Moving Toward Greener Societies: Moral Motivation and Green Behaviour

Abstract

I provide an alternative explanation for why societies exhibit varied environmental behaviours. I use a Kantian moral approach at a microeconomic level. I show that two identical societies (in terms of income level and political system) might follow different paths with respect to their “green” behaviour. Additionally, I identify tipping points that could nudge a society from a polluting behaviour to a green one. I find that the perception of environment within the society can be an important factor in this shift.

Appendices

Appendix

A ‘Kantian’ Index and ‘Optimistic’ Index Equivalence

Here I give an alternative interpretation of the modelled the diversity among agents. In particular we start from the case that each person cares about social well-being with the same intensity, but that the parameter $\alpha$ instead reflects a person’s optimism. From this idea, we can use $\alpha$ as the share of individuals within society that each person thinks (or hopes) will behave as he does. I show here that this approach is equivalent to the approach outlined in the main section of the paper. In the main text, the original utility function is:

$$\begin{aligned} U_i(y_{it}) = u(y_{it}) - \alpha _i \cdot d\big ((1 - \delta ) p_{t-1} + \gamma y_{it}\big ) - (1 - \alpha _i) \cdot d\big ((1 - \delta ) p_{t-1} + \gamma y_t^s\big ) \end{aligned}$$

(A.1)

Now we might think of $\alpha$ as a ‘optimism’ measure instead of a ‘Kantian attitude’ measure. This means that $\alpha$ will now reflect which proportion of the society the agent is expecting (or hoping) to behave as he does. In this new case, we get the following formulation, where $V_i$ is the utility function in this case:

$$\begin{aligned} V_i(y_{it}) = u(y_{it}) - d\big ((1 - \delta ) p_{t-1} + \alpha _i \cdot \gamma \cdot y_{it}\big ) \end{aligned}$$

(A.2)

Following again the same reasoning of the main section, I posit that the agent will behave in a green manner if $V_i(0) \ge V_i(1)$. We proceed again in the same fashion by rearranging terms and getting for both cases (original and new) the following conditions for green behaviour:

(A.4)

We can again define an $\alpha ^*$ that divides the society into those whose behaviour is green and those whose behaviour is grey. The only thing left to do is check if this new function $\theta _2(\cdot )$ has the same properties as the original one $\theta (\cdot )$. Since the right-hand sides of the inequalities are the same, I will only focus on the left-hand sides. In the original version, we had the following properties:

$$\begin{aligned} \frac{\partial \big ( \alpha _i K(p_{t-1}) \big )}{\partial p_{t-1}}> 0 \quad \frac{\partial \big ( \alpha _i K(p_{t-1}) \big )}{\partial \alpha _i}> 0 \quad \frac{\partial ^2 \big ( \alpha _i K(p_{t-1}) \big )}{\partial \alpha _i \; \; \partial p_{t-1}} > 0 \end{aligned}$$

(A.5)

It is easy to verify that the same properties will hold for the case of $K_2(\alpha _i, p_{t-1})$. Hence we arrive at a new $\theta _2(\cdot )$ with the same properties of $\theta (\cdot )$ (although not the same function).

Fig. 8

Alternative case where $\alpha$ is the agent’s ‘naiveness’

We can finally verify the two remarks made about $\theta (\cdot )$ for $\theta _2(\cdot )$:

• There is a level of $\Omega \, p_{t-1} \; (\Omega p_{min})$ below which everyone exhibits grey behaviour:

  • Setting $\alpha = 1 \quad \rightarrow \quad d(\Omega p_{min} + \gamma ) - d(\Omega p_{min}) = H(\rho )$

  • This will actually gives us the same level of $\Omega p_{min}$ as before.

• There will be always some people who exhibit grey behaviour:

  • We can again find some positive $\alpha _i$, such that $K_2(\alpha _i, \Omega p_{t-1}) < H(\rho )$, for any given ${\Omega p_{t-1} > 0}$ and $\rho > 0$. In the same manner, we can see that since $K_2(\cdot )$ is continuous in $\alpha _i$ and that $K_2(\alpha = 0, \Omega \, p_{t-1}) = 0$, then there exists an $\epsilon$ such that $K_2(\epsilon , \Omega \, p_{t-1}) < H(\rho )$ for given $\Omega p_{t-1} > 0$ and $\rho > 0$ (Fig. 8).

