Sustainability and consumption

Abstract

We consider the implications of the three pillars of sustainability (environment, economy and social justice) on consumption in a wealthy country. Building a theoretical model that includes consumers, business, government, the environment, and economic and political relations between nations, we explore how sustainability should affect the consumption behavior of consumers, charitable aid to poorer countries, and responsible environmental practices by businesses. Our model enables us to provide normative implications for consumers, society and business. Importantly, we assume that all stakeholders will optimize their self-interest, and that altruism will only partly explain behavior consistent with sustainability. Among the more non-obvious findings are that (1) the poorer the poor countries are, the less the rich countries should consume, (2) the more sensitive the global political climate is to economic inequity between the rich and poor nations, the less the rich countries should consume, and (3) if aid to poor countries is effective enough, then the more materialistic the society is, the more charitable aid it should give. We also confirm a number of more intuitive findings, such as that business should use more green technology as the taxes on pollution and/or efficiency of green technology increase, and the more resource-intensive consumption is, the less consumers should consume. Taken as a whole, the findings imply that societal consumption patterns should be sensitive to aspects of environmental impact and social justice, even if altruistic motivations are absent.

Appendix

Consumption level

We find the level of consumption, C*, that maximizes happiness, H. This is obtained as follows:

$$ \begin{array}{*{20}{c}} {\partial {\text{H}}/\partial {\text{C}} = {{\text{a}}_{\text{H}}}\left( {\partial {\text{S}}/\partial {\text{C}}} \right) = {{\text{a}}_{\text{H}}}\left[ {1 - 2{{\text{a}}_{\text{S}}}{\text{C}} - \left( {\partial {\text{P}}/\partial {\text{C}}} \right) - \left( {\partial {\text{W}}/\partial {\text{C}}} \right)} \right] = } \hfill \\ { = {{\text{a}}_{\text{H}}}\left[ {1 - 2{{\text{a}}_{\text{S}}}{\text{C}} - {{\text{a}}_{\text{P}}} - 2{{\text{a}}_{\text{W}}}\left( {{\text{C}} - {{\text{C}}_{\text{p}}}} \right)} \right] = 0\,{\text{when}}} \hfill \\ {{\text{C}} * = \left( {1 - {{\text{a}}_{\text{P}}} + 2{{\text{a}}_{\text{W}}}{{\text{C}}_{\text{p}}}} \right){/}\left( {2\left( {{{\text{a}}_{\text{S}}} + {{\text{a}}_{\text{W}}}} \right)} \right)} \hfill \\ {{\partial^2}{\text{H}}/\partial {{\text{C}}^2} = - 2{{\text{a}}_{\text{H}}}\left( {{{\text{a}}_{\text{S}}} + {{\text{a}}_{\text{W}}}} \right) < 0,\,{\text{ensuring}}\,{\text{the}}\,{\text{C}} * \,{\text{provides}}\,{\text{a}}\,{\text{maximum}}.} \hfill \\ \end{array} $$

(A1)

Sensitivity to consumption inequity

To determine the sign of

$$ \partial {\text{C}} * /\partial {{\text{a}}_{\text{W}}} = \left( {2{{\text{C}}_{\text{p}}}{{\text{a}}_{\text{S}}} + {{\text{a}}_{\text{P}}} - 1} \right){/}\left( {2{{\left( {{{\text{a}}_{\text{S}}} + {{\text{a}}_{\text{W}}}} \right)}^2}} \right) $$

(A2)

we first note that C > C_p which means that

$$ \left( {1 - {{\text{a}}_{\text{P}}} + 2{{\text{a}}_{\text{W}}}{{\text{C}}_{\text{p}}}} \right){/}\left( {2\left( {{{\text{a}}_{\text{S}}} + {{\text{a}}_{\text{W}}}} \right)} \right) > {{\text{C}}_{\text{p}}} $$

(A3)

from which we obtain $0 > 2{{\text{C}}_{\text{p}}}{{\text{a}}_{\text{S}}} + {{\text{a}}_{\text{P}}} - 1$, from which (7) follows.

