How Does a “Green” Good Affect Environmental Quality and Social Welfare?

Anja Brumme

doi:10.1515/jbnst-2021-0016

Artikel

How Does a “Green” Good Affect Environmental Quality and Social Welfare?

Anja Brumme

Veröffentlicht/Copyright: 12. Mai 2022

Veröffentlicht von

Veröffentlichen auch Sie bei De Gruyter Brill

Manuskript einreichen Informationen für Autor*innen Erkunden Sie dieses Fachgebiet

Aus der Zeitschrift Jahrbücher für Nationalökonomie und Statistik Band 242 Heft 3

Abstract

In this paper an impure public good model is applied to analyze the effects of introducing a green good, i.e. a consumption good that contributes to preservation of environmental quality. I distinguish three types of consumers: “grays”, who consume the green good and a private good; “greens”, who consume the green good and make additional donations to environmental organizations; and “edge” consumers, who consume only the green good. With respect to environmental quality I find that the gap between voluntary provision and optimal provision is unaffected by the introduction of the green good, no matter if consumers are gray or green. However, in the case of gray agents environmental quality is improved in absolute terms after the green good has been launched whereas it remains at the same level as before if consumers are green. The effect of the green good on the social welfare gap is more likely to be beneficial if agents are gray. The gaps with respect to environmental quality and social welfare are both closed if the agents are edge consumers.

Keywords: environmental quality; equivalent variation; green goods; impure public goods; index of easy riding; Pareto-optimum; social welfare; voluntary provision of public goods

JEL Classification: C72; D64; H41; Q50

Corresponding author: Anja Brumme, Technische Universität Bergakademie, Freiberg, Germany, E-mail: anja.brumme@vwl.tu-freiberg.de

Appendix A: Mathematical Derivations

Derivation of Pareto-Optima

For the calculation of Pareto-optima we employ the same technique as for the Nash equilibria and transfer the maximization problems entirely to characteristics space. Recall problem (6):

max c i , c j , D , q i , q j u i ( y i , Z ) = y i γ Z 1 − γ

s . t . ∑ i = 1 2 w i = ∑ i = 1 2 c i + D + ∑ i = 1 2 q i ,

y i = c i + α q i ,

Z = D + β ∑ i = 1 2 q i ,

u j ( y j , Z ) = y j γ Z 1 − γ = u ‾ j .

For the pure public good benchmark case set q _i = q _j = 0 to obtain

max c i , c j , D u i ( y i , Z ) = y i γ Z 1 − γ

s . t . ∑ i = 1 2 w i = ∑ i = 1 2 c i + D ,

y i = c i ,

Z = D ,

u j ( y j , Z ) = y j γ Z 1 − γ = u ‾ j .

Now substitute the second and third constraint for c _i and D in the first constraint and summarize. This gives the virtual problem (7) which is expressed in characteristics space:

max y i , y j , Z u i ( y i , Z ) = y i γ Z 1 − γ

s . t . ∑ i = 1 2 w i = ∑ i = 1 2 y i + Z ,

u j ( y j , Z ) = y j γ Z 1 − γ = u ‾ j .

The first-order conditions are

(i) γ y i γ − 1 Z 1 − γ − λ 1 = 0 ,

(ii) − λ 1 − λ 2 γ y j γ − 1 Z 1 − γ = 0 ,

(iii) ( 1 − γ ) y i γ Z − γ − λ 1 − λ 2 ( 1 − γ ) y j γ Z − γ = 0 ,

(iv) ∑ i = 1 2 w i − ∑ i = 1 2 y i − Z = 0 ,

(v) u ‾ j − y j γ Z 1 − γ = 0 .

Dividing (ii) by (iii) and canceling yields

− λ 1 ( 1 − γ ) y i γ Z − γ − λ 1 = γ 1 − γ Z y j .

Insert λ ₁ = γy _i ^γ − 1 Z ^1 − γ from (i):

− γ y i γ − 1 Z 1 − γ ( 1 − γ ) y i γ Z − γ − γ y i γ − 1 Z 1 − γ = γ 1 − γ Z y j .

