Can government policies help to achieve the pollutant emissions information disclosure target in the Industry 4.0 era?

Abstract

In the Industry 4.0 era, manufacturers commonly adopt digital technologies such as Internet of Things (IoT) and blockchain technology to improve information disclosure. In this paper, we focus on how the government can properly set an extended producer responsibility (EPR) policy (penalty or subsidy) and impose it on the manufacturer to entice the manufacturer to set the optimal pollutant emissions information disclosure (PEID) level which maximizes the social welfare. In the basic model, we build a simple consumer utility based stylized analytical model. We first derive from the government perspective the social welfare function and obtain the closed-form expression of the optimal level of PEID. Then, we explore the manufacturer’s problem on PEID under the EPR policy. We show how the EPR policy can be set so that the government can entice the manufacturer to set the PEID level which maximizes the social welfare. We also uncover the factors governing the EPR policy, and show the situations under which the EPR policy is in fact a subsidy scheme (i.e., the government sponsors the manufacturer). To derive more insights and check for robustness, we extend the basic model in a number of ways, namely (i) the situation when the manufacturer is risk sensitive, (ii) the case with the extended consumer responsibility (ECR) policy, (iii) the scenario when there is a per unit PEID level dependent operating cost (i.e., a variable cost), and (iv) the case when the platform is not supported by blockchain. We find that the form of EPR policy and the qualitative insights remain valid for the cases when the manufacturer is risk sensitive and there is a PEID level dependent operating cost. Interestingly, we uncover that, unlike the EPR policy, the use of ECR policy fails to help.

Appendices

Appendix 1

See Table 2.

Table 2 A list of notations and abbreviations

Appendix 2: All proofs

Proof of Proposition 1

Solving $dSW/d\xi = - (k - 1)\xi + 1 - m - \theta = 0$ yields $\xi_{SW}^{*} = \frac{1 - \theta - m}{{k - 1}}$.

Checking the first order derivatives uncovers that:

$$ d\xi_{SW}^{*} /d\theta < 0, $$

(24)

$$ d\xi_{SW}^{*} /dm < 0, $$

(25)

$$ d\xi_{SW}^{*} /dk < 0. $$

(26)

Thus, $\xi_{SW}^{*}$ is decreasing in the level of manufacturing pollution emissions $\theta$, the manufacturing cost m and the cost coefficient of improving the PEID level (i.e., k). Moreover, obviously, since p is absent from the formula for $\xi_{SW}^{*}$, it is independent of the selling price.□

Proof of Proposition 2

The manufacturer’s optimal PEID level is $\xi_{M}^{*} = \frac{p - m - e}{k}$.

Checking the first order derivatives uncovers that:

$$ d\xi_{M}^{*} /de < 0, $$

(27)

$$ d\xi_{M}^{*} /dm < 0, $$

(28)

$$ d\xi_{M}^{*} /dk < 0, $$

(29)

$$ d\xi_{M}^{*} /dp > 0. $$

(30)

Thus, from (27) to (30), we can see that $\xi_{M}^{*}$ is increasing in the selling price, and decreasing in manufacturing cost, EPR tax/subsidy and the cost coefficient of improving the PEID level (i.e., k).□

Proof of Proposition 3

(a) Setting $\xi_{M}^{*} = \xi_{SW}^{*}$, we have:

$$ \begin{aligned} \frac{{ p - m - e}}{k} & = \frac{{1 - \theta - m}}{{k - 1}} \\ & \Rightarrow e = (p - m) - \left( {\frac{{(1 - \theta - m)k}}{{k - 1}}} \right). \\ \end{aligned} $$

Thus, the optimal EPR policy is to set the EPR tax/subsidy to be $e^{*}$.