We can finally observe a graph showing both versions of the function $\theta (\cdot )$:

A third and final option might be to suggest that both mechanisms (how Kantian each person is and how optimistic they are) are in place. For simplicity, I skip this alternative. However, if an individual’s Kantian tendency is positively correlated to their optimism, the present results should hold.

B Equivalence of Utility Function with Daube and Ulph (2014)

The utility function used in the present paper is equivalent to the one used in Ulph and Daube (2014) (henceforth, DU14). To verify this equivalence, we can define the following:

$$\begin{aligned} B\equiv & {} d\big ( (1-\delta )p_{t-1} + \gamma y^s \big ) - d\big ( (1-\delta )p_{t-1} + \gamma y \big ) \\ C\equiv & {} \tilde{u} \left( \frac{w + \rho y^{REF}}{1 + \rho } \right) - \tilde{u} \left( \frac{w + \rho y}{1+\rho } \right) \\ U\equiv & {} \mu B - (1-\mu )C \end{aligned}$$

where B and C are Benefits and Costs, respectively, as defined by DU14, but applied to damage and utility function in the present model. $y^{REF}$ takes the role of $\tilde{z}$ in DU14: it is some reference level of dirty consumption. U is the utility function from DU14, where the parameter $\mu$ has a similar role as the parameter $\alpha$ in the present model. DU14 maximize U with respect to y, taking $y^s$ and $y^{REF}$ as given. This gives not necessarily a corner solution with $y=0$ or $y=1$, since they allow agents to buy a mix of products. In the present work, I compare the binary option the agent has, with an wage equal to 1: $U|_{y=w=1}$ to $U|_{y=0,w=1}$. This gives:

$$\begin{aligned} \frac{U|_{y=0} - U|_{y=1}}{1-\mu } = \underbrace{\left( \frac{\mu }{1-\mu } \right) }_{= \alpha } \underbrace{\left[ d\big ( (1-\delta )p_{t-1} + \gamma \big ) - d\big ( (1-\delta )p_{t-1} \big ) \right] }_{K(p)} + \underbrace{\tilde{u}\left( \frac{1}{1+\rho } \right) - \tilde{u}(1)}_{-H(\rho )}\nonumber \\ \end{aligned}$$

(B.1)

which is the condition when the agent behaves green, as in inequality (2.7).

C The Cost of Behaving Green Under Other Consumption Utility Functions

Depending on the functional form of the consumption utility function, the cost of behaving in a green fashion $H(\rho )$ can be an increasing, decreasing, or constant function of the income level w. To illustrate this feature, we can observe how $H(\rho )$ behaviour changes by using a Constant Relative Risk Aversion (CRRA) utility function, as the following one:

$$\begin{aligned} \tilde{u}(c) = \left\{ \begin{array}{ll} \frac{1}{1-\epsilon } c^{1-\epsilon } &{} \quad \text {if } \epsilon > 0, \epsilon \ne 1 \\ \ln (c) &{} \quad \text {if } \epsilon = 1 \end{array} \right. \end{aligned}$$

(C.1)

where $\epsilon$ measures the degree of relative risk aversion. Setting the grey and green consumption levels to w and $w/(1+\rho )$ respectively, we get, for each part of the function:

And hence,

$$\begin{aligned} H(\rho ) = \left\{ \begin{array}{ll} \frac{w^{1-\epsilon }}{1-\epsilon } \left( 1-(1+\rho )^{\epsilon -1} \right) &{} \quad \text {if } \epsilon > 0, \epsilon \ne 1 \\ \ln (1+\rho ) &{} \quad \text {if } \epsilon = 1 \end{array} \right. \end{aligned}$$

(C.2)

We can observe that $H(\rho )$ is constant when $\epsilon = 1$, meaning it is independent of the value of w. In the case where $\epsilon \ne 1$, we have that if $\epsilon < (>) 1$, then $H(\rho )$ is increasing (decreasing) in w.

D Different Dynamics with Social Approval

As stated in Sect. 4, adding a social approval gain to the agent’s utility function does actually change (structurally) the function $\theta (\cdot )$, and therefore the dynamics. Adding social approval to the utility function will lead to a different functional form in the sense that the new $\tilde{\theta }(\cdot )$ function cannot be found by modifying the original parameters and/or by changing the (shape of the) consumption part $\tilde{u}(\cdot )$.