After canceling and rearranging we obtain

y i + y j = ∑ i = 1 2 y i = γ 1 − γ Z .

From (iv) we know that

∑ i = 1 2 y i = ∑ i = 1 2 w i − Z ,

Z ∗ ∗ = ( 1 − γ ) ∑ i = 1 2 w i ,

∑ i = 1 2 y i ∗ ∗ = γ ∑ i = 1 2 w i .

The results for the gray, green, and edge consumers are derived analogously by setting D = 0 , c _i = c _j = 0, c _i = c _j = D = 0, respectively, in (6).

Derivation of conditions (10), (11) and (12) for the determination of consumer types

Recall the original maximization problem (1):

max c i , d i , q i u i ( y i , Z ) = y i γ Z 1 − γ

s . t . w i = c i + d i + q i ,

y i = c i + α q i ,

Z = ∑ i = 1 2 z i = ∑ i = 1 2 d i + β ∑ i = 1 2 q i = D + β ∑ i = 1 2 q i .

As we know that each consumer type will purchase at most two of the three goods, this problem can be simplified and transferred to characteristics space. Starting with the gray consumer, set d _i = 0 to obtain

max c i , q i u i ( y i , Z ) = y i γ Z 1 − γ

s . t . w i = c i + q i ,

y i = c i + α q i ,

Z = ∑ i = 1 2 z i = β ∑ i = 1 2 q i = β ∑ i = 1 2 q i .

Rearranging the third constraint for q _i = (1/β)z _i, the first constraint becomes c _i = w _i − (1/β)z _i, which in turn can be inserted in the second constraint to yield y _i = w _i − (1/β)z _i + (α/β)z _i. Expressed in characteristics space, the three constraints can now be summarized in one constraint:

w i = y i + 1 − α β z i .

Adding the value of spill-ins of the other agent’s public characteristic provision to both sides of this equation results in

w i + 1 − α β z j ≠ i = y i + 1 − α β Z ,

which is equivalent to (13a). (13b) and (13c) can be obtained in the same way by setting c _i = 0 and c _i = d _i = 0, respectively.

By solving the maximization problem in characteristics space we obtain the reaction function of the gray consumer

z i = β ( 1 − γ ) 1 − α w i − γ z j ≠ i ,

and equalizing the reaction functions of both agents i and j gives the Nash equilibrium values stated in Table 1 of Appendix B.

To find the condition for a consumer to be gray, as given by (10), imagine that this agent initially purchases only the green good. This means that she will receive y _i = αw _i of the private characteristic and contribute z _i = βw _i to environmental quality. However, as this type additionally consumes the conventional good, we can conclude that she must prefer a different ratio of the private and public characteristic, i.e. y _i ^∗/z _i ^∗ > α/β. Inserting the Nash equilibrium values of the gray consumer yields

γ ( 1 − γ ) 1 − γ 2 ∑ i = 1 2 w i β 1 − α 1 − γ 1 − γ 2 ( w i − γ w j ) > α β ,

and consequently,

γ ∑ i = 1 2 w i w i − γ w j > α 1 − α .

This is equivalent to expression (10) above.

A green consumer will, according to the same reasoning, prefer more of the public and less of the private characteristic than generated by the green good alone. Hence, y _i ^∗/z _i ^∗ < α/β:

α 1 − β γ ( 1 − γ ) 1 − γ 2 ∑ i = 1 2 w i 1 − γ 1 − γ 2 ( w i − γ w j ) < α β ,

i.e.

γ ∑ i = 1 2 w i w i − γ w j < 1 − β β ,

which gives condition (11).

As α + β > 1 in case (b), α/(1 − α) > (1 − β)/β and we are left with the interval

1 − β β ≤ γ ∑ i = 1 2 w i w i − γ w j ≤ α ( 1 − α ) ,

where consumers choose only the green good and are therefore of the edge type (b3).