(b) From (11), we have $e^{*} =$$(p - m) - \left( {\frac{(1 - \theta - m)k}{{k - 1}}} \right)$, rearranging terms yields:

$$ e^{*} = \left( {\frac{(k - 1)(p - m) - (1 - \theta - m)k}{{k - 1}}} \right). $$

(31)

From (31), since $k - 1 > 0$, we have

$e^{*} \left( {\begin{array}{*{20}c} > \\ < \\ \end{array} } \right)0 \Leftrightarrow (k - 1)(p - m) - (1 - \theta - m)k\left( {\begin{array}{*{20}c} > \\ < \\ \end{array} } \right)0$.

Note that by simple algebra, we have:

$(k - 1)(p - m) - (1 - \theta - m)k\left( {\begin{array}{*{20}c} > \\ < \\ \end{array} } \right)0 \Leftrightarrow \theta \left( {\begin{array}{*{20}c} > \\ < \\ \end{array} } \right)\frac{k(1 - p) + (p - m)}{k}$.

Thus, the optimal EPR policy is a subsidy sponsorship scheme (i.e., $e^{*} < 0$) if and only if the level of manufacturing pollution emissions is sufficiently low (i.e., $\theta < \hat{\theta }$); the optimal EPR policy is a penalty taxation scheme (i.e., $e^{*} > 0$) if and only if the level of manufacturing pollution emissions is sufficiently high (i.e., $\theta > \hat{\theta }$).

Proof of Proposition 4

From (15), we have: $\xi_{M,Risk}^{*} = \frac{(1 + \lambda \sigma )(p - m - e)}{k}$.

(a) Since if $\lambda$ is negative, the manufacturer is risk averse; if $\lambda$ is positive, the manufacturer is risk prone; if $\lambda$ is zero, the manufacturer is risk neutral. Directly from the closed-form expression of $\xi_{M,Risk}^{*} = \frac{(1 + \lambda \sigma )(p - m - e)}{k}$, it is obvious true that for a given e, the optimal PEID level for a risk prone manufacturer is higher than a risk neutral one, which is in turn higher than the risk averse one.

(b) Equalizing $\xi_{SW}^{*} = \xi_{M,Risk}^{*}$ implies $\frac{1 - \theta - m}{{k - 1}} = \frac{(1 + \lambda \sigma )(p - m - e)}{k}$ which is equivalent to setting $e = e_{Risk}^{*} \triangleq (p - m) - \left( {\frac{(1 - \theta - m)k}{{(1 + \lambda \sigma )(k - 1)}}} \right)$.

Checking the analytical expressions of $e_{Risk}^{*}$ shows the following:

$e_{Risk}^{*} \left( {\begin{array}{*{20}c} > \\ < \\ \end{array} } \right)0 \Leftrightarrow \theta \left( {\begin{array}{*{20}c} > \\ < \\ \end{array} } \right)\hat{\theta }_{Risk} ,\,{\text{where}}\,\hat{\theta }_{Risk} = (1 - m) - \left( {\frac{(1 + \lambda \sigma )(p - m)(k - 1)}{k}} \right)$. □

Proof of Proposition 5

Since $e_{Risk}^{*} = (p - m) - \left( {\frac{(1 - \theta - m)k}{{(1 + \lambda \sigma )(k - 1)}}} \right)$, we can see that: (i) If $1 - \theta - m > 0$, then $e_{Risk}^{*}$ is larger when $\lambda$ is larger. (ii) If $1 - \theta - m < 0$, then $e_{Risk}^{*}$ is smaller when $\lambda$ is larger. Since $1 - \theta - m > 0$ $\Leftrightarrow \theta < 1 - m$, and $1 - \theta - m < 0$$\Leftrightarrow$$\theta > 1 - m$. Proposition 5 is shown.□

Proof of Proposition 6

From (18), we have: $\xi_{M,ECR}^{*} = \frac{p - m}{k}$, which is independent of c. Thus, unlike the EPR policy, the ECR policy cannot help entice the manufacturer to set the social welfare maximizing PEID level.□

Proof of Proposition 7

All the proofs follow the case in the basic model (see Propositions 1 to 3). So, we skip the details to save space. □