1 Introduction

Humans require, at a minimum, a certain quantity of goods and services (e.g., food, clothing, shelter, water, etc.) to function in fully autonomous ways and, perhaps more importantly, to not die prematurely. Consumption requires both economic and environmental resources, where economic growth and environmental quality share a theoretical and empirical relationship in the Environmental Kuznets Curve (EKC). The basic EKC posits that environmental harm is increasing in economic growth, where growth is typically measured by gross domestic product (“income”) per capita. At some threshold standard of living, however, further economic growth is associated with reductions in environmental harm. The EKC hence reflects an inverted U-shaped relationship between economic growth and environmental harm.

The notion that environmental harm and standards of living are cointegrated provides an important context through which basic needs or minimum consumption requirements may affect this fundamental relationship. Furthermore, the idea of an adequate standard of living is enshrined in the International Bill of Human Rights within Article 11 of the International Covenant on Economic, Social, and Cultural Rights (ICESCR). Said standard of living is often framed as a human right and, as we will see below, covers, at a minimum, a basket of goods and services required by a human to stay alive. Minimum consumption requirements in the economic sense thus share some characteristics with the objects or components of the right to an adequate standard of living. But beyond these shared characteristics, one issue is the effect on environmental harm and economic growth of attempting to meet a minimum consumption requirement. More precisely, in what ways does a minimum consumption requirement affect the fundamental characteristics of a basic EKC? What are the implications for the economy and the environment from attempting to fulfill minimum consumption requirements?

To generate some answers to these questions, we modify the basic EKC model of Andreoni and Levinson (2001) to incorporate preferences in the spirit of Stone (1954) and Geary (1950) such that the economic agent has a minimum consumption requirement, where said requirement is open to many interpretations. Working with this new model, the answers to the aforementioned questions not only further the extant EKC research, as we are unaware of any such theoretical EKC model which includes minimum consumption requirements, but the answers provide powerful policy implications with respect to the direct and indirect “costs” of privately or publicly meeting the minimum consumption requirement. We find that: (1) at each level of income, an increase in the minimum consumption requirement is associated with higher levels of pollution; and (2) the threshold level of income at which the EKC inverts changes with a change in the minimum consumption requirement. Our results imply that satisfying a minimum consumption requirement is costly both in terms of the resources required to meet this minimum and in terms of the effect it has on pollution and the pollution-growth path of the economy.

To further understand the links between minimum consumption requirements, the right to an adequate standard of living, and the EKC, the remainder of this paper is organized as follows. The next section provides two brief literature reviews: one covering the right to an adequate standard of living as outlined in the ICESCR; and another covering the EKC. This is followed by a section devoted to introducing and extending Andreoni and Levinson’s (2001) EKC model. Next is a section discussing the findings of our theoretical model coupled with a numerical exercise, both of which lend further support to the findings of the EKC model. This is followed by a section of policy implications and caveats, and then the conclusion.

2 The right to an adequate standard of living and the EKC

The right to an “adequate standard of living” is outlined in Article 11 of the ICESCR, which was opened for signature, ratification, and accession in ICESCR (1966) by the Committee for Economic, Social, and Cultural Rights (CESCR) of the United Nations.Footnote 1 In 1977, the ICESCR was entered into force, and as of 2017, it has 166 state parties, 4 signatories (including the United States), and 27 countries that have taken no action. The ICESCR highlights various economic, social, and cultural rights, and the obligations of state parties (e.g., governments) to respect, protect, and fulfill said rights. With respect to the idea of the right to an adequate standard of living, Article 11 notes that:

The States Parties to the present Covenant recognize the right of everyone to an adequate standard of living for himself and his family, including adequate food, clothing and housing, and to the continuous improvement of living conditions. The States Parties will take appropriate steps to ensure the realization of this right, recognizing to this effect the essential importance of international co-operation based on free consent.

Although the above notes that it is the obligations of state parties to “take appropriate steps…” to respect, protect, and fulfill said right, Article 2 of the ICESCR provides grounds for state parties to meet said goals on their own terms:

Each State Party to the present Covenant undertakes to take steps, individually and through international assistance and co-operation, especially economic and technical, to the maximum of its available resources, with a view to achieving progressively the full realization of the rights recognized in the present Covenant by all appropriate means, including particularly the adoption of legislative measures.

