Competition vs cooperation: renewable energy investment under cap-and-trade mechanisms

Introduction Greenhouse gases result in global warming (Pan et al. 2014), leading to challenges to economic development and human survival (Saidur et al. 2007). Of all greenhouse gases, carbon dioxide accounts for more than 50% of climate warming (Zhang et al. 2015). Therefore, reducing carbon emissions becomes a goal of society. Carbon emissions generated by the electricity industry are 31% of total global carbon emissions (Liang et al. 2019). Thus, encouraging utility firms to reduce carbon emissions has become a particular concern to the government. Investing in renewable energy is one of the key methods used to reduce carbon emissions by the electricity industry (Miller et al. 2013; Bélaïd and Youssef 2017), as renewable energy generates much fewer emissions. Firms, however, usually are unwilling to invest in renewable energy without a carbon-pricing mechanism (Zarnikau 2012). As the ecological environment is a public asset, the revenue from investment in carbon emissions reduction is owned by the public collectively and the cost is borne by firms alone. Therefore, the government needs to adopt a carbon-pricing mechanism to internalize external costs. Cap-and-trade mechanisms are the most effective type of carbon Abstract

emissions reduction mechanisms adopted by governments (Xu et al. 2016). Cap-andtrade mechanisms include two types: Grandfathering mechanisms (GM) and benchmarking mechanisms (BM; Ji et al. 2017). Under a GM, the government sets a free total carbon quota for firms based on their historical carbon emissions data. In general, under a GM, the total carbon quota is based on the average of enterprises' carbon emissions in the past three years, showing that a GM focuses on the enterprise's own reduction. For example, Shenzhen (Ji et al. 2017) and the European Union Phase I (Zetterberg et al. 2012) have adopted GMs. Under a BM, the government sets unit carbon quotas for firms based on the average emissions of the industry. The unit carbon quota under a BM is based on the average low-carbon enterprises' unit carbon emission in the industry, showing that a BM focuses on the emission reduction of the industry. For example, Beijing  and the European Union Phase II (Zetterberg et al. 2012) have adopted BMs. China and the European Union (EU) have contributed 60% of global investment in renewable energy (Lv and Spigarelli 2015). Germany aims to achieve 100% renewable energy by 2050 (Hansen et al. 2019), while China will achieve 85% (Yang et al. 2016).
Investment in renewable energy under cap-and-trade mechanisms becomes a goal of many countries with a range of different electricity market attributes. For example, Chinese utility firms, such as State Grid and Southern Power Grid, cooperate to serve their consumers. State Grid and China Southern Power Grid transmit electricity to most areas in China. They are more cooperative than competitive, representing the leadership of the government and making the effort to meet residents' electricity consumption. In addition, their cooperation can help to reduce the security risks of power grid operation and improve the reliability of power supply (Wang 2020). In contrast, America utility firms, such as Eastern Regional Power Committee and Western Regional Power Committee, serve their consumers competitively, as each power grid system is basically selfsufficient and relatively independent. Market cooperation focuses on the overall profit, while competition focusing on the respective profit. Therefore, different market types require different investment in renewable energy.
Investment in renewable energy can reduce carbon emissions by replacing significant amounts of conventional energy. However, it remains unclear whether a BM or a GM is more effective in encouraging utility firms to invest in renewable energy, and which market, a cooperative or a competitive, is more effective in encouraging the investment in renewable energy. This paper attempts to address the following research questions: 1. Which cap-and-trade mechanism, a BM or a GM, encourages a utility firm to invest more in renewable energy? 2. Which market type, cooperative or competitive, encourages a utility firm to invest more in renewable energy?
Our paper makes three contributions to the literature on low-carbon management. First, motived by using both BM and the GM in China and the EU that encourages the utility firms to invest in renewable energy, we consider the different influences of the BM and the GM. This paper identifies which mechanism, the BM or the GM, encourages a utility firm to invest more in the renewable energy in either a cooperative or a competitive market. Second, the BM focuses on the regulation of the unit carbon emission, while the GM focuses on the regulation of the total carbon emissions. Chen et al. (2021a) compare the BM and the GM from the perspective of renewable energy investment, and they only considered a monopolistic firm in the market. Differing from Chen et al. (2021a), this paper considers the influence of not only the GM and the BM on the renewable energy investment, but also the competitive market and the cooperative market on renewable energy investment, to examine the different impacts of cooperative market and competitive market on the renewable energy investment. Third, the results show that BM is more effective in investing in renewable energy. Furthermore, the utility firms in a competitive market invest more under both mechanisms. Therefore, the government should implement a BM in a competitive market to encourage the utility firms to invest in renewable energy.
The rest of this paper is organized as follows: Sect. 2 reviews the relevant studies in the literature and Sect. 3 describes the model framework. Section 4 presents the models and equilibriums. The comparison of BM and GM is presented in Sect. 5. Section 6 provides numerical studies and additional managerial insights. Concluding remarks are presented in Sect. 7.

Literature review
Many studies have discussed carbon emissions reduction mechanisms. Here, we focus on studies closely related to our work, which are in two streams: cap-and-trade mechanisms, and carbon abatement innovation.

Cap-and-trade mechanisms
Cap-and-trade mechanism can classify into two widely used mechanisms, BM and GM. Existing literature on the operational decisions made under a GM can be summarized as single-firm and multiple-firm decision-making. Some scholars have studied the operational decisions making within one firm. For example, Hua et al. (2011) and Chen et al. (2013) point out that firms can use the Economic Order Quantity (EOQ) model to decide the optimal order quantity. Hua et al. (2011) find that the optimal order quantity occurs either at the best EOQ order or the minimum carbon emission order. Chen et al. (2013) determine the conditions to reduce carbon emissions by adjusting the optimal order quantity. He et al. (2015) compare the optimal carbon emissions under cap-and-trade and carbon-tax mechanisms. The mechanism that would produce lower carbon emissions was unclear; however, if unit carbon emission cost of the production is the same as that of holding the product, the difference between the two mechanisms is small. Moreover, Hasan et al. (2021) discuss the technology of the lowest carbon among regulations of the cap-and-trade, the tax, and strict carbon limit. They find that the carbon limit regulation would benefit the lower carbon technology investment.
Scholars have also extensively examined the impact of cap-and-trade mechanisms on the operational decisions of multiple firms, from the perspective of competition or cooperation. From the competition perspective, Du et al. (2013) propose an emissionsdependent supply chain with a manufacturer and an emissions permit supplier. They find that the manufacturer's profit increases with an emissions cap while the supplier's profit decreases, and the utility firms' profits would increase with the carbon quota. Xu et al. (2016) investigate the carbon abatement technology with the consideration of environmental awareness of managing a green supply chain with a manufacturer and a retailer. They find that as the carbon price increases, the investment in carbon emissions reduction technology first increases and then is stable. They also find that with the increase in carbon price, profits of the utility firms increase under a BM and decrease under a GM. Wang et al. (2018) focus on refrigerated logistics services in a fresh-food supply chain under a GM. They find that a transfer payment mechanism encourages firms to accept the carbon mechanism. Sun and Yang (2021) compare carbon emissions of the two competitive manufacturers between GM and tax mechanisms, and they find that cap-and-trade mechanism would mitigate more carbon emissions and benefit social welfare more. From a firm's perspective, Ji et al. (2020) compare social welfares under a wholesale-price contract and a revenue-sharing contract. They find that social welfare under a revenue-sharing contract is higher (lower) than that under a wholesaleprice contract if the consumer's environment awareness is high (low). Feng et al. (2020) focus on the issue of the joint replenishment among retailers under a GM, and find that the retailer with the most altruistic behaviour obtained surplus carbon allowances from other retailers. Cheng et al. (2022) discuss the lower carbon emissions technology for a closed-loop supply chain between GM and tax mechanisms, and they find that these carbon mechanisms could improve the lower carbon emissions technology investment. This paper differs from the above studies. Firstly, this paper focuses on the investment of renewable energy in the electricity market, while the above studies focus on the investment in the low-carbon technologies, to reduce emissions. The investment in renewable energy results in the increase in the production of electricity, while the investment in the low-carbon technology cannot increase the production of electricity. Secondly, the above studies only consider the market type either of cooperation or of competition, while this paper considers both in a unified analysis framework. Thirdly, the above studies focus on the influence of a BM on a firm's operations decision-making, while this paper considers the influence of not only a GM but also a BM on a firm's renewable energy investment.
Several papers have been on BM in the literature. Yang et al. (2018) consider the investment in carbon emission reduction technology for a two-level supply chain with manufacturers and retailers. They find that a BM would mitigates the channel conflict. Liu and Ke (2021) study a supply chain with a retailer and a manufacturer, and discuss the choice of retailers between the market mode and the distributor mode under a BM. They find that if the level of carbon emissions for a product in the retail process is moderate (low) or the platform rate is relatively low (high), both the retailer and the manufacturer prefer the market (distributor) mode. Moreover, Ji et al. (2017) examine the impact of the BM and the GM on carbon emissions considering environmental awareness in the online to the offline supply chain. They find that the BM is conducive to the investment in carbon emission reduction technology.
Renewable energy generates zero carbon emission, and a low-carbon technology is hard to achieve zero carbon emission. The difference that this paper has a focus on the investment in renewable energy while the above papers have a focus the investment in low-carbon technology. In addition, this paper considers the influence of both market types, (competition or cooperation) on renewable energy investment considering both BM and GM.

