沉浸式翻译

2. Background
2. 背景

Costs need to be considered when the economy aims to reduce emissions. There are two ways to measure the costs of emission reductions. The first is the carbon price from the carbon market, such as the EU ETS. For example, as of January 17, 2025, the price of EU Carbon Permits was €79.26 per tonne of CO₂ reduced.
当经济旨在减少排放时，需要考虑成本。有两种方法可以衡量减排成本。首先是来自碳市场的碳价格，例如欧盟 ETS。例如，截至 2025 年 1 月 17 日，欧盟碳许可证的价格为每吨二氧化碳减排 79.26 欧元。

Alternatively, the second method is the cost of subsidies for renewable energy. This is calculated by dividing the total cost of support schemes by the electricity generation from subsidized generators. Based on calculations for the RO scheme and the FIT scheme, the efficiency of these schemes ranged from £200 to £300 per tonne of CO₂ reduced.
或者，第二种方法是可再生能源补贴成本。这是通过将支持计划的总成本除以补贴发电机的发电量来计算的。根据 RO 计划和 FIT 计划的计算结果，这些计划的效率从每吨二氧化碳减排 200 英镑到 300 英镑不等。

In an efficient market, these two values should be more or less consistent. However, the large gap between them indicates that something is missing or unexplored in either the carbon market or the subsidy schemes. The carbon market is highly competitive, and the price should reflect market conditions. Therefore, it is possible that subsidy schemes are being overlooked, leading to excessively high costs for carbon emissions reductions.
在一个有效的市场中，这两个值应该或多或少一致。然而，它们之间的巨大差距表明，碳市场或补贴计划中还存在缺失或未开发的领域。碳市场竞争激烈，价格应反映市场状况。因此，补贴计划可能被忽视，导致碳减排成本过高。

It makes sense to argue that costs need to be covered while the economy encourages the development of renewable energy, meaning that support levels need to be high, particularly for less developed technologies. Nonetheless, we suspect that these seemingly "reasonable" arguments may overlook certain aspects of the market. Specifically, by receiving subsidies and developing renewable energy, generators (particularly large ones) can reduce their fossil fuel generation more easily, making it less costly to reduce emissions and potentially leading to hidden revenues.
认为在经济鼓励可再生能源发展的同时需要支付成本是有道理的，这意味着需要很高的支持水平，特别是对于欠发达的技术。尽管如此，我们怀疑这些看似“合理”的论点可能会忽视市场的某些方面。具体来说，通过获得补贴和发展可再生能源，发电商（尤其是大型发电商）可以更轻松地减少化石燃料的发电量，从而降低减排成本，并可能带来隐性收入。

In other words, without the development of renewable energy, these generators would face higher costs to reduce their emissions due to the upward-sloping marginal abatement cost curve.
换句话说，如果没有可再生能源的发展，由于边际减排成本曲线向上倾斜，这些发电厂将面临更高的减排成本。

Therefore, these hidden revenues should be taken into account and used to challenge the argument for cost-covering subsidies for renewable energy. This arguments may be related to the unintended benefits of subsidies, such as windfall profits, discussed in the literature. But, does the windfall profits for renewable generators?
因此，这些隐性收入应该被考虑在内，并用于挑战可再生能源成本覆盖补贴的论点。这一论点可能与文献中讨论的补贴的意外好处有关，例如暴利。但是，可再生能源发电机的意外之财是否获利？

2.1 The Levelised Costs of Electricity (LCOE)
2.1 平准化度电成本（LCOE）

The levelised cost measures the average net present costs of electricity generation during the life cycle of a station and is calculated as the total costs over the station's lifetime divided by the total electricity generated over the station's lifetime. It allows for the comparison of different energy generation technologies (e.g., fossil fuels, renewables, nuclear) by considering both upfront investment costs and ongoing operational expenses.
平准化成本衡量的是发电站生命周期内发电的平均净现成本，计算方法是发电站生命周期内的总成本除以发电站生命周期内的总发电量。它允许通过考虑前期投资成本和持续运营费用来比较不同的能源生产技术（例如，化石燃料、可再生能源、核能）。

