after some manipulation can be written as πedπsd=A284γ2+10γ+4+2γ84γ2+10γ+4+2γ94γ(γ+1)+9+26454γ(γ+1)+9+169576(2γ+5)>0 for all γ1.

Proposition 2 Using expressions (14) and (26), we obtain tedtsd=A24γ2+10γ+4γ(2γ+5)2γ+4γ(γ+1)+9148(2γ+5)<0 for all γ1.

Proposition 3 Using expressions (13) and (25), we obtain αedαsd=11+22(2γ+1)(γ+2)2γ+39+4γ1+γ12γ0, which results in αedαsdγ2.735.

The remaining parts of the proposition are established in a similar manner, using (16),(28),(15),(27) and (6).

xedxsd=A43+2γ22+6γ39+4γ1+γ42(2γ+1)(γ+2)+159+4γ1+γ245+2γ0, or, xedxsdγ2.735. qedqsd=A43+2γ22+6γ39+4γ1+γ42(2γ+1)(γ+2)+159+4γ1+γ485+2γ0, or, qedqsdγ2.735. (e/q)ed(e/q)sd=γ24γ2+10γ+4+6γ54γ(γ+1)+9+27164γ(γ+1)+932γ(5γ+16)0 or, (e/q)ed(e/q)sdγ2.735.

SWedSWsd=A2(4γ3+284γ2+10γ+454γ(γ+1)+9+34γ2+44γ2+4γ+94γ2+10γ+444γ2+10γ+474γ(γ+1)+9+41γ+304γ2+10γ+4734γ(γ+1)+922(γ+2)(2γ+1)8γ(γ+1)+18+16524γ2+10γ+4+2γ+722γ+4γ(γ+1)+9+120,

or, SWedSWsdγ2.735.

A.3 The Case of no Delegation: Footnote 19

Equilibrium profits per firm in the case of no delegation are given by:

πnd=2γ2+9γ+8A28(2γ+3)2,

and profits in the case of environmental delegation are:

πed=134γ2+10γ+4+2γ4γ2+10γ+4+2γ+11+46A284γ2+10γ+4+2γ+72.

The difference in profits, πedπnd, after some manipulation becomes (2γ+1)54γ2+10γ+42+γ64γ2+10γ+46γ11A28(2γ+3)24γ2+10γ+4+2γ+72.

It is then evident, that this difference is positive for γ1.

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Published Online: 2018-12-11

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