Article 2 is known as the “progressive realization” clause as it provides state parties the opportunity to interpret how they will fulfill the rights and goals found within the ICESCR, if at all, by way of devoting (or not) some share of available resources. Given that the ICESCR is not legally binding in the sense that state parties who fail to take steps to progressively realize the rights and goals found therein will be unlikely to face any formal sanctions, the progressive realization clause gives state parties the leeway to devote a range of resources, as they see fit, and call these resources the maximum available. As a result, signing and ratifying the ICESCR, in certain instances, could be nothing more than cheap talk.

Putting cheap talk aside and taking seriously the international community and its promotion of a rights-based framework, we operationalize the right to an adequate standard of living as a minimum consumption requirement. We place this consumption requirement within the EKC framework to explore how said requirement impacts the time-path of economic growth paired with environmental pollution.

Since Grossman and Helpman’s (1991) seminal EKC study, several theoretical models have been posited to motivate the existence of an EKC. Assuming exogenous growth, Lopez (1994) includes environmental quality stock as a factor of production and shows conditions that can lead to an EKC. Stokey (1998) shows the presence of an EKC depends on consumers’ demand for better environmental quality. Technology is divided into a production technology and relatively more expensive abatement technology. At higher incomes, as the marginal disutility from pollution rises, consumers increase their demand for abatement technologies. John and Pecchenino (1994) develop an overlapping generations model where the presence of an EKC largely depends on agents’ investment in environmental quality while they are young. Lieb (2004) extends John and Pecchenino’s (1994) model to two pollutants and finds an EKC. Antweiler et al. (2001) focus on the effect of trade on the environment. An increase in international trade and economic growth, in general, results in scale, composition, and techniques effects. Scale effect refers to increasing production leading to an increase in pollution. The composition effect describes countries switching from pollution-intensive manufacturing to producing services which are less harmful to the environment as the country grows richer. The technique effect refers to the adoption of green technology as an economy grows. In general, the authors conclude that increases in trade improve environmental quality as composition and technique effects outweigh the scale effect of trade. The authors support their theoretical model empirically by employing panel data estimation techniques on country level sulfur dioxide emissions reported by the Global Environmental Monitoring System (GEMS). Pfaff et al. (2004) divides household consumption into two categories: goods produced by cleaner inputs and goods produced by dirty inputs. If environmental quality is a normal good, cleaner inputs will be substituted for dirty inputs as incomes rise.

Other important theoretical EKC papers include Selden and Song (1995) and Brock and Taylor (2010). Carson (2009) and Stern (2004) provide good summaries of EKC papers including theoretical models. While other papers have used the Andreoni and Levinson (2001) model to investigate issues related to the EKC (Egli and Steger 2007; Thompson 2014), this paper appears to be the first to address the effect of a minimum consumption requirement on the presence of an EKC and its turning point.

3 Extending Andreoni and Levinson’s (2001) EKC to include a minimum consumption requirement

Andreoni and Levinson (2001) demonstrate how an Environmental Kuznets Curve (EKC) can be derived from a microfounded model of utility maximization where utility is given by,

$$ U = C - P, $$
(1)

where \( C \) represents consumption and \( P \) represents pollution. The economic agent thus receives utility from consumption and disutility from pollution. In this context, pollution takes the following form,

$$ P = C - C^{\alpha } E^{\beta } , $$
(2)

where \( E \) represents environmental effort, \( C^{\alpha } E^{\beta } \) is called the “abatement technology.” While Andreoni and Levinson (2001) use an aggregate resource constraint to facilitate solving the utility maximization problem, we use the following budget constraint, where the prices of \( C \) and \( E \) are, respectively, \( r_{C} \) and \( r_{E} \),

$$ M = r_{C} C + r_{E} E. $$
(3)

The utility maximization problem thus becomes the familiar,

$$ \mathop {\hbox{max} }\limits_{C,E} \left\{ {C^{\alpha } E^{\beta } | M = r_{C} C + r_{E} E} \right\}. $$
(4)

The utility maximizing amount of consumption and environmental effort are thus given by,

$$ C^{*} = \frac{\alpha }{\alpha + \beta }*\frac{M}{{r_{C} }}\quad {\text{and}}\quad E^{*} = \frac{\beta }{\alpha + \beta }*\frac{M}{{r_{E} }}. $$
(5)

Combining Eqs. (2) with (5), the optimal quantity of pollution is given by,

$$ P = \frac{\alpha }{\alpha + \beta }*\frac{M}{{r_{C} }} - \left( {\frac{\alpha }{\alpha + \beta }*\frac{1}{{r_{C} }}} \right)^{\alpha } \left( {\frac{\beta }{\alpha + \beta }*\frac{1}{{r_{E} }}} \right)^{\beta } M^{\alpha + \beta } . $$
(6)

After taking the derivative of Eq. (6) with respect to M, Andreoni and Levinson show that the path of P obeys a typical EKC if \( \alpha + \beta > 1 \).