LCOE is calculated as
平准化度电成本（LCOE）的计算方式为

$LCOE= \frac{NPV of total costs over lifetime}{NPV of electricity generated over lifetime} = \frac{\sum_{}^{} (C_{} + O_{} + F_{}) {(1+r)}^{}}{\sum_{}^{} (E_{}) {(1+r)}^{}}$

where t represents year of operation (from 1 to the lifetime of the plant), r denotes the discount rate (reflecting the cost of capital), $C_{}$ is capital expenditures (CAPEX) (e.g., construction costs), $O_{}$ is operating and maintenance costs (OPEX), $F_{}$ is fuel costs (e.g., for coal or gas plants), and $E_{}$ is electricity generated. (what about carbon costs?)
其中 t 代表 y次运营（从 1 到工厂的使用寿命），r 表示dISCOUNT 率（反映资本成本）， $C_{}$ 是c资本支出（CAPEX）（例如，建设成本） $O_{}$ 为o且维护成本（OPEX） $F_{}$ 为 fUEL 成本（例如，对于燃煤或天然气厂）以及 $E_{}$ 是否产生了 Electricity（碳成本呢？

The following figure from Wiki gives an illustration on the LCOE of various technolgoy in from 2009.
下图来自 Wiki，给出了 2009 年以来各种技术的 LCOE 的插图。

https://about.bnef.com/blog/cost-of-new-renewables-temporarily-rises-as-inflation-starts-to-bite/?s=09

Focusing on the UK, the following table from the Electricity Costs in 2023 publised by the UK government, which explain the components of LCOE across four technologies. The values shows that LCOE of renewable technolgoies (wind and solar) are much cheaper than gas-fired plants. The figure also shows that the components of LCOE can include construction costs, operation and maintanance costs, fuel costs, and carbon costs. This help us defines the varaiables in the model design.
下表来自英国政府发布的《2023 年电力成本》，以英国为例，其中解释了四种技术的 LCOE 组成部分。这些值表明，可再生能源技术（风能和太阳能）的 LCOE 比燃气发电厂便宜得多。该图还显示，LCOE 的组成部分可以包括建设成本、运营和维护成本、燃料成本和碳成本。这有助于我们在模型设计中定义可变对象。

Weighted average cost of capital and hurdle rates
加权平均资本成本和门槛率

Weighted average cost of capital (WACC) is a company's average after-tax cost of capital from all sources, including common stock, preferred stock, bonds, and other forms of debt.
加权平均资本成本（WACC）是公司所有来源的平均税后资本成本，包括普通股、优先股、债券和其他形式的债务。

A hurdle rate is the minimum rate of return that a company or investor is willing to accept on an investment project. It's also known as the minimum acceptable rate of return (MARR) or minimum attractive rate of return.
门槛率是公司或投资者愿意在投资项目中接受的最低回报率。它也被称为最低可接受回报率（MARR）或最低有吸引力的回报率。

These two concepts are important in determining the subsidy, so we may end up challenge the use of these two concepts in the support schemes.
这两个概念在确定补贴时很重要，因此我们最终可能会质疑在支持计划中使用这两个概念。

2.1 Model design
2.1 模型设计

In the first scenario, we consider a traditional fossil fuel generator, which meets the total demand of the economy. In the second scenario, we consider a generator with two components: traditional fossil fuel generation and renewable generation.
在第一种情况下，我们考虑传统的化石燃料发电机，它满足经济的总需求。在第二种情况下，我们考虑一台发电机有两个组成部分：传统化石燃料发电和可再生能源发电。

Comparing these two scenarios, we aim to show that the profit of the generator in the second scenario is higher than in the first scenario, with lower carbon emissions. However, this result is contingent on the high level of subsidies provided to renewable generation. There could be an optimal level of subsidy at which the profits of the generators are equal across both scenarios.
比较这两种情景，我们旨在表明第二种情景中发电机的利润高于第一种情景，碳排放量更低。然而，这一结果取决于对可再生能源发电的高水平补贴。可能存在一个最佳补贴水平，即发电商的利润在两种情况下相等。

