# Impact of Firms’ Observation Network on the Carbon Market

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## Abstract

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## 1. Introduction

## 2. Model

#### 2.1. Model Structure

#### 2.2. Low-Carbon Technology and Marginal Abatement Cost Curve

#### 2.3. Agents

#### 2.3.1. Observation Network and Forecast

#### 2.3.2. Abatement-Oriented Decisions

- 1.
- Production Adjustment DecisionIn each period, agent i has a probability of $Pr{A}_{i}$ of adjusting its daily production. We introduce a probability $\left({\beta}_{t}^{i}\right)$ to characterize agent i’s propensity to adjust its production coefficient $\left({\theta}_{t}^{i}\right)$ (Agent i’s daily production is ${q}_{t}^{i}={\theta}_{t}^{i}\times {Q}_{last}^{i}/T$, and ${\theta}_{0}^{i}$ is set to 1, indicating that agent i’s initial daily production was equal to its average daily production in the last year. Then, during the abatement phase, when agent i wants to reduce its production, we let ${\theta}_{t+1}^{i}={\theta}_{t}^{i}-\delta $. In turn, when agent i decides to increase its production, we let ${\theta}_{t+1}^{i}={\theta}_{t}^{i}+\delta $. Here, $\delta $ is an exogenous parameter.). When agent i’s profit of unit emission from the output market $\left(cp{a}_{t}^{i}\right)$ (Here the emission allowance is treated as a production factor. Suppose that the product price is ${P}_{t}^{p}$ per ton, and the production cost is ${c}_{i}$ per ton. The energy intensity of agent i is ${\rho}_{t}^{i}$. The emission factor of the energy is $EF$. Then, profit of unit emission for agent i is calculated as $cp{a}_{t}^{i}=\left(\right)open="("\; close=")">{P}_{t}^{p}-{c}_{i}$.) is higher than a benchmark price $\left(bm{p}_{t}^{i}\right)$ (Here, $bm{p}_{t}^{i}$ is a benchmark price for agent i to make production decision, and it is calculated as $bm{p}_{t}^{i}={pfm}_{t}^{i}\times pr{o}_{i}^{1}$. ${pro}_{i}^{k}(k=1,2,3)$ are agent i’s three behavioural parameters related to its production decision. A detailed explanation of the behavioural parameters can be found in the Appendix of [10].), it might increase its production, and the probability is calculated as ${\beta}_{t}^{i}={\left(\right)open="("\; close=")">cp{a}_{t}^{i}/{bmp}_{t}^{i}-1}^{}{pro}_{i}^{2}$. When agent i’s profit of unit emission from the output market $\left(cp{a}_{t}^{i}\right)$ is lower than a benchmark price $\left(bm{p}_{t}^{i}\right)$, it might decrease its production and the probability is calculated as ${\beta}_{t}^{i}={\left(\right)open="("\; close=")">{bmp}_{t}^{i}/{cpa}_{t}^{i}-1}^{}{pro}_{i}^{3}$.
- 2.
- Low-Carbon Technology Adoption DecisionFor simplicity, we assume that in each period t, agent i only considers the adoption of the available low-carbon technology with the lowest average abatement cost. A probability $\left({\gamma}_{t}^{i}\right)$ is used to characterize its propensity to adopt this technology. Reasonably, we assume that ${\gamma}_{t}^{i}$ is related to four factors: (1) $ba{c}_{t}^{i}$, which is the average abatement cost of the technology being considered, and we assume $\partial {\gamma}_{t}^{i}/\partial ba{c}_{t}^{i}<0$; (2) $be{a}_{t}^{i}$, which is the potential emission abatement of the technology in the remaining periods of the whole abatement phase, and we assume $\partial {\gamma}_{t}^{i}/\partial be{a}_{t}^{i}>0$; (3) $ena{i}_{t}^{i}$, which is agent i’s expected net allowance, which is its holdings of allowance minus the expected total emission in the whole abatement phase, and we assume $\partial {\gamma}_{t}^{i}/\partial ena{i}_{t}^{i}<0$; and (4) $bm{i}_{t}^{i}$ (like $bm{p}_{t}^{i}$, $bm{i}_{t}^{i}$ is a benchmark price for agent i to make production decision, and it is calculated as $bm{i}_{t}^{i}=pf{l}_{t}^{i}\times in{v}_{i}^{1}$), which is the benchmark price for agent i to compare with when making adoption decisions, and we assume $\partial {\gamma}_{t}^{i}/\partial bm{i}_{t}^{i}>0$.On the other hand, as a probability, the value domain of ${\gamma}_{t}^{i}$ is $[0,1]$. Thus, based on the four factors listed above and their relationship with ${\gamma}_{t}^{i}$, we introduce a modified sigmoid function for the calculation of ${\gamma}_{t}^{i}$ as follows (here ${inv}_{i}^{k}(k=1,2,3,4,5,6,7)$ are agent i’s seven behavioural parameters related to its adoption decision; among them, ${inv}_{i}^{2}$, ${inv}_{i}^{4}$, and ${inv}_{i}^{6}$ are larger than 1).$$\begin{array}{c}\hfill {\gamma}_{t}^{i}={\left(\right)open="["\; close="]">\frac{1}{1+{\left(\right)}^{{inv}_{i}^{2}}ba{c}_{t}^{i}/bm{i}_{t}^{i}}}^{}{inv}_{i}^{3}& {\left(\right)open="["\; close="]">\frac{1}{1+{\left(\right)}^{{inv}_{i}^{4}}ena{i}_{t}^{i}}}^{}\\ {inv}_{i}^{5}\end{array}{inv}_{i}^{7}$$