In order to prove this, we recall that the original function $\theta (\cdot )$ comes from Inequality 2.7. There, I proved that for a given value of $\rho$ and a pollution level $p_{t-1}$, there will always be some people exhibiting grey behaviour. I will prove now that this is not the case with social pressure, since it can happen that for given values of $\rho$ and $p_{t-1}$ (and $\beta$), the society can become completely green. Recall the new condition for green behaviour, as in Inequality 4.3 (page 27):

(D.1)

Let us verify whether this hypothesis of everyone behaving in a green manner ($\alpha ^*_t = 0$) is true. In this case, the social approval will be equal to: $S(\alpha ^*_t = 0) = v(1) - v(0) = 1$. Therefore, the previous condition becomes:

$$\begin{aligned} \alpha _i K(\Omega p_{t-1}) \; + \beta \ge \; H(\rho ) \nonumber \end{aligned}$$

Now, to verify that everyone is behaving in a green way, we can simply verify this condition for the least green person, the one purely motivated by economics, who has $\alpha _i = 0$. Therefore we get:

$$\begin{aligned} \beta \ge \; H(\rho ) \end{aligned}$$

(D.2)

which is just the minimum weight of the social approval parameter in the agents’ utility function. In other words, with this level of influence of peer pressure in agents’ utility, even the purely homo-oeconomicus person bears the cost of green behaviour; this is only because of social pressure, not because of a Kantian incentive, since he does not have one.

E Green Policy Details

In the case without policy, we have that the consumption levels of grey and green products per person are equal to 1 and $1/(1+\rho )$, respectively. This is the direct result of having an income fixed to 1 and prices of 1 and $(1+\rho )$, respectively. When in the presence of a green policy, the grey product is taxed with a tax $\tau$ and the green one is subsidized with a subsidy $\sigma$. Hence the new consumptions (per agent) become $1/(1+\tau )$ and $1/(1+\rho -\sigma )$. Assuming a balanced budget, and with $\alpha ^*_t$ as the proportion of grey behaving people, we get:

$$\begin{aligned} \sigma = \tau \frac{\alpha ^*_t (1+\rho )}{(1+\tau -\alpha ^*_t)} \end{aligned}$$

(E.1)

We can see that the new value of $\rho$ is $\hat{\rho } = \rho - \tau -\sigma$. Therefore, for a desired level of $\hat{\rho }$ we can calculate $\tau$ and $\sigma$. Using equation (E.1.1) to substitute $\sigma$ along with the previous equation, we get a quadratic equation for $\tau$:

$$\begin{aligned} \tau ^2 + \tau (1 + \alpha ^*_t \rho + \hat{\rho } -\rho ) - (1-\alpha ^*_t)(\rho - \hat{\rho }) = 0 \end{aligned}$$

(E.2)

The remaining question is if the new curve $\hat{\theta }(\cdot )$ (the one with the policy implemented) will be less than the original one, $\theta (\cdot )$ (except for $p_t$ values where $\hat{\theta }(\cdot ) = 1$). Recall that $\theta (\cdot )$ comes from the division of the private cost of behaving green, $H(\rho )$, and the social cost of behaving grey, K(p) (Eq. (2.8)). $H(\rho )$ is the difference of utility of consumption when behaving grey and green. A direct result of the policy is a decline in this private cost, which can be verified using the following inequality:

$$\begin{aligned} \tilde{u}\left( \frac{1}{1+\tau }\right) - \tilde{u}\left( \frac{1}{1+\rho -\sigma }\right) < \tilde{u}(1) - \tilde{u}\left( \frac{1}{1+\rho }\right) \end{aligned}$$

(E.3)

Finally, K(p) is the social cost of behaving grey from the Kantian perspective (where the agent assumes that everyone behaves as he does). In particular, if the grey behaviour is chosen, the agent evaluates this term using the assumption that everyone is buying the grey product. This translate to have an infinitesimal value of $\tau$ (using the limit yields to zero) and $\sigma \approx \rho - \hat{\rho }$. Therefore, in the Kantian view, the grey consumer still consumes one unit of grey product and hence K(p) is unchanged. Therefore, $\hat{\theta }(\cdot ) < \theta (\cdot )$.