There are several key considerations
有几个关键考虑因素:

Market Structure: Should we consider a monopoly market or a perfectly competitive market? The key difference is whether the generator has the ability to influence market-wide variables such as prices and demand.
市场结构：我们应该考虑垄断市场还是完全竞争市场？关键区别在于生成器是否能够影响整个市场的变量，例如价格和需求。

Functional Relationships: We need to establish concave or convex relationships between variables to generate a deterministic solution and equilibrium. Without such relationships, the model may result in explosive solutions without equilibrium.
函数关系：我们需要在变量之间建立凹或凸关系，以生成确定性解和平衡。如果没有这种关系，该模型可能会导致没有平衡的爆炸性解。

Should we consider the analysis at the economy level or the generator’s level, or a group of generators?
我们应该考虑经济层面的分析，还是生成器的层面，或者一组生成器？

The maginal abatement costs curve may be crucial in this analysis.
maginal 减排成本曲线在此分析中可能至关重要。

Further considerations can be added as we progress with the model construction.
随着模型构建的进展，可以添加更多的注意事项。

2.2 The first scenario
2.2 第一种情况

Assume that there is a generator in the economy with fossible fuel generation only. Its profit function is written as
假设经济中有一台发电机只生产可燃燃料。它的 profit 函数写成

$\begin{matrix} π_{} = p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{} # (1) \end{matrix}$

where represents the electricity generation from traditional fossil fuel units, $p^{}$ is the market electricity price, $p^{}$ is the price of fossil fuels, $h^{}$ denotes the heat efficiency, $v^{}$ refers to the variable costs of operation and maintenance, $p^{}$ is the carbon price, and $e^{}$ is the emission factor. $F$ represents the sunk costs, which are uncorrelated with the quantity of electricity generated. Here, we need to explain each term in detail.
其中，代表传统化石燃料机组的发电量， $p^{}$ 是市场电价， $p^{}$ 是化石燃料 $h^{}$ 的价格，表示热效率， $v^{}$ 是指运营和维护成本的可变成本， $p^{}$ 是碳价格， $e^{}$ 是排放因子。 $F$ 表示沉没成本，与发电量无关。在这里，我们需要详细解释每个术语。

The first term, , $p^{}$ , denotes the revenue from selling electricity to customers. The electricity price, $p^{}$ , can be determined by the national demand for electricity, as $p^{} (D)$ . However, unlike other markets, the demand for electricity is relatively fixed at any given time, although it fluctuates during peak and off-peak hours. The electricity price can be considered fixed and exogenous in a perfectly competitive market, and it remains fixed even when a monopoly exists due to the inelastic demand. Furthermore, the electricity price can be fixed through policy regulation.
第一个术语， $p^{}$ 表示向客户出售电力的收入。电价 $p^{}$ ，可以由国家电力需求决定，如 $p^{} (D)$ 。然而，与其他市场不同的是，电力需求在任何给定时间都是相对固定的，尽管它在高峰和非高峰时段会波动。在一个完全竞争的市场中，电价可以被认为是固定的和外生的，即使由于需求缺乏弹性而存在垄断，电价也保持固定。此外，电价可以通过政策监管来固定。

The second term, $(I^{} + O^{})$ , measures the construction costs and O&M costs of generating electricity. The construction costs $I^{}$ may not direclty depend on the quantity of electricity generated, but it is related to the capacity of the generation plant. The O&M costs include both variable costs, which directly related to the electricity generation, and fixed costs, which is more related to the capacity of the power plants. We need to be careful that variable may be more direclty related to the size of the power plants (in MW), but this size determines the quantity of electricity generation.
第二个术语衡量 $(I^{} + O^{})$ 发电的建设成本和 O&M 成本。建设成本 $I^{}$ 可能并不完全取决于发电量，但它与发电厂的容量有关。运维成本包括与发电直接相关的可变成本和与发电厂容量更相关的固定成本。我们需要注意的是，变量可能与发电厂的规模（以兆瓦为单位）的关系更为密切，但这个规模决定了发电量。