Appendix B: Tables

Table 1:

Nash equilibrium levels of the private and public characteristics and Nash utility levels in the pure public good (case (a)) and impure public good (cases (b1)–(b3)) frameworks.

		y i ∗	z i ∗	Z ∗	u i ( y i ∗ , Z ∗ )
(a)	Benchmark	γ ( 1 − γ ) 1 − γ 2 ∑ i = 1 2 w i	1 − γ 1 − γ 2 ( w i − γ w j )	( 1 − γ ) 2 1 − γ 2 ∑ i = 1 2 w i	( γ 1 − γ ) γ ( 1 − γ ) 2 1 − γ 2 ∑ i = 1 2 w i
(b1)	Gray consumers	γ ( 1 − γ ) 1 − γ 2 ∑ i = 1 2 w i	β 1 − α 1 − γ 1 − γ 2 ( w i − γ w j )	β 1 − α ( 1 − γ ) 2 1 − γ 2 ∑ i = 1 2 w i	γ γ ( 1 − γ ) 1 − γ 2 ( β 1 − α ( 1 − γ ) ) 1 − γ ∑ i = 1 2 w i
(b2)	Green consumers	α 1 − β γ ( 1 − γ ) 1 − γ 2 ∑ i = 1 2 w i	1 − γ 1 − γ 2 ( w i − γ w j )	( 1 − γ ) 2 1 − γ 2 ∑ i = 1 2 w i	( 1 − γ ) 2 1 − γ 2 ( α 1 − β γ 1 − γ ) γ ∑ i = 1 2 w i
(b3)	Edge consumers	αw _i	βw _i	β ∑ i = 1 2 w i	( α w i ) γ ( β ∑ i = 1 2 w i ) 1 − γ

Table 2:

Pareto-optimal levels of the private and public characteristics and Pareto utility levels in the pure public good (case (a)) and impure public good (cases (b1)–(b3)) frameworks.

		∑ i = 1 2 y i ∗ ∗	y i ∗ ∗	z i ∗ ∗	Z ∗ ∗	u i ( y i ∗ ∗ , Z ∗ ∗ )
(a)	Benchmark	γ ∑ i = 1 2 w i	γw _j	w _i − γw _j	( 1 − γ ) ∑ i = 1 2 w i	( γ w j ) γ ( ( 1 − γ ) ∑ i = 1 2 w i ) 1 − γ
(b1)	Gray consumers	γ ∑ i = 1 2 w i	γw _j	β 1 − α ( w i − γ w j )	β 1 − α ( 1 − γ ) ∑ i = 1 2 w i	( γ w j ) γ ( β 1 − α ( 1 − γ ) ∑ i = 1 2 w i ) 1 − γ
(b2)	Green consumers	α γ 1 − β ∑ i = 1 2 w i	α γ 1 − β w j	w _i − γw _j	( 1 − γ ) ∑ i = 1 2 w i	( α γ 1 − β w j ) γ ( ( 1 − γ ) ∑ i = 1 2 w i ) 1 − γ
(b3)	Edge consumers	α ∑ i = 1 2 w i	α w i	β w i	β ∑ i = 1 2 w i	( α w i ) γ ( β ∑ i = 1 2 w i ) 1 − γ

Table 3:

Index of easy riding values and social welfare gaps in the pure public good (case (a)) and impure public good (cases (b1)–(b3)) frameworks.

		IER	EV
(a)	Benchmark	1 − γ 1 − γ 2	u ‾ i ∗ ∗ 1 1 − γ ( 1 − γ ) ( γ w j ) γ 1 − γ − u ‾ i ∗ ( γ 1 − γ ) γ ( 1 − γ ) 2 1 − γ 2
(b1)	Gray consumers	1 − γ 1 − γ 2	u ‾ i ∗ ∗ 1 1 − γ β ( 1 − γ ) 1 − α ( γ w j ) γ 1 − γ − u ‾ i ∗ ( β 1 − α ) 1 − γ ( γ 1 − γ ) γ ( 1 − γ ) 2 1 − γ 2
(b2)	Green consumers	1 − γ 1 − γ 2	u ‾ i ∗ ∗ 1 1 − γ ( α γ 1 − β w j ) γ 1 − γ − u ‾ i ∗ ( α 1 − β γ 1 − γ ) γ ( 1 − γ ) 2 1 − γ 2
(b3)	Edge consumers	1	0