Carbon abatement innovation in the electric power industry
Investment in the carbon abatement innovation in the electric power industry has attracted much attention with a focus on the investment in carbon abatement technology and the investment in renewable energy. There is an essential difference in the effectiveness of investment between in carbon abatement technology and in renewable energy. The investment in carbon abatement technology can change the carbonemissions efficiency of products but not the capacity, while the investment in renewable energy expands production capacity. Du and Mao (2015) adopt a coal-electricity enterprise's dataset from China to analyse the costs of carbon abatement and carbon efficiency. They find that the cost of carbon abatement increases from 142.14 $/t in 2004 to 163.14 $/t in 2008. Zhang et al. (2018) develop an option game model with asymmetric electricity enterprises to discuss the relationship between decarbonization price and carbon abatement technology. They find that a low (high) decarbonization price encourages an electricity enterprise with low (high) carbon emissions to invest in carbon abatement technology. Differing from the above papers with a focus on carbon abatement technology, this paper finds that the investment in renewable energy increases with carbon price, implying that an appropriate increase in the carbon price is conducive to the transformation of the low-carbon energy.
Some studies have discussed the investment in renewable energy. Alizamir et al. (2016) focus on the investment in renewable energy under a feed-in tariff policy. They point out that when the diffusion and learning rate of renewable energy is related to the region, Investors should invest in renewable energy in the current period, and otherwise they will delay the investment. Kök et al. (2016) study the impact of peak-flat pricing on renewable energy investment, and find that under certain conditions, peak pricing can motivate the utility firms to invest in renewable energy. Kök et al. (2020) discuss the impacts of subsidizing inflexible/flexible energy sources on the investment in renewable energy, and find that such subsidies will increase/decrease the investment in renewable energy. These papers did not to consider the impacts of cap-and-trade mechanisms on the investment in renewable energy. Differing from these papers, this paper examines the influence of different carbon allowances (GM and BM) on the investment decision in renewable energy, and the influence of market types on the investment in renewable energy.
Several studies have examined the influence of cap-and-trade mechanism on carbon abatement innovation in electric power industry. Chen et al. (2021a) discuss the renewable energy investment under cap-and-trade mechanisms for a utility firm. They find that BM is more conducive to renewable energy investment than GM. Chen et al. (2021b) discuss the carbon abatement technology investment under cap-and-trade mechanisms for an electricity supply chain with a peak-valley pricing policy. They find that the peak-valley pricing policy will encourage the electricity generator to invest more carbon abatement technology than the flat pricing policy. Yan et al. (2022) compare the cap-and-trade mechanism to the renewable portfolio standard mechanism for renewable energy investment. Their results suggest that firms should adopt these mechanisms. Chen et al. (2021c) consider renewable energy investment with market effort under capand-trade mechanisms. They show that BM is beneficial to marketing efforts, while GM is not. These studies focus on the investment behavior of carbon abatement innovation in a single electricity market. Our paper focuses on the investment in renewable energy considering both competitive and cooperative electricity markets.

Model framework
We consider two utility firms in a regional market that invest in renewable energy in response to carbon emission restriction mechanisms. Each firm can purchase (sell) its carbon quota in a carbon-trading market when it has insufficient (excessive) carbon quota unit. The duopoly competes in electricity quantity under Cournot competition. The consumers are sensitive to electricity market prices. Following common practice and the studies in the literature (e.g., Willems 2002; Yan and Folly 2014), we assume that the same electricity market prices apply to both firms: where a is the potential market demand for electricity, b is the sensitivity coefficient of electricity production, and q i is the electricity production from utility firm i , where i = 1, 2 . Electricity supply from a utility firm is equal to electricity demand since supply and demand are balanced in real-time in electricity markets.
As in Albadi (2008), Lee (2014), and Kök et al. (2016), the total cost is a function of conventional energy, which is assumed to be a convex function: where c i and D i are the cost coefficient and production of conventional energy for utility firm i , where i = 1, 2 . The convex function assumption is based on the fact that a utility firm usually uses its most efficient generators first and then uses less efficient ones. As a result, the marginal cost increases significantly with the increase in production.
We also assume that the cost function of the investment in renewable energy for firm i is: where d i and k i are the cost coefficient and the investment in renewable energy of utility firm i . This assumption follows studies in the literature (Menanteau et al. 2003;Tahvonen and Salo 2001). As the advanced technology requires more investment, which results in the increase in demand for renewable energy, more expensive locations for solar and wind energy should be considered.
As the unit carbon quota ( e 0 ) under the benchmarking mechanism (BM)and the total carbon quota ( E i ) under the grandfathering mechanism (GM) for Firm i are restricted by the government,e 0 ≥ 0 and E i ≥ 0, a > max w(2bdi+ci(2b+di))dj ej −2bwdi(cj +dj )ei cidi(cj +dj ) , w(2bdi+ci(2b+di))dj ej −bwdi(cj +dj )ei (bdi(cj+dj)+ci(b+di)(cj+dj)) , ( In this paper, we consider two strategies of the duopoly ( R = {M, C} ), either cooperation ( M ) or competition ( C ) in the market (as illustrated in Fig. 1) under the two capand-trade mechanisms (GM and BM). We first discuss the strategy in which the two firms determine the electricity production and renewable energy investment decisions cooperatively to maximize their total joint profits, under both GM and BM. Then, we discuss the strategy where the two firms compete in a market and each firm determines the electricity production and investment in renewable energy to maximize its own profit, under both GM and BM. Therefore, four models will be discussed.

Cooperation in the market
We first discuss the duopoly's strategy in which the two firms make decisions cooperatively, under both GM and BM ( R = M ), to maximize their overall profit. We start with a discussion under the GM.

Under a grandfathering mechanism (MG)
The two utility firms maximize their joint profit ( π MG ) under GM by setting the electricity production ( q MG 1 , q MG 2 ) and their investment in renewable energy ( k MG 1 , k MG 2 ). The profit of the duopoly ( π MG ) is as follows: With Eqs. (1)-(4), we have the optimal electricity production ( q MG * 1 , q MG * 2 ) and renewable energy investment ( k MG * 1 , k MG * 2 ) for the two firms, and the associated electricity price ( p CB * ) and the total carbon emissions ( E CB * 1 , E CB * 2 ) can be summarized in Lemma 1 as follows.
Lemma 1 Under MG, there exist the optimal electricity production quantities (q MG * 1 , q MG * 2 ) and renewable energy investment levels (k MG * 1 , k MG * 2 ) that are given in

Under a benchmarking mechanism (MB)
In the cooperative market (M) under the BM, the two firms maximize the total profit ( π MB ) by deciding the electricity production quantities ( q MB 1 , q MB 2 ) and the investment levels in renewable energy ( k MB 1 , k MB 2 ) jointly. The total profit of the two utility firms ( π MB ) is: With Eqs. (4)-(7), we have the optimal electricity production quantities ( q MB * 1 , q MB * 2 ) and renewable energy investment levels ( k MB * 1 , k MB * 2 ) for two firms, and the associated electricity price ( p CB * ) and the total carbon emissions ( E CB * 1 , E CB * 2 ) are summarized in Lemma 2.

Competitive market
In the competitive market, we consider the two utility firms competing for electricity production to maximize their respective profits. To examine the effects of GM/BM in a competitive market, we start with the discussion of GM.