Environmental sacrifice

The level of environmental sacrifice, X*, that maximizes happiness is obtained as:

$$ \begin{array}{*{20}{c}} {\partial {\text{H}}/\partial {\text{X}} = {{\text{a}}_{\text{H}}}\left( {\partial {\text{S}}/\partial {\text{X}}} \right) + {{\text{b}}_{\text{H}}} - 2{{\text{c}}_{\text{H}}}{\text{X}} = - {{\text{a}}_{\text{H}}} + {{\text{b}}_{\text{H}}} - 2{{\text{c}}_{\text{H}}}{\text{X}} = 0\,{\text{when}}} \hfill \\ {{\text{X}} * = \left( { - {{\text{a}}_{\text{H}}} + {{\text{b}}_{\text{H}}}} \right)/2{{\text{c}}_{\text{H}}}} \hfill \\ {{\partial^2}{\text{H}}/\partial {{\text{X}}^2} = - 2{{\text{c}}_{\text{H}}} < 0,\,{\text{ensuring}}\,{\text{that}}\,{\text{X}} * {\text{provides}}\,{\text{a}}\,{\text{maximum}}.} \hfill \\ \end{array} $$

(A4)

Charitable aid to poorer countries

The level of charitable aid to poor countries that maximizes happiness is:

$$ \begin{array}{*{20}{c}} {\partial {\text{H}}/\partial {\text{A}} = {{\text{a}}_{\text{H}}}\left( {\partial {\text{S}}/\partial {\text{A}}} \right) + {{\text{d}}_{\text{H}}} - 2{{\text{e}}_{\text{H}}}{\text{A}} = {{\text{a}}_{\text{H}}}\left( { - \left( {\partial {\text{W}}/\partial {\text{A}}} \right) - 1} \right) + {{\text{d}}_{\text{H}}} - 2{{\text{e}}_{\text{H}}}{\text{A}} = } \hfill \\ { = {{\text{a}}_{\text{H}}}\left( {{{\text{b}}_{\text{W}}} - 2{{\text{C}}_{\text{W}}} - 1} \right) + {{\text{d}}_{\text{H}}} - 2{{\text{e}}_{\text{H}}}{\text{A}} = 0\,{\text{when}}} \hfill \\ {A * = \left\{ {{{\text{a}}_{\text{H}}}\left( {{{\text{b}}_{\text{W}}} - 2{{\text{c}}_{\text{W}}} - 1} \right) + {{\text{d}}_{\text{H}}}} \right\}/2{{\text{e}}_{\text{H}}}} \hfill \\ {{\partial^2}{\text{H}}/\partial {{\text{A}}^2} = - 2{{\text{e}}_{\text{H}}} < 0,\,{\text{which}}\,{\text{means}}\,{\text{we}}\,{\text{have}}\,{\text{a}}\,{\text{maximum}}.} \hfill \\ \end{array} $$

(A5)

Adoption of green technology

The level of green technology that maximizes profits can be found as:

$$ \begin{array}{*{20}{c}} {\partial \Pi /\partial {\text{G}} = - {\text{t}}\left( {\partial {\text{P}}/\partial {\text{G}}} \right) - 1 = {\text{t}}{{\text{b}}_{\text{P}}} - 2{\text{t}}{{\text{c}}_{\text{P}}}{\text{G}} - 1 = 0\,{\text{when}}} \hfill \\ {{\text{G}} * = \left( {{\text{t}}{{\text{b}}_{\text{P}}} - 1} \right){/}\left( {2{\text{t}}{{\text{c}}_{\text{P}}}} \right)} \hfill \\ {{\partial^2}\Pi /\partial {{\text{G}}^2} = - 2{\text{t}}{{\text{c}}_{\text{p}}} < 0,\,{\text{ensuring}}\,{\text{a}}\,{\text{maximum}}.} \hfill \\ \end{array} $$

(A6)