References

Andreoni, J. (1989). Giving with impure altruism: applications to charity and Ricardian equivalence. J. Polit. Econ. 97: 1447–1458, https://doi.org/10.1086/261662.Suche in Google Scholar

Andreoni, J. (1990). Impure altruism and donations to public goods: a theory of warm-glow giving. Econ. J. 100: 464–477, https://doi.org/10.2307/2234133.Suche in Google Scholar

Auld, D.A.L. and Eden, L. (1990). Public characteristics of non-public goods. Publ. Finance 45: 378–391.Suche in Google Scholar

Bergstrom, T., Blume, L., and Varian, H. (1986). On the private provision of public goods. J. Publ. Econ. 29: 25–49, https://doi.org/10.1016/0047-2727(86)90024-1.Suche in Google Scholar

Besley, T. and Ghatak, M. (2007). Retailing public goods: the economics of corporate social responsibility. J. Publ. Econ. 91: 1645–1663, https://doi.org/10.1016/j.jpubeco.2007.07.006.Suche in Google Scholar

bp (2021). Bp statistical review of world energy 2021. BP p.l.c., London.Suche in Google Scholar

Chan, N.W. and Dinelli, M. (2020). Optimal cost sharing for green goods. J. Assoc. Environ. Resour. Econ. 7: 1033–1068, https://doi.org/10.1086/709883.Suche in Google Scholar

Chan, N.W. and Kotchen, M.J. (2014). A generalized impure public good and linear characteristics model of green consumption. Resour. Energy Econ. 37: 1–16, https://doi.org/10.1016/j.reseneeco.2014.04.001.Suche in Google Scholar

Clark, C.F., Kotchen, M.J., and Moore, M.R. (2003). Internal and external influences on pro-environmental behavior: participation in a green electricity program. J. Environ. Psychol. 23: 237–246, https://doi.org/10.1016/s0272-4944(02)00105-6.Suche in Google Scholar

Cornes, R. and Hartley, R. (2007). Aggregative public good games. J. Publ. Econ. Theor. 9: 201–219, https://doi.org/10.1111/j.1467-9779.2007.00304.x.Suche in Google Scholar

Cornes, R. and Sandler, T. (1984). Easy riders, joint production, and public goods. Econ. J. 94: 580–598, https://doi.org/10.2307/2232704.Suche in Google Scholar

Cornes, R. and Sandler, T. (1994). The comparative static properties of the impure public good model. J. Publ. Econ. 54: 403–421, https://doi.org/10.1016/0047-2727(94)90043-4.Suche in Google Scholar

Cornes, R. and Sandler, T. (1996). The theory of externalities, public goods and club goods, 2nd ed. Cambridge University Press, New York.10.1017/CBO9781139174312Suche in Google Scholar

Deaton, A. and Muellbauer, J. (1991). Economics and consumer behavior. Cambridge University Press, Cambridge, Mass., New York, Melbourne, Port Chester, Sydney.Suche in Google Scholar

Diaz-Rainey, I. and Ashton, J.K. (2011). Profiling potential green electricity tariff adopters: green consumerism as an environmental policy tool? Bus. Strat. Environ. 20: 456–470, https://doi.org/10.1002/bse.699.Suche in Google Scholar

Engelmann, D., Munro, A., and Valente, M. (2017). On the behavioural relevance of optional and mandatory impure public goods. J. Econ. Psychol. 61: 134–144, https://doi.org/10.1016/j.joep.2017.04.002.Suche in Google Scholar

Finus, M. and Rübbelke, D. (2013). Public good provision and ancillary benefits: the case of climate agreements. Environ. Resour. Econ. 56: 211–226, https://doi.org/10.1007/s10640-012-9570-6.Suche in Google Scholar

Frackenpohl, G. and Pönitzsch, G. (2015). Bundling public with private goods. University of Bonn, Bonn.10.2139/ssrn.2596673Suche in Google Scholar

de Groot, J.I.M. and Steg, L. (2010). Relationships between value orientations, self-determined motivational types and pro-environmental behavioural intentions. J. Environ. Psychol. 30: 368–378, https://doi.org/10.1016/j.jenvp.2010.04.002.Suche in Google Scholar