Under a grandfathering mechanism (CG)
In the competitive market, under a GM, the two utility firms decide on the levels of renewable energy investment first and then on electricity production quantities based on the total carbon quotas. The government sets the total carbon quotas according to the past records on the output of utility firm. Thus, the two utility firms in the competitive market under a GM have the motivation to invest in renewable energy. Each utility firm produces electricity and sells it to the consumer market. In addition, they can buy and sell carbon quotas in the carbon-trading market. Each utility firm's profit ( π CG i ) is as follows: With Eqs. (1)-(3), and (6), we have the optimal electricity production quantities ( q CG * 1 , q CG * 2 ) and renewable energy investment levels ( k CG * 1 , k CG * 2 ) of the two firms, and the associated electricity price ( p CB * ) and the total carbon emissions ( E CB * 1 , E CB * 2 ) are summarized in Lemma 3.

Under a benchmarking mechanism (CB)
In a competitive market under GB, the two utility firms first decide on their renewable energy investment levels and then on the electricity production quantities (10) bd 1 [3bd 2 +c 2 (3b+2d 2 )]+c 1{ bd 2 (3b+2d 1 )+c 2 [b(3b+2d 1 )+d 2 (2b+d 1 )]} , and simultaneously based on the unit carbon quota. The government sets the unit carbon quota according to the carbon emission level of the electric power industry. Thus, the two utility firms in the competitive market under a GB have the motivation to invest in renewable energy. Each utility firm produces electricity and sells it to the consumer market. In addition, they can buy and sell carbon quotas in a carbon-trading market. The utility firm i 's profit ( π CG i ) is as follows: With Eqs. (11)-(13), the optimal decisions of the two utility firms on the market electricity production quantities ( q CB * 1 , q CB * 2 ), renewable energy investment levels ( k CB * 1 , k CB * 2 ), and the associated electricity price ( p CB * ) and the total carbon emissions ( E CB * 1 , E CB * 2 ) are summarized in Lemma 4. Lemma 4 Under CB, there exist the optimal electricity production quantities (q CB * 1 , q CB * 2 ) and renewable energy investment levels (k CB * 1 , k CB * 2 ) that are given in (14). The electricity price (p CB * ) and total carbon emissions (E CB * 1 , E CB * 2 ) are given in (15).

The comparison of BM and GM
In this section, we compare the equilibriums under the BM and GM mechanisms in cooperative and competitive markets, R = {M, C} , respectively. We first compare the electricity production quantities and prices. We summarize the results in Proposition 1.
, and Proposition 1 shows that as compared with GM, BM is more conducive to producing electricity. In the competitive market, the two utility firms compete for the marketing share. Under BM, the firms can obtain the unit carbon quota, leading to the reduced carbon emissions costs and renewable energy subsidies. At the initial stage of renewable energy development, a firm needs financial subsidies from the government, which is a mandatory policy. In the process of marketization, the government introduces a carbon cap-and-trade mechanism, such as a BM, and transforms it into a market-oriented policy. When a renewable energy utility firm starts to make profit, the government reduces the subsidies. For example, China's Ministry of Finance points out that carbon trading reduces the pressure of the government subsidies (MFPRC 2021). Thus, the utility firms are motivated to produce more electricity. On the other hand, the total carbon quotas under the GM that firms can obtain can be viewed as a one-time subsidy. Thus, the utility firms have less motivations to produce electricity, as compared to under a BM. This suggests that the BM can encourage the firms to invest more in renewable energy.
Proposition 1 also shows that as compared to the case under GM, the BM is a better solution in encouraging the utility firms to produce electricity in both cooperative and competitive markets. In the cooperative market, the utility firms aim to maximize their overall profit. When the government implements a BM, the utility firms bear lower costs of carbon emissions with the unit carbon quota. Thus, the utility firms produce more electricity to be profitable. Meanwhile, in the competitive market, the utility firms produce more electricity under the BM. Thus, the total electricity production will be higher under BM than under GM. This suggests that the BM can be effective in guaranteeing electricity production in any market type. As electricity production is an essential to the economics, the BM is a more suitable policy for the government.
Proposition 1 shows that the electricity price under the BM is lower than that under the GM in both market types. The reason is that the BM can provide utility firms a unit carbon quota to reduce their burdens in carbon emissions, resulting in a lower electricity price; utility firms who can obtain a total carbon quota under the GM will set a higher electricity price. From reports of the impacts of BM and GM on electricity prices in China, Shenzhen adopted a GM in the electric power industry and the electricity prices ranged between 9.71 and 13.71 ¢/kWh (DFE 2019); Beijing adopted a BM and the electricity prices varied between 6.86 and 11.00 ¢/kWh (STSBJ 2019). This suggests that the government should adopt a BM to set lower electricity prices for consumers.
With Lemmas 1-4, we compare the optimal renewable energy investment levels from the perspective of the utility firms. We summarize the results in Proposition 2.

Proposition 2. The results of comparing renewable energy investment in four models
Proposition 2 shows that utility firms invest more in renewable energy under the BM than under the GM. Under the BM, the utility firms who invest in renewable energy receive a unit subsidy based on the unit carbon quota allocated by the government. Meanwhile, utility firms who invest in renewable energy will not receive a subsidy to reduce investment cost and will receive lower total carbon quotas as these quotas are based on historical emissions data, which reduces their investment enthusiasm. Thus, the BM is more suitable for encouraging utility firms to invest in renewable energy.
Proposition 2 also shows that the BM encourages the electric power market to invest more in renewable energy than it would under the GM. Many countries and regions have announced that renewable energy would be the dominant energy source by 2050. Encouraging utility firms to invest in renewable energy is critical in this process. The BM is undoubtedly more conducive to achieving the government's goals in increasing renewable energy investment in both competitive and cooperative markets. Note that there is no difference in renewable energy investment under the BM and the GM when the carbon price is zero.
With Lemmas 1-4, we compare the optimal total carbon emissions from the perspective of the utility firms. We summarize the results in Proposition 3.

Proposition 3. The results of comparing total carbon emissions are: E CG
Proposition 3 shows that under the BM, the utility firm will generate more carbon emissions than under the GM. Although the utility firm invests more in renewable energy under the BM, it also generates produce electricity, which may require more conventional energy generation that produces carbon emissions. While under the GM, the utility firm will produce less electricity that generates fewer carbon emissions. This suggests that the BM can encourage utility firms' investments in renewable energy, which reduces the production using conventional energy.
Proposition 3 also shows that the GM encourages utility firms to generate fewer carbon emissions in the electric power market. If a government's goal is to reduce carbon emissions, the GM is a better choice, as it reduces the usage of conventional energy.
We now discuss the impacts of carbon emission mechanisms on customer surplus and social welfare, which can be calculated as Cs * = (q * 1 +q * 2 ) 2 2b and Fs * = Cs * + π * , respectively. With Lemmas 1-4, we have the following results: Lemma 5. The result of comparing customer surplus in four models is: Cs RG * < Cs RB * .
Lemma 5 shows that the customer surplus under the BM is higher than that under the GM, implying that customers can be more beneficial as a utility firm produces more electricity under the BM. Meanwhile, the utility firms will produce less electricity production under the GM, resulting in lower customer surplus. This suggests that the BM is better than the GM from the perspective of customer surplus.