The third term, $p^{} h^{}$ , is the fuel costs, which depends on the usage of fossil fuels. $p^{}$ represents the price of fossil fuels, such as gas or coal, and $h^{}$ is the heat conversion coefficient, which measures the amount of fossil fuel required to generate one unit of electricity (kWh or MWh).
第三个项 $p^{} h^{}$ 是燃料成本，它取决于化石燃料的使用情况， $p^{}$ 代表化石燃料（如天然气或煤炭）的价格， $h^{}$ 是热转换系数，它衡量产生一个单位电力所需的化石燃料量（kWh 或 MWh）。

The fourth term, $p^{} e^{}$ , indicates the costs of carbon emission. $p^{}$ is the carbon price determined in the carbon market, $e^{}$ is the emission intensity (also known as emission factor?) depends on the type of fuels for each unit of electricity generated, and $e^{} ∙$ is the total emissions given the quantity of electricity generation is
第四项 $p^{} e^{}$ 表示碳排放的成本。 $p^{}$ 碳价格是否由碳市场决定， $e^{}$ 是否排放强度（也称为排放因子？取决于每单位发电的燃料类型， $e^{} ∙$ 给定发电量的总排放量为 .

Assume the genreator aims to maximise its profit, we take the first order condition as
假设流派的目标是最大化其利润，我们将第一个订单条件视为

$\begin{matrix} \frac{d π_{}}{d} = p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{} # (2) \end{matrix}$

which is the difference between the electricity price and the costs of generation and emissoins. If this FOC is greater than zero,
即电价与发电和发电成本之间的差额。如果此 FOC 大于零，则

$\begin{matrix} \frac{d π_{}}{d} = p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{} >0 # (3) \end{matrix}$

The generator will produce as much as it can. Note that it won’t be infinite due to the demand constriant in the economy (this condition becomes relevant when the generator is the only supplier in the economy). Or it is constrained by its capacity. This condition should hole in reality, otherwise no traditional generators are willing to supply electricity.
发电机将尽可能多地生产。请注意，由于经济体中的需求构成因素，它不会是无限的（当生成器是经济体中唯一的供应商时，此条件变得相关）。或者它受到其容量的限制。这个条件应该在现实中出现漏洞，否则没有传统的发电机愿意供电。

In contrast, if the FOC is less than zero,
相反，如果 FOC 小于零，则

$\frac{d π_{}}{d} = p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{} <0$

which implies that the generator will not generate at all as each unit of electricty brings loss to the generator,
这意味着发电机根本不会产生，因为每个单位的电力都会给发电机带来损耗，

While above two inequality implies explosive solution, we can implying additional condition to find the optimal quantity of electricity.
虽然上述两个不等式意味着爆炸性解，但我们可以暗示找到最佳电量的额外条件。

Assume that the emission factor, $e^{}$ , depends on the quantity. This is pausible given the concept of marginal abatement cost curve (MACC), which is upward sloping curve and indicatese that the carbon emissions is increasing with the quantity as the generator start to genearte with the lowest emissions units first. The upward sloping curve implies that $f^{} >0$ , while $f''>0$ implies a convex curve, i.e., the speed of change is faster. Therefore, start from the inquality (3), the term $p^{} ∙ e^{}$ will be incresing until the equation is equal to zero.
假设发射因子 $e^{}$ 取决于数量。考虑到边际减排成本曲线（MACC）的概念，这是可行的，该曲线是向上倾斜的曲线，表明随着发电机首先以最低排放的单位生成，碳排放量随数量增加。向上倾斜的曲线意味着 $f^{} >0$ ，而 $f''>0$ 意味着凸曲线，即变化的速度更快。因此，从不等式（3）开始，项 $p^{} ∙ e^{}$ 将递增，直到方程等于零。

$p^{} - (p^{} h^{} + v^{}) - p^{} ∙ e^{} =0$

At this point, substitiing the functional form, the quantity of eletricity, , can be solved.
在这一点上，代入功能形式，电数，就可以解决。

Wait, the FOC may become
等等，FOC 可能会变成

$p^{} - (p^{} h^{} + v^{}) - p^{} ∙ e^{} ()- p^{} ∙ \frac{d e^{}}{d} ∙ =0$

which is a quadratic function of
它是 .

