# Competition vs cooperation: renewable energy investment under cap-and-trade mechanisms – Financial Innovation

#### ByWei Chen, Jing Chen and Yongkai Ma

Aug 23, 2022

We use numerical studies to illustrate major results and the influence of exogenous variables on the equilibrium results and provide additional insights. Specifically, we focus on (1) the impacts of a carbon price on renewable energy investment, electricity production, electricity price, and the profits of the utility firms; (2) the impacts of the unit carbon emission on renewable energy investment, electricity production, and the profits of the utility firms; (3) the impact of unit carbon quota on renewable energy investment and profits of the utility firms; and (4) impact of total carbon quotas on profits of the utility firms.

### Impacts of carbon price

This subsection explores the impacts of a carbon price on renewable energy investment, electricity production, electricity price, and the profits of the utility firms. The following parameters are set according to the conditions of results derived in this paper,(mathrm{a}=100 (mathrm{MW}),mathrm{b}=0.8(mathrm{$}/mathrm{kWh}),{{c}_{1}={0.1($/MW),c}_{2}=0.1($/MW),e}_{1}={3(kg/kWh),e}_{2}=3(Kg/kWh),{d}_{1}={0.2($/MW),d}_{2}=0.2($/MW),{e}_{0}=2(Kg/kWh), {E}_{1}={20(t),E}_{2}=20(t),) and (win {0left($/kWhright),1($/kWh)}). Results are shown in Fig. 2a–d, and observations are presented as follows. Figure 2a shows the impact of carbon price on renewable energy investment. Firstly, renewable energy investment increases with the carbon price. An increase in carbon price result in the increase in the carbon emission cost of conventional energy, which encourages the utility firms to invest in renewable energy for zero carbon emissions. Secondly, as compared to the GM, the BM encourages more investment in renewable energy, because a utility firm can obtain carbon quotas from renewable energy. Finally, a competitive environment encourages more investment in renewable energy than a cooperative environment does because the utility firms face not only the constraints of carbon regulations in the competitive markets but also the pressure from competitors, leading to more investment in renewable energy by the utility firms. Figure 2b shows the impact of carbon pricing on electricity production. Firstly, electricity production decreases with the carbon price because a higher carbon price forces the utility firms to bear more carbon costs, resulting in the decrease in the electricity production. Secondly, as compared to the GM, a utility firm can produce more electricity under the BM because it can obtain a unit carbon quota, which helps to reduce the cost of current carbon emissions, leading to the increase in electricity production. Finally, as compared to a cooperative market, a competitive market encourages more production of electricity. In a competitive market, the utility firm tries to gain as much as possible in the marketing share, resulting in producing more electricity. Figure 2c shows the impact of carbon pricing on electricity prices. Firstly, the electricity price increases with the carbon price. With the increase in carbon price, the utility firms bear higher carbon emission costs, which will be transferred to consumers due to higher electricity prices. Secondly, as compared to the GM, the utility firms can set a lower electricity price under the BM. Utility firms can enjoy subsidies from the unit carbon quota, resulting in the lower overall costs and electricity prices. Finally, as compared to the case in a cooperative market, a competitive market allows to set lower electricity prices. In a competitive market, the utility firm tries to capture the electricity market by setting a lower electricity price, which is also one of the motivations of electricity reform. Figure 2d shows the impact of carbon pricing on profits. Firstly, with the increase in carbon price, the utility firms’ profits increase under the BM and decrease under the GM. With the increase in carbon price, the utility firms obtain more carbon quotas by investing more in renewable energy and can be more profitable under the BM; meanwhile, under the GM, the utility firms still have to pay the costs of carbon emissions, leading to the decrease in their profits. Secondly, as compared to the GM, a utility firm can obtain a higher profit under the BM. Utility firms incur higher carbon emissions costs, which squeezes their profits. Finally, as compared to the case in the cooperative market, the profit of a utility firm in the competitive market is lower. Firms will set higher prices to obtain more profits in a cooperative market, and is less profitable in a competitive market due to intense price competition. ### Unit carbon emission The impacts of unit carbon emission on renewable energy investment, electricity production, and profits of the utility firm are illustrated by setting (mathrm{a}=100 (mathrm{MW}),mathrm{b}=0.8(mathrm{$}/mathrm{kWh}),{{c}_{1}={0.1($/MW),c}_{2}=0.1($/MW), e}_{2}=3(Kg/kWh),{w=0.8($/Kg),d}_{1}={0.2($/MW),d}_{2}=0.2 ($/MW),{e}_{0}=2(Kg/kWh), {E}_{1}={20(t),E}_{2}=20(t),) and ({e}_{1}in {0left(Kg/kWhright),1(Kg/kWh)}). #### Impact of unit carbon emission on renewable energy investment We analyse the impact of the unit carbon emission of utility firm 1 on renewable energy investment under different carbon regulations. Figure 3a, b show the renewable energy investment under the BM, while Fig. 3c, d show the renewable energy investment under the GM. We have the following observations. Figure 3a, b show that in both competitive and cooperative markets, renewable energy investment increases with the increase in the unit carbon emission of utility firm 1. The mechanism of the two markets is different. Specifically, in the competitive market, the unit carbon emission of utility firm 1 increases, which leads to more carbon emission costs from conventional energy. Thus, the utility firm is encouraged to invest more in renewable energy. Furthermore, to maintain market share, utility firm 1 will invest in renewable energy as much as possible to make up for conventional energy, which leads to the limited growth for utility firm 2. In the cooperative market, utility firms 1 and 2 