Lemma 6. The BM is better for renewable energy investment, while the GM is better for reducing the total carbon emissions.
With Propositions 2-3 and Lemma 5, we can conclude that the BM is better for renewable energy investment and customer surplus, while the GM is better for reducing the total carbon emissions. Our results suggest that the government needs to balance the investment in renewable energy (customer surplus) and carbon emissions reduction.
In the long run, the BM is a better mechanism as it facilitates to improve energy infrastructure and customer surplus; in the short term, GM is better in reducing carbon emissions. The government can choose the appropriate carbon mechanism according to different goals.
We assume E 1 = E 2 = E , in which two utility firms have the same total carbon quotas. This assumption does not affect the analyses and major insights in this paper, as the total carbon quotas are set by the government. By comparing the profits obtained under BM and GM in different markets, we have the results that are summarized in Proposition 4.
Proposition 4 illustrates that which mechanism benefits the total profit of the two firms and the profit of each firm depends on the total carbon quotas. The total carbon quotas can be viewed as subsidies to the utility firms, which relieves the pressure of carbon emissions. Thus, if the government sets a lower total carbon quota, the utility firms will incur higher carbon emissions costs, leading to lower profits. On the other hand, if the government sets a higher total carbon quota, the utility firms are more profitable. The government's regulation affects the profits of utility firms via the carbon quota mechanism in any type of market. A low total carbon quota discourages the utility firms to produce electricity due to the costs of excessive carbon emissions. A high carbon quota encourages the investment in renewable energy because the total carbon emissions generated in one cycle are related to the next cycle. This suggests that the government should consider the production efficiency of the utility firms when setting total carbon quotas.
Let c 1 = c 2 ,d 1 = d 2 , and e 1 = e 2 . We then focus on discussion the impact of market type on the social welfare and profits of the utility firms. The results are summarized in Lemma 7 and Proposition 5, respectively. Lemma 7. The results of comparing social warfare in four models are: 1. When E < E , then Fs CG * < Fs CB * and Fs CG * ≥ Fs CB * otherwise. 2. When E < E , then Fs MG * < Fs MB * and Fs MG * ≥ Fs MB * otherwise. Lemma 7 shows that which mechanism is better off for the social warfare depends on the total carbon quotas. If the total carbon quotas are lower, the social welfare is lower under the GM than under the BM in both competitive and cooperative markets. As the utility firms incur higher costs under the GM with lower total carbon quotas, leading to lower social welfare. If the total carbon quotas are higher, the social welfare is higher under the GM than that under the BM. Thus, the higher total carbon quotas result in a higher social welfare. This suggests that the government can set different total carbon quotas to influence the social welfare under the GM and the BM.
Comparing the profits in cooperative and competitive markets under different carbon mechanisms, we have the following results.
Proposition 5 shows that a cooperative market benefits the utility firms from obtaining more profits than they would in a competitive market. The intuition is that when the two utility firms cooperate, they reduce the costs of internal bargaining as they aim to maximize the overall profit. Meanwhile, when two utility firms compete to each other, they aim to maximize their profits. Moreover, the government's carbon mechanism will not affect the impacts of market attributes on the profits of the utility firms. From the perspective of profit, the utility firms have an incentive to cooperate. The government will encourage utility firms to cooperate but aim to prevent them from pursuing profits exclusively.

Numerical studies
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,a = 100(MW), b = 0.8($/kWh), c 1 = 0.1($/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($/MW ), e 0 = 2(Kg/kWh), E 1 = 20(t), E 2 = 20(t), and w ∈ {0($/kWh), 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, Fig. 2 The impacts of carbon price on total renewable energy investment, total electricity production, electricity price, and profits under the BM and the GM 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.

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.  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, a = 100(MW), b = 0.8($/kWh), 20(t), and e 0 ∈ {1 kg/kWh , 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.

Fig. 7 Total carbon quotas
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, a = 100(MW), b = 0.8($/kWh), 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.

Discussions
This paper discusses the influence of the cap-and-trade mechanisms on renewable energy investment in a competitive market and a cooperative market respectively, to provide managerial insights into the government, utility firms, and consumers.
Let us first take the perspective of the government. Firstly, the government should encourage the utility firms to involve in competitive markets, inducing more investment of renewable energy. Secondly, the government should adopt a BM, as the BM encourages more investment in renewable energy. Therefore, the BM in the competitive market is a more attractive to motivate utility firms to invest in renewable energy. Finally, the increase in the carbon price can lead to more investment in renewable energy, while reducing the demand of electricity in the consumer market. Therefore, setting an appropriate carbon price will induce more investment in renewable energy while maintaining the electricity demand.
Let us take the perspective of the utility firms. Firstly, they are more likely to cooperate in the market because both are more profitable. Secondly, if the utility firms are encouraged to actively practice the GM, the total carbon quotas increase. Finally, a utility firm's profit increases with the decrease in its own carbon emissions. It is suggested that utility firms should pay attention to reducing their unit carbon emission and provide lowcarbon traditional energy.
For the perspective of consumers, they prefer to a BM, because the BM results in a higher consumer surplus. In addition, further educating consumers' knowledge on carbon mechanisms helps to develop the low-carbon economy.

Conclusions
Carbon emissions cause climate change. Governments have implemented carbon mechanisms to regulate the carbon emissions behaviour of firms. In practice, the GM and the BM have been adopted by utility firms, which has encouraged them to invest in renewable energy in many regions such as China and the EU, in either the cooperative or the competitive markets. In our paper, we compare the optimal levels of renewable energy investment and electricity production under the BM and the GM in both the cooperative and the competitive markets to identify which system is more effective in encouraging utility firms to invest in renewable energy. Our study helps firms make decision on the investment in the renewable energy.
We develop a profit maximization model in which two utility firms make decisions on renewable energy investment and electricity production in cooperative or competitive markets. The main results are as follows.
(1) As compared to the GM, utility firms will invest more in renewable energy under the BM in both cooperative and competitive markets. Moreover, under both the GM and the BM, utility firms will invest more in renewable energy in a competitive market than in a cooperative market.
(2) A competitive market encourages more investment in renewable energy than a cooperation market does. However, the profit of total profits of the two firms in cooperative market is higher than in competitive market. (3) We show that utility firms will have higher electricity production and total carbon emissions under the BM than under the GM. (4) With the increase in one utility firm's unit carbon emission, the other utility firm's renewable energy investment and electricity production will increase.
From the perspective of energy low-carbon transformation, the government can adopt the BM to motivate the utility firms to invest more in renewable energy. The government should encourage market competition, as the competitive market can induce more investment in renewable energy than the cooperative market does. Therefore, competitive market should be encouraged, and BM should be implemented. Furthermore, the government should appropriately raise the carbon price, which also encourages more investment in renewable energy. Finally, increasing the unit carbon quota can increase not only the investment in renewable energy, but also the profits of enterprises. Therefore, the government should appropriately increase the unit carbon quota.
This paper examines the renewable energy investment under cap-and-trade mechanisms in both cooperative and competitive markets. We discuss the influence of different market types on renewable energy investment, which is helpful to achieve the goal of low-energy transformation. The work can be extended to three directions in the future work. Firstly, this paper discusses the relationship between competition and cooperation with the two utility firms. The study can be extended to the setting in which an electricity supply chain has multiple electricity generators and electricity retailers. The research can investigate the influences of the cap-and-trade mechanisms on the renewable energy investment. Secondly, this paper discusses the renewable energy investment under cap-and-trade mechanisms, which can be extended to investigate an electricity generator invest in renewable energy and the low-carbon technology under different carbon mechanisms. Thirdly, this paper studies the impact of the single-cycle cap-and-trade mechanism on the renewable energy investment, which can be extended to examine the renewable energy investment for a two-cycle setting.

Proof of Lemma 5
With Lemmas 1-4 and the customer surplus function Cs * = (q * 1 +q * 2 ) 2 2b , we can easily obtain the results presented in Lemma 5.


The Inflation Surge of 2021–22: Scarcity of Goods and Commodities, Strong Labor Markets and Anchored Inflation Expectations

The key to understanding the series of supply shocks that have hit inflation is the nature of the COVID-19 recession.

Forum work, supply shocks are, by defi nition, short term and transitory, while slack averages out over the business cycle. Therefore, over the medium term, the Phillips curve approach implies that infl ation would converge towards infl ation expectations, and changes in infl ation expectations have permanent eff ects on infl ation. 2 Two hypotheses, not mutually exclusive, may explain the recent surge in infl ation.
One hypothesis argues that a series of supply shocks have caused the surge in infl ation. This surge would therefore be transitory yet it could be very persistent, because with a series of successive shocks it could take an extended period of time until all the shocks fade away. The other hypothesis argues that the surge in infl ation is permanent, driven by excessively expansionary demand policies that generated too rapid an erosion of slack and lifted infl ation expectations.
The two hypotheses can be diffi cult to tell apart in real time if, as it is the case, a series of simultaneous but unrelated price shocks aff ect a wide range of sectors of the economy. The breath and scope of these price shocks make them observationally equivalent to a macro shock to infl ation, driven by demand growth outstripping supply. But the implications of each hypothesis are very diff erent. This article analyzes the three components of the Phillips curve as way to tell which of the hypothesis is more valid.