Hansla, A., Gamble, A., Juliusson, A., and Gärling, T. (2008). Psychological determinants of attitude towards and willingness to pay for green electricity. Energy Pol. 36: 768–774, https://doi.org/10.1016/j.enpol.2007.10.027.Suche in Google Scholar

Hattori, K. (2005). Is technological progress pareto-improving for a world with global public goods? J. Econ. 84: 135–156, https://doi.org/10.1007/s00712-004-0106-6.Suche in Google Scholar

Koppel, H. and Schulze, G.G. (2013). The importance of the indirect transfer mechanism for consumer willingness to pay for fair trade products—evidence from a natural field experiment. J. Consum. Pol. 36: 369–387, https://doi.org/10.1007/s10603-013-9234-0.Suche in Google Scholar

Kotchen, M.J. (2005). Impure public goods and the comparative statics of environmentally friendly consumption. J. Environ. Econ. Manag. 49: 281–300, https://doi.org/10.1016/j.jeem.2004.05.003.Suche in Google Scholar

Kotchen, M.J. (2006). Green markets and private provision of public goods. J. Polit. Econ. 114: 816–834, https://doi.org/10.1086/506337.Suche in Google Scholar

Kotchen, M.J. (2009). Voluntary provision of public goods for bads: a theory of environmental offsets. Econ. J. 119: 883–899, https://doi.org/10.1111/j.1468-0297.2008.02215.x.Suche in Google Scholar

Kotchen, M.J. and Moore, M.R. (2007). Private provision of environmental public goods: household participation in green-electricity programs. J. Environ. Econ. Manag. 53: 1–16, https://doi.org/10.1016/j.jeem.2006.06.003.Suche in Google Scholar

Kotchen, M.J. and Moore, M.R. (2008). Conservation: from voluntary restraint to a voluntary price premium. Environ. Resour. Econ. 40: 195–215, https://doi.org/10.1007/s10640-007-9148-x.Suche in Google Scholar

Kotchen, M.J., Moore, M.R., and Clark, C.F. (2001). Environmental voluntary contracts between individuals and industry: an analysis of consumer preferences for green electricity. In: Orts, E.W. and Deketelaere, K. (Eds.), Environmental contracts: comparative approaches to regulatory innovation in the United States and Europe. Kluwer Law International, London, The Hague, Boston, pp. 409–423.Suche in Google Scholar

Lancaster, K. (1966a). A new approach to consumer theory. J. Polit. Econ. 74: 132–157, https://doi.org/10.1086/259131.Suche in Google Scholar

Lancaster, K. (1966b). Change and innovation in the technology of consumption. Am. Econ. Rev. 56: 14–23.Suche in Google Scholar

Lancaster, K. (1971). Consumer demand: a new approach. Columbia University Press, New York, London.Suche in Google Scholar

Lange, A., Schwirplies, C., and Ziegler, A. (2017). On the interrelation between the consumption of impure public goods and the provision of direct donations: theory and empirical evidence. Resour. Energy Econ. 47: 72–88, https://doi.org/10.1016/j.reseneeco.2016.11.002.Suche in Google Scholar

Lipsey, R.G. and Rosenbluth, G. (1971). A contribution to the new theory of demand: a rehabilitation of the giffen good. Can. J. Econ. 4: 131–163, https://doi.org/10.2307/133523.Suche in Google Scholar

Mitra, A. and Moore, M.R. (2018). Green electricity markets as mechanisms of public-goods provision: theory and experimental evidence. Environ. Resour. Econ. 71: 45–71, https://doi.org/10.1007/s10640-017-0136-5.Suche in Google Scholar

Munro, A. and Valente, M. (2016). Green goods: are they good or bad news for the environment? Evidence from a laboratory experiment on impure public goods. Environ. Resour. Econ. 65: 317–335, https://doi.org/10.1007/s10640-015-9898-9.Suche in Google Scholar

Murdoch, J.C. and Sandler, T. (1984). Complementarity, free riding, and the military expenditures of NATO allies. J. Publ. Econ. 25: 83–101, https://doi.org/10.1016/0047-2727(84)90045-8.Suche in Google Scholar