I just checked with GPT, which suggest that, for a tranditional generator, the costs should be an increasing function of the quantity, while the emission intensity should be constant?
我刚刚用 GPT 检查了一下，它表明，对于传统生成器，成本应该是数量的递增函数，而发射强度应该是恒定的？

So the alternative constrain can be the fuel prices and carbon prices, but this needs to deviate from the case of perfectly competitive market, in which individual generator has no impact on the market prices.
因此，替代约束可以是燃料价格和碳价格，但这需要偏离完全竞争市场的情况，在完全竞争市场中，单个发电机对市场价格没有影响。

2025.01.22 We may not even need the first order conditions. We can simply compare the profit function.
2025.01.22 我们甚至可能不需要第一个订单条件。我们可以简单地比较 profit 函数。

2.3 The second scenario
2.3 第二种情况

In the second scenario, the generator has both tranditional generation units and the renewable geneation units, its profit function now can be written as
在第二种情况下，发电机同时具有传统的发电单元和可再生的发电单元，其 profit 函数现在可以写成

$π_{} = p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{}$

$+ p^{} - (I^{} + O^{}) + s^{}$

where the profit function now depends on two components. The first three terms are associated with the tranditional generators, and they are explain already. The last three terms are related to the renewable geneation. $p^{}$ is the revenue from selling electritiy from renewable sources, $(I^{} + O^{})$ is the construction costs and O&M costs of renewable electricity, and $s^{}$ is the subsidiy received for the electricity generation. Note that fuel costs and carbon costs do not occur to renewable energy.
其中 Profit 函数现在取决于两个组件。前三个术语与传统生成器相关联，并且已经解释了它们。最后三个项与可更新生成有关。 $p^{}$ 是销售可再生能源电力的收入， $(I^{} + O^{})$ 是可再生电力的建设成本和运维成本， $s^{}$ 是发电获得的补贴。请注意，可再生能源不会产生燃料成本和碳成本。

The puzzling point is that we may have two first order conditions as
令人费解的是，我们可能有两个一阶条件，即

$\frac{d π_{}}{d} = p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{}$

which determines the level of
，它决定了 $.$

But there is another FOC which is
但还有另一个 FOC，即

$\frac{d π_{}}{d} = p^{} - (I^{} + O^{}) + s^{}$

Which determines the optimal level of renewable eletricity. If the subsidy level is high, the second FOC is greater than zero, so the generator will produce the maximum quantity it can. We cannot have the case that all energy are from renewable sources so we must have a condition to restrict the volume of renewable energy.
这决定了可再生电的最佳水平。如果补贴水平很高，则第二个 FOC 大于零，因此生成器将生产它所能生产的最大数量。我们不能假设所有能源都来自可再生能源，因此我们必须有一个条件来限制可再生能源的数量。

The first possible contraint is to impose a maximum quantity $S^{}$ due to natural factors (e.g., sunlight hours, wind speed). This is a certain fraction of the total demand.
第一个可能的约束是由于自然因素（例如，日照时间、风速）而施加最大数量 $S^{}$ 。这是总需求的一部分。

The second possible constraint is that there is additional costs known as the system costs (or the balancing costs), which can be an increasing function of the reneweable electrictiy. This rising system costs implies that the renewable electricty will only reach a certain level.
第二个可能的约束是存在称为系统成本（或平衡成本）的额外成本，这可能是可再生电力的增加功能。这种不断上升的系统成本意味着可再生电力只会达到一定水平。

So the sequence of getting the equlirbirum in the second scenario is that we first get the quantity of electricity generation from renewable sources, and then use the total demand as fixed, to calculate the quantity of electrictiy from fossil fuels.
因此，在第二种情况下，获得 equlirbirum 的顺序是，我们首先获得可再生能源的发电量，然后使用固定的总需求来计算化石燃料的发电量。

OK, now there is a problem. The quantity of renewable energy now should reach its maximum, and it is independent of the level of subsidy! If this is the case, how can I find the optimal level of subsidy???
好了，现在有一个问题。现在可再生能源的数量应该达到最大值，而且它与补贴水平无关！如果是这种情况，我该如何找到最佳的补贴水平???