Transitory supply shocks: Scarcity of goods and commodities
The key to understanding the series of supply shocks that have hit infl ation is the nature of the COVID-19 recession. It was not a standard recession triggered by overheating or by fi nancial instability. Instead, it was triggered by a health shock that forced policymakers to shut down the economy, and suddenly put it in an induced economic coma. To support the economy during the coma, large fi scal and monetary policy easing packages were deployed with the objective of supporting incomes for those out of work, and minimizing hysteresis among workers and fi rms Global infl ation has increased to levels not seen in 40 years. This increase has been widespread: In February 2022, year-on-year headline infl ation was 7.9% in the US, 5.9% in the eurozone and 6.2% in the UK, and it is likely to peak in the 8%-9% range. Excluding food and energy, year-on-year infl ation was 6.4% in the US, 2.7% in the eurozone and 5.2% in the UK. 1 Other measures of underlying infl ation, such as median or trimmed infl ation, have showed increases of a similar magnitude, suggesting that price increases are becoming widespread and no longer concentrated on a few items. However, while infl ation is a global phenomenon, some countries have bucked the trend: Year-on-year headline infl ation in Japan, for example, was just 0.9% in February 2022.
This acceleration in infl ation, which started around mid-2021, has been a surprise, after a few decades of very low infl ation. This paper looks at the drivers of the infl ation surge, its prospects and its implications for monetary policy. The discussion is focused on the US, but the main conclusions also apply to the EU and the UK: While the upside risks to infl ation are higher than they have been in decades, the appropriate policy mix infl ation will likely stabilize around the target.

Why has infl ation increased? A series of unfortunate events
We use the Phillips curve as an organizing principle for this discussion: Infl ation would be a function of slack, infl ation expectations, and supply shocks. In this frame-Forum sons, including years of underinvestment in fossil fuels, not enough renewable energy capacity and a geopolitical risk premium. The Russian invasion of Ukraine has added to this supply shortage and risk premia. Because energy commodities are a critical input for metals and food, the energy price surge had severe spillovers in the rest of the commodity complex. As a result, global commodity prices have skyrocketed. The Bloomberg commodity index, a broad basket of commodities including energy, metals and food, has appreciated over 100% since the COVID-19 trough in March 2020.
These scarcity eff ects in goods and commodities are, by defi nition, transitory shocks, though likely very persistent. Figure 2 shows the outlier nature of these price shocks. While US core goods infl ation has historically averaged about zero, it is running at well over 10% year on year. Barring new shocks, it stands to reason that goods prices will at least stabilize, and thus their infl ation rate will decline to zero. Their infl ation rate could also become negative, for example, if the lagged production generated by these scarcity eff ects eventually results in an excess supply of goods, or if the geopolitical risk priced in commodity markets subsides.

Erosion of slack: The "great renegotiation"
Of course, the enabling factor for this large array of price shocks is strong demand growth -these scarcity eff ects would not have happened had demand growth been weak. Demand has been strong due to the expansionary policy mix implemented across all countries, including the very large US fi scal stimulus adopted in early 2021. The diff erences in fi scal stimulus across countries, and the so that the disruption to the structure of the economy was minimal.
This policy strategy was very successful. As a result, the economic reopening was also very abrupt, and the economy bounced back very fast. But while economic policies succeeded at preventing a deterioration of potential output, the composition of output changed in an unexpected way: The risk of COVID-19 contagion penalized the consumption of services, triggering a large shift in the consumption of goods vs services. 3 In graphic terms, people suddenly stopped going to the gym and bought a bicycle. This meant that the global supply of durable goods became utterly insuffi cient overnight. Something similar happened to the production of semiconductors, the demand for which skyrocketed well above available supply due to, among other reasons, the need to manufacture all the computers needed to work from home. Since semiconductors are a critical input for the car production, this generated a global scarcity of cars. 4 Moreover, the global trading system and supply chains, optimized for effi ciency and with little slack, broke down in multiple places with a global shortage of containers and trucks, and were not able to handle this sudden surge in global goods demand (see the discussion in Celasun et al., 2022). The result was a global supply bottleneck which, combined with robust demand growth, generated severe scarcity eff ects in goods markets, aff ecting multiple items in the CPI basket.
Scarcity eff ects generate non-linear increases in prices: the same amount of demand generates an outsized increase in prices. For example, with car inventories at alltime lows, the price of used cars in the US increased by almost 50% in 2021. Figure 1 illustrates the outsized impact of the price increases in cars on US infl ation. While cars represent less than 10% of the CPI basket, it has generated about 50% of core CPI infl ation. The counterfactual is clear: Had demand been better distributed across goods and services, the same amount of demand would have generated a much smaller increase in prices.
This sudden increase in the global demand for goods also generated a sharp increase in the global demand for energy. Goods are more energy intensive to produce than services -think again about the comparison between going to the gym and buying a bicycle. This met a commodity market that was undersupplied for a variety of rea-3 To wit: US durable goods consumption is 20pp above the pre-COV-ID-19 level, while services consumption has just recovered the pre-COVID-19 level. This divergence is less acute in the EU, which explains the milder increase in core infl ation, as scarcity eff ects in goods have been much less pronounced (see Lane, 2022 It is possible that the Phillips curve has become steeper -that the coeffi cient of the unemployment gap has increased, thus generating more infl ation for a given erosion of slack. But it does not appear so initially. Figure 4 shows the relationship between the unemployment gap (the difference between the unemployment rate and the Congressional Budget Offi ce's estimate of the NAIRU) and core services infl ation (the more sensitive part of infl ation, a priori, to slack), for the last three expansions (defi ned as the periods when the unemployment rate was declining). It shows that diff erential timing of the reopening of the economy, are factors explaining why the infl ation surge started in the US, and only later appeared in the UK and the EU. 5 But how much infl ation did the erosion of slack generate? Was it enough to explain the large upside surprise in core infl ation? Slack, defi ned as the diff erence between the unemployment rate and the non-accelerating infl ation rate of unemployment (NAIRU), is an unobserved variable, but its near term evolution can be proxied by the change in the unemployment rate. Figure 3 shows the evolution of the consensus forecast for the US unemployment rate and for core personal consumption expenditure (PCE) year-on-year in 2021Q4. It shows that as of 2021Q1, the unemployment rate was forecast to end the year at 5.5%, and core PCE was forecast to end at 1.7%. Alas, the unemployment rate fell to 4.2% in 2021Q4 while core PCE rose to 4.5%. In other words, the surprise in unemployment was 1.3 percentage points, while the surprise in core PCE was 2.8 percentage points. Under the Phillips curve specifi cation that prevailed prior to the COVID-19 crisis, which estimated a coeffi cient of about 0.1 for the unemployment gap (see Reifschneider and Wilcox, 2022), this unexpected decline in the unemployment rate would have generated just about 0.1-0.2 percentage points of additional core infl ation.
It is possible that the NAIRU has increased, and that this decline in unemployment represents a bigger erosion of slack. While employment has recovered to pre-COVID-19 levels, the labor force participation rate is still below, likely refl ecting a combination of retirements and COVID-19 related hesitancy. Crump et al (2022)     Forum fundamental transformation of jobs that is not infl ationary. After all, the key variable aff ecting future infl ation is not wage growth, but wage growth relative to productivity. The COVID-19 pandemic has led to a potentially permanent increase in online commerce, as consumers have become used to ordering online and habit formation is typically persistent. This implies an increase in the market share of commercial distribution of Amazon and similar fi rms, with an important implication: Amazon applies the principles of manufacturing to commercial distribution and can therefore generate higher productivity growth than the in-person retail sector. 6 Thus, a growing share of the services sector is becoming like the manufacturing sector, and thus susceptible to productivity gains. Amazon can aff ord to pay higher wages that match this higher productivity growth, de facto putting a fl oor in low skilled wages and generating competitive pressures for the rest of the low wage sector, which must match these higher wages to retain workers and, along the way, increase their productivity if they want to survive. The increasingly monopsonistic nature of the US labor market gives large fi rms an advantage that exacerbates these eff ects.
The fi nal element is the markup of prices over marginal costs. Empirically, markups have behaved in a countercyclical manner: During periods of high unemployment, fi rms benefi t from lower wage growth and build large markups, and as the unemployment rate declines and wage growth picks up, fi rms absorb the increase in labor costs by reducing markups, allowing them to keep prices stable and retain market share. But this countercyclical nature of markups is an empirical fact, not a fundamental property of the economy, and may have been the result of a globalization-driven multidecade trend that limited wage gains and fi rms pricing power. In an environment where all labor inputs are increasing and all companies are raising prices, it is possible that markups no longer behave in a countercyclical manner, thus increasing the probability of a wage-price spiral.
Overall, the contribution of slack to the infl ation surge has likely been very small and, while wage growth has accelerated and pricing power seems widespread, it is too early to tell if it is a one-off or will lead to a permanent increase in infl ation.