- 3.
- Allowance Trading DecisionIn this model, there are $NK$ ticks in each period, each of which is denoted by s. On each tick, an agent is randomly selected to trade with other agents in the carbon market. The trading process is organized based on the continuous double-auction mechanism.Once selected, an agent first considers whether to trade as a buyer or a seller. Then, it will submit a bid or ask order to the order book. The order is a combination of a limit price $P{O}_{t,s}^{i}$ and a limit volume $V{O}_{t,s}^{i}$, meaning that agent i would like to sell (or buy) $V{O}_{t,s}^{i}$ units of allowance at a price no lower (or higher) than $P{O}_{t,s}^{i}$. Following the work by Raberto and Cincotti [23], we let agent i decides its limit price and volume randomly according to the current allowance price and its allowance gap (a detailed introduction can be found in our previous work [10]).Additionally, concerning agent i’s decision of trading direction, we introduce a probability $\left({\xi}_{t,s}^{i}\right)$ to characterize its propensity to trade as a buyer or seller, and it is calculated as follows. When the current price of allowance $\left({P}_{t,s}^{a}\right)$ is higher than the benchmark price $\left(bm{t}_{t,s}^{i}\right)$ (The calculation of $bm{t}_{t,s}^{i}$ is different from $bm{p}_{t,s}^{i}$ and $bm{i}_{t,s}^{i}$ for containing the influence of agent i’s net allowance $\left(ena{t}_{t,s}^{i}\right)$, the difference between holdings of allowance and expected total emission in the whole abatement phase. Here we reasonably assume that the higher (or lower) $ena{t}_{t,s}^{i}$ is, the lower (or higher) agent i’s $bm{t}_{t,s}^{i}$ is, and the higher propensity for agent i to trade as a seller. Because given other factors equal, when agent i’s $ena{t}_{t,s}^{i}$ is high, it faces a lower probability of being fined by the end of the abatement phase, and a higher probability of losing the value of excess allowance in hands. In order to characterize this impact of $ena{t}_{t,s}^{i}$ on $bm{t}_{t,s}^{i}$, we also introduce a modified sigmoid function as follows: $bm{t}_{t,s}^{i}={pfm}_{t}^{i}\times \left(\right)open="\{"\; close="\}">1+0.05\times \left(\right)open="\{"\; close="\}">{\left(\right)open="["\; close="]">1/\left(\right)open="("\; close=")">1+{\left(\right)}^{{tra}_{i}^{1}}ena{t}_{t,s}^{i}}^{}{tra}_{i}^{2}$.), agents might trade as a seller, and the probability is calculated as ${\xi}_{t,s}^{i}={\left(\right)open="("\; close=")">{P}_{t,s}^{a}/{bmi}_{t}^{i}-1}^{}tr{a}_{i}^{3}$. When the current price of allowance $\left({P}_{t,s}^{a}\right)$ is lower than the benchmark price $\left(bm{t}_{t,s}^{i}\right)$, agents might trade as a buyer, and the probability is calculated as ${\xi}_{t,s}^{i}={\left(\right)open="("\; close=")">{bmt}_{t,s}^{i}/{P}_{t,s}^{a}-1}^{}tr{a}_{i}^{4}$ (here, ${tra}_{i}^{k}(k=1,2,3,4)$ are agent i’s four behavioural parameters related to its allowance trading decision). This probabilistic framework also follows the idea of Raberto and Cincotti [23], but the introduction of $bm{t}_{t,s}^{i}$ reflects the abatement motivation of agents’ allowance trading behaviours.

## 3. Simulation Settings

## 4. Results and Discussion

#### 4.1. Allowance Price and Low-Carbon Technology Adoption

#### 4.2. Allowance Trading Volume and Total Production

#### 4.3. Efficiency of Carbon Emission Trading Mechanism

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Yu, S.-m.; Zhu, L.
Impact of Firms’ Observation Network on the Carbon Market. *Energies* **2017**, *10*, 1164.
https://doi.org/10.3390/en10081164

**AMA Style**

Yu S-m, Zhu L.
Impact of Firms’ Observation Network on the Carbon Market. *Energies*. 2017; 10(8):1164.
https://doi.org/10.3390/en10081164

**Chicago/Turabian Style**

Yu, Song-min, and Lei Zhu.
2017. "Impact of Firms’ Observation Network on the Carbon Market" *Energies* 10, no. 8: 1164.
https://doi.org/10.3390/en10081164