aim to maximize their overall profit. Thus, when the unit carbon emission of utility firm 1 are high, utility firm 2 will invest more in renewable energy. Figure 3c, d further illustrate the validity of the above conclusions. Whether the BM or the GM is adopted by the government, the market type and energy costs of renewable energy and conventional energy should be considered, which affects how utility firms invest in renewable energy. #### Impact of unit carbon emission on electricity production We now analyse the impact of the u nit carbon emission of utility firm 1 on electricity production under different carbon regulations. Figure 4a, b show the electricity production under the BM, and Fig. 4c, d show the electricity production under the GM. Figure 4a, b show that the electricity production of utility firm 1 decreases with unit carbon emission while that of utility firm 2 increases. An increase in unit carbon emission reduces its carbon emission efficiency and increases its carbon emission cost, which increases utility firm 2’s market competitiveness. However, the market mechanism is different. In a competitive market, the reduction in its own efficiency will lead to a reduction in market share, which leads to the increase in utility firm 2’s electricity production; in a cooperative market, the utility firms’ demands will be adjusted internally to obtain market share. Figure 4a, b also show that the electricity production of utility firm 1 in a cooperative market will decline at a more rapid rate than that in a competitive market, and that of utility firm 2 is lower in a cooperative market than in a competitive one. This is because the unit carbon emission of utility firm 1 increase, which indicates that its market competitiveness decreases. Thus, utility firm 1 will significantly reduce its market share from the perspective of maximizing overall profit under cooperation, while utility firm 1 will reduce the possibility of market share decline by investing in renewable energy in a competitive market. Moreover, utility firm 2 competes for more market share in a competitive market, which leads to more electricity production than in a cooperative market. Figure 4c, d further illustrate the validity of the above conclusions. Whether the BM or the GM is adopted by the government depends on the market type as it affects investment in renewable energy by the utility firms. #### Impact of unit carbon emission on profit We now analyse the impact of unit carbon emission on electricity profits under different market types. Figure 5a, b show the electricity profits in a competitive market and Fig. 5c, d show these impacts under cooperation. Figure 5a, c show that the profit of utility firm 1 decreases with unit carbon emission in a cooperative market, while the profit of utility firm 2 increases. Figure 5a shows that the profit of utility firm would decrease under the competitive market because the increase in unit carbon emission leads to a reduction in carbon emission efficiency, which increases the cost of carbon emissions and decreases the profit. Figure 5b shows that the profit of utility firm 2 will increase because the increase in the unit carbon emission of utility firm 1 gives utility firm 2 more market share, resulting in an increased profit. Figure 5c shows that the increasing unit carbon emission would lead to a decrease in profits due to the cost of carbon emissions. Figure 5a–c also show that the profits under the BM are higher than that under the GM, as a utility firm under the BM can obtain a unit carbon quota from the government, which increases its profit. From the perspective of utility firms, the implementation of the BM may be more attractive. ### Impact of unit carbon quota This subsection explores the impacts of a carbon quota on renewable energy investment and profits of the utility firms using parameters, (mathrm{a}=100 (mathrm{MW}),mathrm{b}=0.8(mathrm{$}/mathrm{kWh}),{{c}_{1}={0.1($/MW),c}_{2}=0.1($/MW),e}_{1}={3(kg/kWh),e}_{2}=3(Kg/kWh),{d}_{1}={0.2($/MW),d}_{2}=0.2($/MW),w=0.8($/kWh), {E}_{1}={20(t),E}_{2}=20(t),) and ({e}_{0}in {1left(kg/kWhright),3(kg/kWh)}). From Fig. 6a–d, we have the following observations. The investment in renewable energy will increase in both the competitive and cooperative markets with the unit carbon quota. The main reason is that with the increase in unit carbon quota, the investment in renewable energy will receive more subsidies. Therefore, utility firms have the incentive to invest more renewable energy. Moreover, the investment in renewable energy in a competitive market is higher than that in a cooperative market. The reason is that in the competitive market, both utility firms have the motivation to invest more in renewable energy to have a higher marketing share. The profits of utility firms under the BM increase with the unit carbon quota. Because the increase in unit carbon quota will help utility firms to gain more benefits. The profit under the cooperative market is higher than that under the competitive market because the competition results in the losses in profits. Therefore, a competitive market encourages renewable energy investment, but a cooperative market helps to improve profits, implying that the government needs to set an appropriate unit carbon quota between renewable energy investment and profits. ### Impact of total carbon quotas This subsection explores the impacts of a carbon quota on renewable energy investment and utility firm profit using the following, (mathrm{a}=100 (mathrm{MW}),mathrm{b}=0.8(mathrm{$}/mathrm{kWh}),{{c}_{1}={0.1($/MW),c}_{2}=0.1($/MW),e}_{1}={3(kg/kWh),e}_{2}=3(Kg/kWh),{d}_{1}={0.2($/MW),d}_{2}=0.2($/MW),w=0.8(\$/kWh), {e}_{0}={2(Kg/kWh), E}_{2}=20(t),) and ({E}_{1}in {0left(tright),40(t)}). With Fig. 7a–d, we have the following observations.

The total carbon quota is determined based on the historical data of the utility firm. The increase in the total carbon quota would improve the utility firm’s own profit. The profit of utility firm 1 would increase, while utility firm 2 remains unchanged. Since the total carbon quotas would encourage the utility firm 1 to invest in renewable energy, the total profits of two utility firms would increase with the total carbon quotas.