Infl ation expectations: Increasing from too low levels, now compatible with the infl ation objective
The third element of the Phillips curve is infl ation expectations. Short-term measures of infl ation expectations have increased, mostly the reaction to the increase in food and 6 See the discussion in Ubide (2022). the current episode is for now roughly consistent with the past experience -though the number of observations is small and thus caution is warranted. However, for a steeper Phillips curve to explain the infl ation surge, the coeffi cient would have had to increase tenfold.
The relationship between slack and infl ation is driven by two factors: the relationship between slack and wages (the original Phillips curve was a relationship between unemployment and wages) and the relationship between wages and prices, which is driven by markups and pricing power. Thus, this apparent stability of the Phillips curve could be masking moves in these two relationships.
In fact, the rapid increase in wage growth (the Atlanta Fed tracker shows year-on-year wage growth of 5.8% in February 2022) could be signaling an incipient steepening of the Phillips curve. A main driver of this strong wage growth could be the policies implemented in the US to deal with the COVID-19-related lockdowns -rather than furloughing workers and keeping the employer-employee relationships, as most other developed countries did, the US opted for income support via cash checks and enhanced unemployment benefi ts. This led to a large and sudden increase in unemployment, followed by a large and sudden recovery in employment. This led to the "great renegotiation", with record high amounts of workers searching for new jobs upon reopening. In an environment of strong economic activity, this large-scale renegotiation of contracts has given workers bargaining power to demand higher wages -something that is apparent in the acceleration of wage growth for job switchers, which reached 6.6% in February 2022. This great renegotiation has happened mostly at the lower end of the pay distribution. The Atlanta Fed data shows that while wage growth for the fi rst quartile has accelerated to the highest levels since 2001, wage growth for the second, third and fourth quartiles is broadly similar to the last decade. This acceleration of wage growth for low-wage jobs may have been exacerbated by the restrictions to immigration, as immigrants have traditionally been more willing to fi ll jobs at the lower end of the pay scale. To a large extent, the observed dynamics of wage growth are similar to a sudden increase in the "market minimum wage" driven by the great renegotiation. As such, it could just be a oneoff adjustment in wage levels -though, in the context of a rapid increase in commodity prices, there is a material risk that workers will also want to be compensated for their loss in real incomes, demanding further wage increases and thus triggering a wage-price spiral (see Blanchard, 2022). The lack of unionization in the US labor market reduces this risk, but only time will tell.
At the same time, it is possible that this faster wage growth at the lower end of the pay scale is driven by a Forum infl ation expectations remain well anchored -if not now, when would infl ation expectations de-anchor, one could ask. But vigilance is certainly warranted as the tails of the distribution of market-based infl ation expectations are widening (see Hilsher et al., 2022).

Implications for monetary policy: A diff erent policy strategy
Overall, the conclusion is that there is, for now, little information in the current acceleration of infl ation that casts doubt on the future stability of infl ation. But infl ation is, after all, an economic policy phenomenon, and thus this conclusion is critically dependent on the continuation of a policy mix, both monetary and fi scal, that ensures that infl ation expectations remain well anchored so that, if and when the infl ation shocks fade, infl ation can return to target. The concept of the policy mix is critical: Fiscal policy is the right instrument to address the hit on incomes from the price surge, allowing monetary policy to adjust accordingly.
What should monetary policy do? With infl ation expectation at target and the labor market very close to approaching maximum employment, monetary policy must now adjust and increase interest rates towards neutral levels. For as long as infl ation expectations remain well anchored, this can be achieved with a series of rate increases and a clear commitment to do whatever it takes to ensure price stability. Forward guidance is a symmetric tool that should also be used during tightening cycles. In fact, by the time the Fed started to raise rates in March 2022, 30-year mortgage rates had already increased by 150 basis points since mid-2021, tightening fi nancial conditions. Forward guidance also operates in the risk space in a cyclically adjusted manner (see Ubide, 2017). During times of low infl ation, forward guidance contributes to re-energy, the most salient prices. But short-term infl ation expectations have not, in the past, been a good predictor of infl ation: Reifschneider and Wilcox (2022) show that one-year-ahead infl ation expectations have been negatively correlated with infl ation one year out. Longer-term measures of infl ation expectation are more relevant for future infl ation and have increased from the excessively low levels that were prevailing pre-COVID-19, but have stabilized at levels compatible with the 2% infl ation objective.
For example, Figure 5 shows the evolution of US 5-year, 5-year infl ation expectations derived from three diff erent approaches: survey of professional forecasters, consumer surveys and fi nancial markets. These three measures are at levels similar to or below the levels prevailing in the 2004-2007 period, when there was widespread consensus that price stability had been achieved.
However, the breath of the surge in prices could cast doubt on the underlying stability of measured infl ation expectations. If infl ation expectations were to become more adaptive (more backward looking, reacting more to the recent infl ation prints), then the anchoring of infl ation expectations would be at risk. Figure 6 shows the estimates of the adaptive component of US infl ation expectations, from a model that decomposes the evolution of 5-year, 5-year infl ation expectations as a function of forward-looking and adaptive components. 7 It shows that while there was an increase in the adaptive component during the 2014-19 low infl ation period, refl ecting defl ationary fears, there is little evidence now that long-term infl ation expectations are becoming adaptive, refl ecting infl ationary fears. It is comforting that, despite the 40-year high in measured infl ation and the widespread and salient increases in prices, long-term 7 The model decomposes infl ation expectations as a function of lagged infl ation and the central bank target, with time varying betas that are constrained to sum to one. It is estimated via a fi ve-year rolling regression. Forum laxing the eff ective lower bound (ELB) constraint by conveying certainty about the future rate path and promoting risk taking. During periods of high infl ation, forward guidance can contribute to tightening fi nancial conditions by limiting the information about the future pace of rate increases and limiting risk taking.
The current tightening cycle will be, by design, diff erent from past cycles. In the past, monetary policy was preemptive -it started to tighten policy while the unemployment rate was still above the NAIRU. For example, the Fed started raising rates in 2015 with the unemployment rate at 5.1%, about 1.5 percentage points higher than the 3.5% level achieved in 2019, and with core PCE at 1.1%, well below the 2% objective -so that the tightening cycle would be gradual. However, in doing so, monetary policy was, de facto, treating the infl ation objective as a ceiling, not a symmetric target, and the outcome was suboptimal, with infl ation and infl ation expectations staying below target. The innovation of this cycle, in part by design but also in part due to the surprisingly strong recovery, is that monetary policy has sought to overcome the ELB constraint by no longer being preemptive, waiting to start the tightening cycle until the unemployment rate had reached the NAIRU and infl ation was at target. Therefore, the tightening process starts later in the cycle than before. But this also means that it can and will likely be less gradual.
But can monetary policy deliver a faster tightening process and yet also achieve a smooth landing? Some Fed tightening cycles have ended in recession, but others have not. History may not be a good guide: There are few observations (just seven tightening cycles since the 1980s) and the initial conditions, productivity trends and shocks of each cycle have been diff erent. For example, during the 1980-2000 period, the Fed engaged in a strategy of opportunistic disinfl ation, with the objective of starting each expansion with a lower level of infl ation than that prevailing at the peak of the previous cycle. This means that each tightening cycle aimed at lowering the level of trend infl ation, not just stabilising infl ation at target. And this required, most of the time, a recession to shift the infl ation dynamics lower.
The 2004-07 episode ended with a fi nancial crisis, and the 2015-18 episode ended with the COVID-19 recession.
This time is also diff erent because the Fed only wants to stabilize infl ation and infl ation expectations at target, not reduce the trend level of infl ation. If infl ation expectations remain anchored and supply shocks fade, the Fed can achieve this by raising rates to a bit above neutral levels and stabilize the unemployment rate at the NAIRU. Once there, the Fed must decide whether it wants to keep infl ation at 2% or, considering that infl ation typically declines during recessions, stabilize core infl ation in the 2%-2.5% range so that it averages 2% over the business cycle. This strategy of opportunistic refl ation (as suggested in Ubide, 2017) would help overcome the ELB constraint and boost future growth.
In the end, central banks must accept that a symmetric infl ation objective requires taking some upside risk with infl ation. Let us not forget that many central banks, especially the ECB, have struggled since 2007 to lift infl ation to target. There is a clear trade-off : the less upside infl ation risks are accepted, the more the infl ation objective is a ceiling, and not a midpoint, and the more future growth is foregone.