Muth, R.F. (1966). Household production and consumer demand functions. Econometrica 34: 699–708, https://doi.org/10.2307/1909778.Suche in Google Scholar

Oberholzer-Gee, F. (2001). Your contribution counts! An empirical analysis of the decision to support solar energy. In: Orts, E.W. and Deketelaere, K. (Eds.), Environmental contracts: comparative approaches to regulatory innovation in the United States and Europe. Kluwer Law International, London, The Hague, Boston, pp. 425–434.Suche in Google Scholar

Olson, M. (1971). The logic of collective action. Harvard University Press, Cambridge, Mass.Suche in Google Scholar

Posnett, J. and Sandler, T. (1986). Joint supply and the finance of charitable activity. Public Finance Q. 14: 209–222, https://doi.org/10.1177/109114218601400206.Suche in Google Scholar

Pugliese, T. and Wagner, J. (2011). Competing impure public goods and the sustainability of the theater arts. Econ. Bull 31: 1295–1303.Suche in Google Scholar

Rowlands, I.H., Scott, D., and Parker, P. (2003). Consumers and green electricity: profiling potential purchasers. Bus. Strat. Environ. 12: 36–48, https://doi.org/10.1002/bse.346.Suche in Google Scholar

Sandler, T. (1996). A game-theoretic analysis of carbon emissions. In: Congleton, R.D. (Ed.), The political economy of environmental protection: analysis and evidence. University of Michigan Press, Ann Arbor, pp. 251–272.Suche in Google Scholar

Sandmo, A. (1973). Public goods and the technology of consumption. Rev. Econ. Stud. 40: 517–528, https://doi.org/10.2307/2296585.Suche in Google Scholar

Sexton, S.E. and Sexton, A.L. (2014). Conspicuous conservation: the prius halo and willingness to pay for environmental bona fides. J. Environ. Econ. Manag. 67: 303–317, https://doi.org/10.1016/j.jeem.2013.11.004.Suche in Google Scholar

Statista (2020). Nachhaltiger Konsum. Statista Dossier did-49771-1, Hamburg.Suche in Google Scholar

Tripathi, A. and Singh, M.P. (2016). Determinants of sustainable/green consumption: a review. Int. J. Environ. Technol. Manag. 19: 316–358, https://doi.org/10.1504/ijetm.2016.082258.Suche in Google Scholar

Vicary, S. (2009). The voluntary provision of a public good in an international commons. Can. J. Econ. 42: 984–996, https://doi.org/10.1111/j.1540-5982.2009.01535.x.Suche in Google Scholar

Vicary, S. (2011). Public goods and the commons: a common framework. J. Publ. Econ. Theor. 13: 47–69, https://doi.org/10.1111/j.1467-9779.2010.01492.x.Suche in Google Scholar

Wichman, C.J. (2016). Incentives, green preferences, and private provision of impure public goods. J. Environ. Econ. Manag. 79: 208–220, https://doi.org/10.1016/j.jeem.2016.06.003.Suche in Google Scholar

Willer, H., Schaack, D., and Lernoud, J. (2017). Organic farming and market development in Europe and the European Union. In: Willer, H. and Lernoud, J. (Eds.), The world of organic agriculture: statistics & emerging trends 2017. Research Institute of Organic Agriculture FiBL and IFOAM - Organics International, Bonn, pp. 207–243.Suche in Google Scholar

Yadav, R. and Pathak, G.S. (2016). Young consumers’ intention towards buying green products in a developing nation: extending the theory of planned behavior. J. Clean. Prod. 135: 732–739, https://doi.org/10.1016/j.jclepro.2016.06.120.Suche in Google Scholar

Received: 2021-04-30

Accepted: 2022-04-04

Published Online: 2022-05-12

Published in Print: 2022-06-27

Sie haben derzeit keinen Zugang zu diesem Inhalt.

Artikel in diesem Heft

https://doi.org/10.1515/jbnst-2021-0016

Schlagwörter für diesen Artikel

environmental quality; equivalent variation; green goods; impure public goods; index of easy riding; Pareto-optimum; social welfare; voluntary provision of public goods