So the question is actually simpler, will the generator continue to produce renewable energy even the subsidy is not high enough to make profit from renewable energy? Possibly yes because they make some saving from the tranditional generation.
所以问题其实更简单，即使补贴不高，发电机还会继续生产可再生能源吗，以从可再生能源中获利？P 表面上是的，因为他们从传统一代中节省了一些资金。

A comparion of the profit
利润比较

The profit in the first scenario, with tranditional generation only
第一种情况下的配置文件t，仅生成 t

$π_{} = p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{}$

with FOC > 0 as
其中 FOC > 0 为

$\frac{d π_{}}{d} = p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{} >0$

This implies that the generator will produce at the maximum determined by its capacity.
这意味着发电机将以其容量决定的最大值进行生产。

If we assume that the whole economy is supplied by electricity from fossil fuels, then there is economy-wide constraint as
如果我们假设整个经济由化石燃料的电力供应，那么整个经济的约束条件是

$=Q$

so the profit of generators or THE generator is
所以生成器或 THE 生成器的利润是

$π_{} = p^{} Q - (I^{} + O^{}) Q - p^{} h^{} Q - p^{} e^{} Q$

In the second scenario, the profit is (may be we should consider $p^{}'$ which is a lower price due to the merit order effect)
在第二种情况下，利润是（可能我们应该考虑 $p^{}'$ 由于功绩顺序效应，哪个价格较低）,

$π_{} = + = p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{}$

$+ p^{} - (I^{} + O^{}) + s^{}$

with FOC>0 for tranditional and renewable energy. The FOC for renewable energy is
其中 FOC>0 用于传统和可再生能源。可再生能源的 FOC 为

$p^{} - (I^{} + O^{}) + s^{} >0$

$s^{} > (I^{} + O^{}) - p^{}$

This is the arguments for the level of subsidy, which should be higher than the costs to attract investments. This is something we would like to chanllenge in this study.
这就是补贴水平的论据，补贴水平应该高于吸引投资的成本。这是我们希望在这项研究中挑战的事情。

Now the economy is supplied by the combination traditional energy and renewable energy, so the economy wide constraint is
现在经济由传统能源和可再生能源相结合供应，因此整个经济的制约因素是

$+ =Q$

Or we can assume that
或者我们可以假设

$=αQ$

and
一个nd

$= (1-α) Q$

where $α$ is the maximum fraction of electricity from renewable sources.
其中 $α$ 是来自可再生能源的最大电力比例。

From the profit function in the second scenario, if the FOC for the traditional parts and the renewable parts are both greater than zero, then the generator should produce both at its maximum given its capacity. However, this may work for an individual suppliers, but it does not work at the economy level, as the total demand is constrained.
从第二种情况的利润函数来看，如果传统零件和可再生零件的 FOC 都大于零，那么发电机应该在给定其容量的情况下以最大速度生产两者。然而，这可能对单个供应商有效，但在经济层面上不起作用，因为总需求受到限制。

By reducing one unit of electricity from tranditional sources, the generator’s profit is reduced by
通过减少传统来源的一单位电力，发电机的利润减少了

$∆ =- [p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{}] <0$

By increasing one unit of electricity from renewable sources, the generator’s profit is increaesd by
通过增加一个单位的可再生能源电力，发电机的利润增加

$∆ = p^{} - (I^{} + O^{}) + s^{} >0$

Therefore, this switch will change the generator’s profit by
因此，此开关将 generator 的利润更改为