Conclusion
The surge in infl ation has been due mostly to large and widespread price level shocks, in a context of strong demand growth and anchored infl ation expectations. As such, there is little information in the current infl ation surge that suggests this increase in infl ation will be permanent. Conditional upon the right fi scal policy response to cushion the hit on incomes -this is more critical in the eurozone, where the shock from the Russian invasion of Ukraine is large and infl ation expectations are still fragile after a decade of very low infl ation, and it is therefore too early to declare mission accomplished on the reanchoring of infl ation expectations at the 2% target -a well-managed adjustment of monetary policy should be able to stabilize infl ation at the target. The current infl ation environment is extraordinary and will require nimble and symmetric decision-making. There is no room for complacency, but no need to panic either.


To breathe or not to breathe?

Listeria monocytogenes uses respiration to sustain a risky fermentative lifestyle during infection.

RESPIRO-FERMENTATION
To breathe or not to breathe?
Listeria monocytogenes uses respiration to sustain a risky fermentative lifestyle during infection. LAUREN C RADLINSKI AND ANDREAS J BÄUMLER B acteria are masters at tuning their metabolism to thrive in diverse environments, including during infection. Constant, lifeor-death competition with host immune systems and other microorganisms rewards species that maximize the amount of energy they derive from limited resources.
Living organisms produce energy in the form of a small molecule called adenosine triphosphate (ATP). ATP is generated by breaking down, or oxidizing, high energy molecules such as sugars through a series of electron transfer reactions. These redox (reduction/oxidation) reactions require an intermediate electron carrier such as nicotine adenine dinucleotide (NADH) that must be re-oxidized (NAD + ) in order for the cell to continue producing ATP by oxidizing highenergy electron donors.
During respiration, NAD + is regenerated when electrons are transferred to a terminal electron acceptor such as oxygen. In organisms that cannot respire, ATP is produced through a less energy-efficient process called fermentation. Fermenting organisms also oxidize highenergy electron donors to produce ATP: however their strategy for regenerating NAD + requires depositing electrons on an organic molecule such as pyruvate. Thus, fermenting organisms sacrifice potential ATP by producing waste products that are not fully oxidized.
Listeria monocytogenes is an important foodborne pathogen with an unusual metabolic strategy that falls somewhere between respiration and fermentation. This bacterium carries the genes for two respiratory electron transport chains that can use either oxygen or an extracellular metabolite such as fumarate or iron as a terminal electron acceptor (Corbett et al., 2017;Light et al., 2019). However, unlike most respiring organisms, L. monocytogenes lacks the enzymes required to fully oxidize sugars and instead produces partially reduced fermentative end products including lactic and acetic acid (Trivett and Meyer, 1971). Despite this, respiration is absolutely essential for L. monocytogenes to cause disease (Corbett et al., 2017) -in fact, mutants that cannot respire are considered safe enough to be used in vaccine development (Stritzker et al., 2004). Now, in eLife, Samuel Light (University of Chicago) and colleagues -including Rafael Rivera-Lugo and David Deng (both from the University of California at Berkeley) as joint first authors -report on why respiration is essential for an organism that gets its energy through fermentation (Rivera-Lugo et al., 2022).
By comparing the waste products L. monocytogenes generates in the presence or absence of oxygen (a terminal electron acceptor), Rivera-Lugo et al. observed that oxygen shifts the composition of L. monocytogenes fermentative end products from primarily lactic to exclusively acetic acid. Compared to lactic acid, acetic acid is a slightly more oxidized waste product, the production of which generates more ATP but insufficient NAD + to sustain itself. Thus, while acetic acid production generates more energy, it comes at the cost of redox balance, which could incur a potential reduction in cellular viability. Indeed, Rivera-Lugo et al. observed that genetically disrupting respiratory pathways inhibited L. monocytogenes growth within immune cells and prevented the bacterium from causing disease in mice.
Based on these results, Rivera-Lugo et al. surmised that L. monocytogenes relies on respiration either to re-oxidize the surplus NADH that results from acetic acid fermentation (and re-establish redox balance), or to generate proton motive force (PMF). PMF is generated when protons are pumped across the bacterial membrane during respiration. The energy stored in the resulting proton gradient can be used by the cell to power important cellular activities such as solute transport and motility.
Redox balance and PMF generation are difficult processes to separate as they involve the same cellular machinery. To determine which of the two is essential for the pathogenesis of L. monocytogenes, Rivera-Lugo et al. genetically modified the bacterium to express an unusual NADH oxidase (NOX) previously described in the bacterium Lactococcus lactis (Neves et al., 2002). NOX decouples the production of NAD + and PMF by transferring electrons from NADH directly to oxygen without pumping protons across the membrane (Titov et al., 2016). This tool allowed the team to separate these two processes by restoring NAD + regeneration, without increasing PMF. When Rivera-Lugo et al. expressed NOX in a L. monocytogenes mutant that cannot respire, NOX activity restored acetic acid production, intracellular growth, cell-tocell spread, and pathogenesis of the bacterium. This result implies that the primary purpose for L. monocytogenes respiration during infection is NAD + regeneration, not PMF production.
While balancing redox may allow L. monocytogenes to produce more ATP through the fermentation of acetic acid, it does not explain why a respiration-deficient mutant cannot grow in a host. During infection, L. monocytogenes infects and replicates within host cells, then commandeers the cell's own machinery to spread to neighboring cells. In line with previous observations (Chen et al., 2017), Rivera-Lugo et al. report that genetically inhibiting respiration causes L. monocytogenes to lyse -burst open and die -within host cells.
When a bacterium lyses inside a cell, it releases a number of molecules that initiate an antimicrobial response and significantly reduce the bacterium's ability to cause disease (Sauer et al., 2010). Thus, the tendency for a respiration-deficient mutant to lyse within host cells may inadvertently trigger the host's immune response and lead to clearance of the pathogen from the host. Rivera-Lugo et al. showed that restoring NAD + regeneration with NOX stopped L. monocytogenes from lysing within infected cells and restored the bacterium's ability to colonize a mouse. Together Figure 1. Effects of inhibiting respiration in L. monocytogenes. (A) L. monocytogenes uses respiration to restore redox balance during growth through acetic acid fermentation by transferring electrons from NADH to an electron acceptor such as oxygen (O 2 ). This regenerates NAD + to serve as an essential cofactor in the oxidative metabolic reactions that produce ATP. (B) Inhibiting respiration causes an imbalance between NAD + and NADH, leading to NADH accumulation and lysis of L. monocytogenes during intracellular growth. This leads to a loss of pathogenesis.
these findings imply that respiration-mediated redox balance is crucial for maintaining L. monocytogenes viability during infection (Figure 1).
The findings of Rivera-Lugo et al. address a long-standing mystery as to why respiration is required for successful L. monocytogenes infection. One outstanding question is how the accumulation of NADH leads to lysis. Understanding the molecular mechanism behind this phenomenon, and determining whether inhibiting respiration externally (with a drug, for example) leads to lysis, could reveal new therapeutic approaches for targeting organisms that employ similar respiro-fermentative metabolic strategies during systemic infection.


