# Chapter 7 Stability of Industry level climate coalitions with enforcement policies

**Should I just focus here on the grand coalition ??** or investigate whether our main conclusions regarding the ‘stabilizing’ effect of taxation hold for partial coalitions, that is, cartels in which not all the firms in the industry collude?

**changing market structure will allow us with assign different abatement benefits while keeping high abatamenet costs for the small firm think the case of china with high abatement cost and large share of abatement benefits**

## 7.1 A static Taxation scheme

\[\begin{equation} \begin{cases} \tau^{CO_2} = P_{CO_2} \\ \tau^{SO_x} = P_{SO_x} \\ \end{cases} \end{equation}\]

## 7.2 A dynamic Taxation scheme

We also consider a dynamic tax policy in a feedback form which depends on the industry’s pollution stock, with the aim of inducing a stable coalition. Thus, accounting for the feedback effect that exists within a dynamic framework, where pollution can accumulate into a stock over time. The tax rate depends on the state variable, the stock of emissions.

Given dynamic tax policies, the tax rate charged at time t will be given by \(\tau_t^{CO_2}\) and \(\tau_t^{SO_x}\). The case where \(\alpha=0\) corresponds to a ‘myopic’ environmental regulator who does not react to changes in industry emissions. It is highly likely that if the state of the environment evolves in either direction, the regulator would ideally wish to revise the tax rate accordingly. Thus, it makes sense in this context to consider a dynamic tax.

Let \(α≥ 0\), the dynamic carbon and sulfur tax follow the path

\[\begin{equation} \begin{cases} \tau^{CO_2}_{t} = P_{CO_2} + \bigg( \alpha \times \frac{S_t^{CO_2 }}{ S_1^{CO_2 } } \bigg) \\ \tau^{SO_x}_{t} = P_{SO_x} + \bigg( \alpha \times \frac{S_t^{SO_x }}{ S_1^{SO_x } } \bigg) \\ \end{cases} \end{equation}\]

Another Design :

\[\begin{equation} \begin{cases} \tau^{CO_2}_{t} = P_{CO_2} + \bigg( \alpha \times \frac{S_{t+1}^{CO_2 } - S_{t}^{CO_2}}{ S_t^{CO_2 } } \bigg) \\ \tau^{SO_x}_{t} = P_{SO_x} + \bigg( \alpha \times \frac{S_{t+1}^{SO_x } - S_{t}^{SO_x }}{ S_1^{SO_x } } \bigg) \\ \end{cases} \end{equation}\]

- The optimal tax is dependent on the current pollution stock, and it may be negative when the pollution stock such that the optimal tax rule may give firms a subsidy for an initial time interval even though ????

### 7.2.1 Question : which values of alpha that renders the grand coalition stable

Hypothese; **A uniform tax has no impact on the stability of the coalition (Note \(\alpha=0\) reports on the static tax scheme)**

examine the regulator’s choice of $$ , the parameter/ rate adjusting the dynamic tax path in the pollution stock, given that the regulator wishes to maximize welfare.This is determined by the degree to which the pollutant is damaging, that is, the level of $_D $. \(\alpha = 1.5\) and investigate whether the coalitions are stable ???

This is determined by the degree to which the pollutant is damaging,

**varying the pollutant’s damage over the industry**

relatively small: \(\gamma_D = 1.5\) | intermediate: \(\gamma_D = 5\) | very harmful \(\gamma_D =20\) | |
---|---|---|---|

\(\alpha = 0\) | |||

\(\alpha = 1.5\) | |||

\(\alpha = 3.5\) | |||

\(\alpha = 5\) | |||

\(\alpha = 20\) | |||

\(\alpha = 50\) |

Table will be filled with ITCM as a KPI for the whether or not the the grand coalition is stable (maybe only focus on grand coalition here)

## 7.3 expextation :

show that the implementation of a tax on pollution emissions can modify substantially the collusive behaviour amongst polluting firms.

It is particularly important to understand the implications of having a Markovian tax since environmental policies are likely to be more tied to some index of aggregate pollution levels, such as the stock of pollution.

Under a uniform tax rate, the cartel is never stable as long as there are more than two firms in the industry.

However, if the tax rate evolves with the state of the pollution damage and is indexed on aggregate pollution levels such as the stock of pollution, we showed that the cartel that includes all the firms in industry can be stable.