$∆ π_{} =∆ +∆ =- [p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{}] + p^{} - (I^{} + O^{}) + s^{}$ $= (I^{} + O^{}) - (I^{} + O^{}) + p^{} h^{} + p^{} e^{} + s^{}$

which include the difference between the construction costs and O&M costs between tranditional generation and renewable generation, the costs of fossil fuel saved, the costs of carbon emissions saved, and the subsidy received. As long as this change in profit is greater than zero, the generator should have the motivation to switch to renewable energy,
其中包括传统发电和可再生能源发电之间的建设成本和运维成本之间的差额、节省的化石燃料成本、节省的碳排放成本以及获得的补贴。只要这种利润变化大于零，发电商就应该有动力改用可再生能源，

$∆ π_{} >0$

$(I^{} + O^{}) - (I^{} + O^{}) + p^{} h^{} + p^{} e^{} + s^{} >0$

$s^{} > (I^{} + O^{}) - (I^{} + O^{}) - p^{} h^{} - p^{} e^{}$

$s^{} = (I^{} + O^{}) - (I^{} + O^{}) - p^{} h^{} - p^{} e^{}$

Which is the mimimum level of subsidy that is needed for the switch.
Which 是转换所需的最低补贴水平。

Now, here is a different conditions for the level of subsidy! Recall the level of subsidy from the FOC for renewable energy, which gives the minimum level of subsidy to encourage renewable energy investment,
现在，这是补贴水平的不同条件！ R ecall FOC 对可再生能源的补贴水平，它给出了鼓励可再生能源投资的最低补贴水平，

$s^{} > (I^{} + O^{}) - p^{}$

$s^{} = (I^{} + O^{}) - p^{}$

Meanwhile, from the first order condtion for tranditioanl parts,
同时，对于传统零件的一阶条件，

$p^{} - (I^{} + O^{}) - p^{} h^{} - p^{} e^{} >0$

So we know that
我们知道

$s^{} > s^{}$

That does not make sense? Because we like to have smaller $s^{}$ . Unless the above FOC does not hold? Or the price is determined by marginal costs, not the LOCE? What is wrong? Or possible, the FOC for the traditional parts are less than zero? This may be possible if we consider the average electricity price, while these tranditional generators makes profit while the price is high during peak time.
这没有意义吗？ B因为我们喜欢更小 $s^{}$ 除非上述 FOC 不成立？或者价格是由边际成本决定的，而不是 LOCE？这是怎么回事？或者，传统零件的 FOC 小于零？如果我们考虑平均电价，这可能是可能的，而这些传统的发电机在高峰时段价格较高时获利。

A further consideration is that the price should be lower when there are more renewable energy, due to the merit order effect. Put this consideration in to the anlaysis of comparing $s^{}$ and $s^{}$
进一步的考虑是，由于功绩顺序效应，当可再生能源更多时，价格应该更低。将这个考虑放入比较 $s^{}$ 和 $s^{}$

Until now, we have assume that fuel price and carbon price. Further saving come from the lower fossile fuels prices and carbon prices if they respond to the demand. When the economy is swithching to reneewables, the volumen of renewable energy is $αQ$ , which is also the reduced generation from tranditional parts. Assume the decline in the fuel price is ${∆p}^{}$ and ${∆p}^{}$ , then the saving from lower prices by the existing tranditional generation is
到目前为止，我们一直假设燃料价格和碳价格。如果化石燃料价格和碳价格满足需求，则还可以进一步节省成本。当经济转向可回收物时，可再生能源的体积是 $αQ$ ，这也是传统部分的减少发电量。假设燃料价格的下降是 ${∆p}^{}$ 和 ${∆p}^{}$ ，那么现有传统发电从较低价格中节省的是

$({∆p}^{} + {∆p}^{}) = ({∆p}^{} + {∆p}^{}) (1-α) Q$

This is the saving from lower price. Are they the hidden revenue we aim to explain? We need to find the price elasticity of fuel price and carbon price.
这是从较低价格中节省的费用。它们是我们旨在解释的隐藏收入吗？我们需要找到燃料价格和碳价格的价格弹性。