THE NEXUS BETWEEN INTERNATIONAL TAX COMPETITIVENESS AND THE SHADOW ECONOMY: A CROSS-COUNTRIES ANALYSIS

. The article is devoted to the study of the essence and peculiarities of the growth of tax competitiveness of the country in the conditions of a significant amount of shadowing of incomes and legalization of illegally obtained funds. The object of the study is the levels of shadow economy and tax competitiveness of the country. In the paper the 5,348 particular: bringing the domestic regulatory framework to the requirements of the international community, reducing corruption, reducing time spent on filing and filing tax reports, optimizing the tax burden. Conclusions. The results of the study form the basis for the development of new and improvement of existing recommendations for the prevention of the use of shadow schemes of with drawal and their further legalization in Ukraine in terms of the tax channel of shadowing the

Introduction. Peculiarities of economic development of a large number of countries with medium and low levels of development are budget deficits, constant capital outflows, high levels of labor migration and soon. The precondition for these processes is the low efficiency of certain components of public policy, the reform of which does not ensure the formation of sustainable competitive advantages of economies over other economies, and leads to the outflow of highly skilled workers, relocation of tax bases in countries with more favorable tax conditions in terms of starting and running a business, investing money.
Ukraine's constantly growing need for financial resources highlights the need to find additional and monitor existing sources of filling the state budget, attract financial resources by in creasing the country's investment attractiveness, registration and business in Ukraine by nonresidents and more. One of the indicators that characterizes the country's attractiveness to international investors and business partners, the favorableness of its business environment is the level of tax competitiveness. The understanding of the governments of most countries of the world of the importance of this indicator in the implementation of international economic and investment policy necessitates the government to intensify its efforts to form a competitive advantage in the process of implementing its tax policy.
Literature review and the problem statement. Today, the definition of «tax competitiveness of the country» is characterized by in consistentapproachestoitsunderstanding, lowlevelofresearchand a wide variety of interpretations. C. Tibou [10] in his research considers the concept of tax competitiveness of local governments, which means the process of reducing the level of local government tax burden in their territories. According to the author, this concept should be equated with the tax autonomy of local governments. A sufficient level of tax autonomy allows local governments to compete for the right to register business in their territory by manipulating the size of tax rates and fees, the introduction of preferential tax regimes, exemption from taxation of certain tax bases.
D. Bradfordand W. Oates [2] emphasized that along with the economic benefits, these manifestations of tax competition have a number of negative consequences for the economy. According to the authors, one of the main threats to the implementation of the semeasures by public authorities, in the framework of increasing tax competitiveness, is to reduce the state's ability to provide the population with a sufficient level of public goods.
A. Boyko and J. Samusevych [1], I. Tiutiunyk, O. Mazurenko [6] considered tax competition as a prerequisite for economic growth and de-shadowing of the economy. Taxcompetitive jurisdictions receive significantly greater economic benefits due to more favorable conditions for business registration and profit in their territory compared to competitors. Ultimately, this leads to a significant increase in the level of tax burden in other jurisdictions and an even greater evasion of taxes by economic entities [7].
Thus, the lack of a common understanding of the nature and role of tax competitiveness in the economic development of the country highlights the need for more detailed study of the content of this concept and its relationship with the shadow economy.
The purpose of this research is to estimate the nexus between tax competition and shadow economy.
Research  According to the WoS and Scopus databases, the vast majority of publications on tax competitiveness are published in high-ranking journals in the first and second quarters ( Table 1). The largest number of works (217 for the WoS database and 176 for the Scopus database) was published in International Tax and Public Finance journal. OSviewer t ories (Fig. 2) ompetitiven owed us to me time, the ues of tax also much third and 1 According to the results of the analysis, a very close relationship between tax competitiveness is observed with the concept of shadowing of the economy. In order to confirm the hypothesis of the existence of this relationship, we will analyze the relationship between these indicators using the Ordinary Least Squares method. The results of the cross-country analysis are shown in Table 3. The results of the Ordinary Least Squares test confirmed a statistically significant nexus between tax competition and shadow economy. Thus, the de-shadowing of the economy can be considered as an effective tool to increase the level of tax competitiveness of the country.
Today, among the whole set of tools to increase the level of tax competitiveness of the country, the use of incentive tax benefits is widely used [14; 15]. Most often, these tools are used by: 1) countries with economies in transition, which have not yet completed the transition from a socialist to a market tax system and which use these incentives as an alternative to other mechanisms to withdraw funds from the shadows; 2) in developing countries, these incentives are aimed at neutralizing other short comings (low level of infrastructural development, out dated regulatory frame work, high level of bureaucracy, etc.), which stimulate economic entities to shadow activities (Fig. 3). At the same time, tax incentives themselves can not serve as a catalyst for shadow activities, as the general features of the tax system (tax base, tax rates, etc.) are more important for participants in shadow operations [7; 11].
Countries with economies in transition are quite attractive for shadow with drawals. A number of their legislative provisions still correspond to the conditions of the socialist economy and do not fully correlate with the conditions of taxation of market economies.
This leads to a gap between the tax bases, which must be accrued in accordance with the standards of a market economy and actually accrued in these countries, and thus reduce the level of tax competitiveness of the country.
At the same time, the lack of a coherent and stable regulatory framework is a stimulus for the growth of shadow activities and reduce the level of tax competitiveness of the country. The main feature of the tax legislation of many developing countries and countries with economies in transition is its constant revision and amendment. This increases the risk of shadow activity in the implementation of capital-intensive projects and complicates the procedures for monitoring and controlling the movement of resources.
Despite the additional difficulties for government regulators in incurring additional costs for both the government (planning and forecasting tax revenues) and taxpayers, growing uncertainty about future tax results, their existence intensifies the flow of investment to the country to obtain additional benefits.
Thus, the reduction of shadow operations is possible due to increased control over economic entities. Given the important role of tax payments in the economic development of the country, one of the components of the roadmap for de-shadowing the economy is forecasting the amount of tax evasion from changes in the level of macroeconomic stability in the country.
The basis of this process should be the introduction of tools for estimating and forecasting the amount of tax arrears received by the budget due to the implementation of shadow schemes of tax evasion. The consequences of these actions, as a rule, have a destructive effect on the country's economic development, which is growing every year (including due to the cumulative and synergistic effect). Fig. 4 shows the dynamics of changes in tax evasion (TI) as the difference between the total amount of uncollected tax payments and the amount of losses due to tax benefits, tax exemptions, errors and miscalculations of tax payments. Forecasting the amount of tax losses through the use of shadow schemes can be done using a continuous function, which has the following form: where � -the amount of tax losses due to the use of shadow schemes in the period t, %; � -the amount of tax losses due to the use of shadow schemes in the base period, %; ∝ -a function that reflects the impact of tax losses on the level of tax competitiveness of the country.
The α function takes into account the threats and benefits of using shadow schemes to conceal income. At the same time, according to the results of the analysis of the threat of shadowing of incomes, they are usually long-term, and the refore in the evaluation process should take into account their future value. The benefits of income shadowing due to value added in the economy by increasing employment (even in the shadow economy), GDP growth through the sale of shadow products (in the official and shadow markets) are more valuable now than in the future.
Thus, the established patterns can form the basis for determining the projected values of budget losses from the use of shadow operations and will serve as a basis for implementing the road map for de-shadowing the economy in the context of improving macroeconomic stability.
The generalization of the analyzed measures of de-shadowing of the economy carried out in Table 4 forms the basis for the formation of a road map of de-shadowing of the economy. Their implementation will increase the level of publicity and transparency in the work of state bodies, financial monitoring and control bodies, reduce bureaucracy and corruption in the country, simplify financial monitoring and control over tax administration processes, increase the stability of the national economy by removing some illegally obtained income and, ultimately, an increase in the country's level of tax competitiveness.  Conclusions. The results of the study form the basis for the development of new and improvement of existing recommendations for the prevention of the use of shadow schemes of with drawal and their further legalization in Ukraine in terms of the tax channel of shadowing the economy.
The priority measures should be: increasing the efficiency of tax and customs services by conducting impartial inspections, reducing corruption in government agencies; organization and systematization of the relationship between individual agencies by establishing cooperation between individual entities of the financial sector and government institutions; development of the system of international cooperation in the direction of prevention of participation of domestic economic entities in transnational schemes of concealment of incomes and their removal to the territory of other states; improving the procedure for calculating and paying taxes, reducing the time spent on filling out and maintaining tax reporting; strengthening the responsibility for tax evasion, including increasing the amount of material and the introduction of criminalliability for the shadowing of income in particularly large amounts in the event of damage to the state in particularly large amounts; to introduce electronic cashflow monitoring services (including through the use of artificial intelligence and machine learning), development of a methodology for identifying risky financial transactions, improving the tools for implementing the tax system, etc. Improving the tax system can be seen as a guarantee of economic growth and development of the country, stimulating the development of certain sectors of the economy, bringing out of the shadows a significant amount of financial flows. Such measures include a review of individual vectors of taxpolicy, rates and objects of taxation, types and amounts of tax benefits, etc.