Our model is not much different from Andreoni and Levinson’s. We augment Eq. (1) to the following,

$$ U = \left( {C - \gamma } \right) - P, $$
(7)

where \( \gamma \) is the minimum consumption requirement in the spirit of Stone–Geary preferences. We also modify Eq. (2) such that it becomes,

$$ P = C - \left( {C - \gamma } \right)^{\alpha } E^{\beta } . $$
(8)

Although it’s possible, we do not consider a minimum requirement on environmental effort as expending environmental effort is subjective whereas requiring a certain amount of food or water to live is a physiological imperative. Based on Eq. (8), it appears that an increase in \( \gamma \) is associated with an increase in pollution, which implies that a minimum consumption requirement has a negative impact on abatement or a positive impact on emissions. To further examine this relationship, because it is likely the case that both \( C \) and \( E \) depend on \( \gamma \), it is important to solve the relevant utility maximization problem.

Applying the same substitutions and math to arrive at a utility maximization problem, the optimal levels of consumption and environmental effort, which now depend on \( \gamma \), are given by,

$$ C_{\gamma }^{*} = \frac{\alpha }{\alpha + \beta }*\frac{1}{{r_{C} }}\left( {M + \frac{\beta }{\alpha }r_{C} \gamma } \right) \quad {\text{and}}\quad E_{\gamma }^{*} = \frac{\beta }{\alpha + \beta }*\frac{1}{{r_{E} }}\left( {M - r_{C} \gamma } \right). $$
(9)

Based on the functional forms in Eq. (9), it is easily shown that \( \frac{{\partial C_{\gamma }^{*} }}{\partial \gamma } \ge 0 \) and \( \frac{{\partial E_{\gamma }^{*} }}{\partial \gamma } \le 0 \). In other words, consumption is increasing in the minimum consumption requirement and environmental effort is decreasing. The expression for the optimal amount of pollution is now given by,

$$ P = \frac{\alpha }{\alpha + \beta }*\frac{1}{{r_{C} }}\left( {M + \frac{\beta }{\alpha }r_{C} \gamma } \right) - \left[ {\frac{\alpha }{\alpha + \beta }*\frac{1}{{r_{C} }}\left( {M + \frac{\beta }{\alpha }r_{C} \gamma } \right) - \gamma } \right]^{\alpha } \left[ {\frac{\beta }{\alpha + \beta }*\frac{1}{{r_{E} }}\left( {M - r_{C} \gamma } \right)} \right]^{\beta } , $$
(10)

which is equivalent to Eq. (6) for \( \gamma = 0 \). The equation for pollution now depends on the minimum consumption requirement where, for a given level of income, the change in pollution for a change in said requirement is given by,

$$ \frac{\partial P}{\partial \gamma } = \frac{{\partial C_{\gamma }^{*} }}{\partial \gamma } - \left\{ {\alpha \left[ {\frac{{\partial C_{\gamma }^{*} }}{\partial \gamma } - 1} \right]\left( {C_{\gamma }^{*} - \gamma } \right)^{\alpha - 1} \left( {E_{\gamma }^{*} } \right)^{\beta } + \beta \left( {C_{\gamma }^{*} - \gamma } \right)^{\alpha } \left( {E_{\gamma }^{*} } \right)^{\beta - 1} \frac{{\partial E_{\gamma }^{*} }}{\partial \gamma }} \right\} , $$
(11)

where it can be shown that \( \frac{\partial P}{\partial \gamma } \ge 0 \) thereby implying that pollution is increasing in the minimum consumption requirement. Rewriting Eq. (11) as,

$$ \frac{\partial P}{\partial \gamma } = \frac{{\partial C_{\gamma }^{*} }}{\partial \gamma } - \theta , $$
(12)

