## Abstract

We analyze the interdependence between green attitude and equilibrium development of environmental quality in an endogenous growth model. Individuals take only part of their impact on pollution into account, hence there is a negative externality of capital accumulation on environmental quality. Increasing wealth or increasing pollution enhance green attitude and reduce the externality, because individuals care more about the environment if their income is higher or if pollution is more obvious. The time path of pollution as well as the evolution of equilibrium growth are shown to depend crucially on the determinants of green attitude. Ongoing growth may lead to complete internalization of the environmental externality if green attitude improves with increasing wealth, e.g. as a consequence of an increase in environmental education. In contrast, if green attitude is determined exclusively by the level of environmental quality, pollution remains at a suboptimally high level. The interdependence of wealth and pollution in the determination of environmental awareness implies more complex dynamics. Capital growth enhances green attitude and thereby decreases pollution. Improved environmental quality in turn may increase capital growth due to less green attitude and therefore slow down convergence to the sustainable balanced growth path.

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## Notes

- 1.
- 2.
Due to linear production technology defined later in Eq. (6), the interdependency between pollution and capital stock is equivalent to pollution out of production.

- 3.
In Schumacher and Zou (2008) individual perception of pollution is parametrized, too, and can differ from actual pollution. Yet in their paper, misperception refers to pollution stock and flow, not on the individual impact on pollution.

- 4.
Alternatively one might interpret \(1-\delta \) as degree of rivalry for environmental pollution. This is analogous to the presentation of congestion effects in the context of public goods (compare e.g. Edwards 1990; Glomm and Ravikumar 1994; Turnovsky 2000 chap. 13). Most environmental goods are characterized by partial rivalry, i.e. they are described by \(1>\delta >0\). Organic food, e.g., reduces individual pollution loads. This represents a kind of consumption rivalry. At the same time, the production of organic food also reduces pollution loads of the entire cultivable land. This benefits the other producers equally, i.e. there is no rivalry. This interpretation is applied in Soretz (2007).

- 5.
For numerical analysis, we specify individual awareness as \(\delta (k,P)= k^{\xi _k}P^{\xi _P}\).

- 6.
The time preference rate could also be assumed to decrease in green attitude. In this paper, we assume \(\rho \) independent from green attitude because we focus on the implications of green attitude on free riding behavior and the corresponding changes in the negative externality rather than on short-sightedness.

- 7.
This result is closely related to the assumption of a one-sector economy. If there were, e.g. an additional sector for human capital that accumulates without pollution, pollution had neither impact on the optimal nor on the equilibrium growth rate (e.g. Gradus and Smulders 1993) Besides, it is shown that the equilibrium environmental quality is the lower, the lower is the extent of environmental pollution that individuals perceive as being the outcome of their own activity. Nevertheless, the dynamics resulting from the interdependence between capital accumulation, green attitude and pollution are more complex.

- 8.
In the following, we use the notation \(\dot{x}= \partial x/\partial t\) and \(\hat{x}= \dot{x}/x\).

- 9.
This condition will become obvious as soon as dynamic equilibrium is solved, see (18).

- 10.
- 11.
We verified that the displayed results do not change in the ranges \(0<\rho \le 0.2, 0<\varepsilon \le 0.9, 0.1\le A\le 4, -5\le \xi _P\le 0, -5\le \xi _k\le 0\). Nevertheless, where necessary we set the parameters as follows. Since we use the

*Ak*technology with a broad measure of capital, we choose the capital coefficient relatively small and set \(A=0.4\). With \(\gamma =0.8<1\) pollution is decided to be less important for utility than consumption. The rate of time preference is set to \(\rho =0.05\) and intertemporal substitution to \(\varepsilon =0.1\), which is a quite small value, but results in regular values for steady state capital growth around 1.5–2 %. The impact of wealth or pollution on green attitude are set to relatively small values \(\xi _k = -0.2\) and \(\xi _P=-0.2\) because we believe that individual behavior will not change rapidly. - 12.
The dynamics would not change substantially for a positive lower bound of \(\delta \). Nevertheless, we keep the assumption \(\lim _{k\rightarrow \infty }\delta =0\) in order to simplify numerical analysis.

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## Additional information

The authors are grateful to valuable comments from Sjak Smulders, from SURED and St. Petersburg Workshop participants, and from three anonymous referees.

## Appendix: Derivation of Transitional Dynamics

### Appendix: Derivation of Transitional Dynamics

Transition to the long-run equilibrium is determined by the evolution of the consumption ratio, *c* / *k*, the pollution level, *P*, and the growth rate of capital, \(\hat{k}\). Inserting (16) within (15) and solving for \(\hat{P}\) yields

One can see that the attitude towards the environment will centrally influence the development of pollution.

The dynamics can be determined from the growth rate of capital, \(\hat{k}\), given in (13) and that of the consumption ratio, \(\widehat{c/k} = \hat{c} - \hat{k}\). It is straightforward that the growth rate of capital is determined predominantly by the consumption ratio, *c* / *k*

with

Hence, if wealth exerts influence on environmental awareness, with \(\delta _k < 0\) and \(\delta _{kk}> 0\) by assumption, \(\mu _k\) is a decreasing and convex function in *k*. If instead green attitude depends only on pollution, \(\delta _k = 0\) and \(\mu _k\) is independent from *k*.

The growth rate of the consumption ratio, \(\widehat{c/k}\), can be calculated from the growth rate of consumption (14) and capital accumulation (13). Using \(\hat{P}\) from (27) and the consumption growth rate (14) in \(\widehat{c/k}\) results in

Inserting (13) and solving for the growth rate of the consumption ratio yields

which leads to the evolution of the consumption ratio as given by

The numerator of \(\mu _c\) decreases in *k* if and only if wealth is a determinant of environmental awareness, \(\delta \)

Hence, if green attitude depends only on pollution, \(\mu _c\) is independent from *k*, too. Nevertheless, if wealth has an impact on environmental awareness, the slope of \(\mu _c\) with respect to *k* cannot be evaluated unambiguously, because the derivative of the denominator is ambiguous. However Fig. 11 shows that for all usual parameter settings \(\mu _c\) is a convex and falling function of *k* whenever \(\delta _k<0\).

Unequivocally the \(\hat{k}=0\) locus will be situated above the \(\widehat{c/k}=0\) locus whenever positive growth is feasible

To sum up, \(\mu _k\) and \(\mu _c\) are convex functions in *k* if there is an impact of capital on green attitude. They are both flat lines, if only pollution has an impact on green attitude. Moreover, \(\mu _k\) is larger than \(\mu _c\). The resulting phase diagrams are given in Fig. 4.

Finally, for infinitely large capital, the \(\hat{k}=0\) locus as well as the \(\widehat{c/k}=0\) locus become flat lines as

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Ott, I., Soretz, S. Green Attitude and Economic Growth.
*Environ Resource Econ* **70, **757–779 (2018). https://doi.org/10.1007/s10640-016-0061-z

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### Keywords

- Pollution
- Endogenous growth
- Green attitude

### JEL Classification

- O1
- O4
- Q2
- Q5