This is a figure for the carbon market (for the carbon permit). In the first scenario, the emission is high and the carbon price is also high. The big retangle is the carbon costs that tranditional generators needs to pay. In the second scenario, due to the development of renewable energy, the emission is lower, so the demand curve for carbon permit shifts to the left, leading to a lower price and quantity. In this case, the costs of carbon emissions is the small retangle.
这是碳市场（碳许可证）的数字。在第一种情况下，排放量高，碳价也高。最大的解决办法是传统发电商需要支付的碳成本。在第二种情况下，由于可再生能源的发展，排放量较低，因此碳许可的需求曲线向左移动，导致价格和数量较低。在这种情况下，碳排放的成本是小的反纠。

Therefore, if the generators do not develop renewable technology, they needs to pay a lot more on the carbon costs. So the saving from lower carbon costs MUST be taken into account. Blue area is the saving from less traditional generation, and red area is the saving from lower carbon prices.
因此，如果发电商不开发可再生能源技术，他们需要支付更多的碳成本。因此，必须考虑降低碳成本带来的节省。蓝色区域是非传统发电带来的节省，红色区域是较低碳价格带来的节省。

The followng figure plot the marginal abatment costs curve. I need to think a bit more about its implication on our analysis.
下图绘制了边际 abatment 成本曲线。我需要更多地考虑一下它对我们分析的影响。

Early notes
早期笔记

They may even receive tax credits for research and development in renewable energy.
他们甚至可能因可再生能源的研发而获得税收抵免。

We should analyze how a vertically integrated energy company benefits from subsidies supporting renewable energy. This analysis should focus on vertically integrated companies for two main reasons: first, they are the common model in the UK, and second, they provide insights into how such companies can capitalize on the energy transition. In a competitive market with independent traditional and renewable generators, we would likely observe a decline in the former and the growth of the latter within the industry. However, a vertically integrated firm may benefit more directly from subsidies rather than facing such competitive shifts.
我们应该分析垂直整合的能源公司如何从支持可再生能源的补贴中受益。这项分析应侧重于垂直整合的公司，主要有两个原因：首先，它们是英国的常见模式，其次，它们提供了关于这些公司如何利用能源转型的见解。在拥有独立传统和可再生能源发电商的竞争性市场中，我们可能会观察到行业内前者的下降和后者的增长。然而，垂直整合的公司可能更直接地从补贴中受益，而不是面临这种竞争转变。

We assume a rising marginal abatement costs curve, i.e., it is getting more expensive to reduce carbon emissions. Assume a downward sloping abatement costs curve, the first derivative is negative because the function is decreasing as
我们假设边际减排成本曲线上升，即减少碳排放的成本越来越高。假设一条向下倾斜的减排成本曲线，一阶导数为负，因为该函数的递减量为

$f^{} (x) <0$

Further, we assume that the curve is concave up, meaning it becomes less steep as xxx increases (the slope is getting less negative).,
此外，我们假设曲线是凹的，这意味着随着 xxx 的增加（斜率的负值越来越小），它变得不那么陡峭。

$f^{} (x) >0$

In the first period, the company is solely based on the traditional generation. Assume there is no requirement for carbon reduction, the profit is
在第一阶段，该公司完全基于传统一代。假设没有减碳要求，利润为

$π=q* p^{} -q*AC-FC$

where pe is the electricity price, AC is the generation costs (mainly fuel costs), F is the fixed costs or sunk costs or maintenance costs.
其中 pe 是电价，AC 是发电成本（主要是燃料成本），F 是固定成本或沉没成本或维护成本。

Now the government impose a price on carbon or a restriction on the carbon emissions. Assume that the quantity remains the same, the revised profit is
现在政府对碳进行定价或限制碳排放。假设数量保持不变，修正后的利润为

$π=Q* p^{} -Q*AC-FC- \int_{}^{} ABC(x) dx$

This shows that the traditional firms needs to pay additional costs on the carbon emissions reduction.
这表明传统企业需要为碳减排支付额外的成本。