it remains to show that \( \frac{{\partial C_{\gamma }^{*} }}{\partial \gamma } \ge \theta \). Based on Eq. (9), it is clear that \( \frac{{\partial C_{\gamma }^{*} }}{\partial \gamma } \ge 0 \) and \( \frac{{\partial E_{\gamma }^{*} }}{\partial \gamma } \le 0 \). Assuming (1) \( \alpha \ge 0 \); (2) \( \beta \ge 0 \); (3) \( C_{\gamma }^{*} - \gamma \ge 0 \); and (4) \( E_{\gamma }^{*} \ge 0 \), it is clear to see that \( \frac{\partial P}{\partial \gamma } \ge 0 \) because \( \frac{{\partial C_{\gamma }^{*} }}{\partial \gamma } - 1 \le 0 \) primarily as a result of \( \alpha \ge 0 \). Furthermore, under the same assumptions of Eq. (6) for Andreoni and Levinson (2001), an EKC exists in Eq. (10) if \( \alpha + \beta > 1 \). Although it would be helpful to find a closed form solution for the turning point of Eq. (10) to then directly discuss how the minimum consumption requirement affects the turning point, the fact is that \( P \) is not separable in \( M \) because of the nonlinearity of Eq. (10) and the minimum consumption requirement and therefore a closed form solution is unattainable.

4 Numerical exercise and discussion of results

For a given set of parameters, it is straightforward to demonstrate the above results in a simple numerical simulation as seen in Fig. 1.Footnote 2 By increasing \( M \) in 0.1 unit increments and assuming \( r_{C} = r_{E} = 1, \)\( \gamma = 0.5 \), and \( \alpha + \beta > 1 \), the above statics demonstrate that relative to when the minimum consumption requirement is zero, the EKC that accounts for the minimum consumption requirement is shifted higher in pollution-income space. But it’s not just a simple upward shift, as the minimum consumption requirement is increased from zero, the threshold level of \( M \) at which pollution starts to decline is relatively larger. In other words, not only does fulfilling the minimum consumption requirement generate additional pollution for a given level of \( M \), but it also prolongs the period during which pollution is growing in \( M \). This implies that economic growth within an economy that accounts for non-zero, perhaps growing, minimum consumption requirements will experience greater levels of pollution at each level of \( M \) and also a longer period during which pollution is increasing in \( M \).

Fig. 1
figure 1

Two EKCs under the following conditions: income increments of 0.1; \( r_{C} = r_{E} = 1 \); \( \gamma = 0.5 \); and \( \alpha + \beta > 1 \)

Full size image

5 Some policy implications, and some caveats

This extension of the EKC assumes that baseline consumption cannot simply be zero, and that there must be a minimum consumption requirement for the economic agent. Whether this implies some minimum bundle of goods necessary for subsistence living or some element of meeting basic needs, the results suggest that accounting for such a requirement is costly both in terms of the resources required to meet this minimum and in terms of the effect it has on pollution and the pollution-growth path of the economy. The model and numerical exercise demonstrate that including a minimum consumption requirement increases the level of pollution at each level of \( M \). If we interpret the minimum consumption requirement within a human rights framework, where the minimum must be respected, protected, and fulfilled in some practical sense, then this model demonstrates that such human rights are expensive. They are expensive in the sense of devoting financial resources to meet, at least, the minimum consumption requirement, but also in the sense of the direct and indirect (i.e., external) costs imposed on the environment. Policy makers will thus have to consider the unintended consequences associated with respecting, protecting, and fulfilling said human rights.

While the above results are interesting, they are not without various caveats. For example, the above model assumes a single agent with unique minimum consumption requirement. It’s important to note that multiple agents would differ in their respective ability to meet or surpass their minimum consumption requirement. Furthermore, if agents are unable to meet their own minimum consumption requirements, a government that attempted to do so would have to figure out ways to obtain said resources, one of which is obviously redistribution. With respect to the nature of pollution, the above model assumes a technology that is invariant to differences in pollution across produced goods and services. A more realistic model should account for differences in pollution across consumption goods. Lastly, it would be prudent to conduct a quantitative analysis by estimating, in some form, Eq. (10), but the non-separability of \( P \) and \( M \) and the fact that data on minimum consumption requirements do not readily exist make it extremely difficult to conduct a meaningful analysis free of many forms of endogeneity.

6 Conclusion

By introducing a minimum consumption requirement into Andreoni and Levinson’s (2001) EKC model, we demonstrated that pollution is increasing in the minimum consumption requirement, and at each level of income. With a numerical exercise, we also showed that the threshold level of income at which the EKC inverts is also increasing in the minimum consumption requirement. Together these results suggest that fulfilling a minimum consumption requirement is costly in terms of the economic resources required to do so, but also in terms of the effect the requirement has on pollution and the time path of the EKC. Yet, we aren’t suggesting that policy-makers ignore minimum consumption requirements in light of these (expensive) findings, but rather that they consider the opportunity costs of redistributing resources to meet these requirements should that become a policy goal. Furthermore, that individuals, regardless of government interventions or the lack thereof, understand how their choices and minimum consumption requirements impact their economic and environmental resource base.