Carbon-Adjusted Electricity Prices Analysis

• Carbon-adjusted electricity prices are measures that integrate carbon costs into pricing through formulations such as pass-through coefficients, marginal emissions surcharges, and dual pricing mechanisms.
• Pass-through estimates vary non-linearly with carbon price levels, fuel switching, and regional constraints, affecting both green and conventional electricity pricing.
• Advanced methodologies, including econometric decompositions and machine-learning models, facilitate accurate estimation of carbon-adjusted prices and inform endogenous market designs.

Searching arXiv for recent and foundational papers on carbon-adjusted electricity prices, pass-through, and market design. Carbon-adjusted electricity prices are electricity price measures, pass-through estimates, or market-clearing prices in which carbon costs, carbon emissions, or carbon preferences are embedded in the valuation of electricity. The term does not denote a single canonical formula. In empirical pass-through studies, the adjustment is the fraction of emission-allowance or carbon-tax cost transmitted into wholesale prices (Wehrle et al., 2018, Duttilo et al., 3 Apr 2026). In emissions-accounting formulations, the adjustment augments or corrects the wholesale price by a term proportional to marginal emissions (Dahlke, 2018). In market-design research, the adjustment is endogenous: carbon-aware clearing creates differentiated prices for green and black electricity, or agent-specific prices for consumers and generators based on carbon allocation (Jong et al., 2024, Jiang et al., 1 Aug 2025, Chen et al., 2023).

1. Conceptual formulations

Several formulations recur in the literature. Some are ex post corrections of an observed price; others are equilibrium prices generated by the clearing mechanism itself. The distinction matters because a pass-through coefficient, a marginal-emissions surcharge, and a carbon-aware locational price solve different problems even when all are described as “carbon-adjusted” (Duttilo et al., 3 Apr 2026, Dahlke, 2018, Jong et al., 2024, Jiang et al., 1 Aug 2025).

Formulation	Expression	Representative paper
Pass-through correction	$p_{t,\text{adj}}^e \approx p_t^e - \theta C_t$	(Duttilo et al., 3 Apr 2026)
Emissions-adjusted marginal effect	$$\Delta P_{\text{carbon-adjusted}} = \Delta P_{\text{wholesale}} + \lambda \cdot \Delta e$$	(Dahlke, 2018)
Dual green/black pricing	$${\rm LMP}_{n}^{(\textcolor{nicegreen}{\bf g})} = {\rm LMP}_{n}^{({\bf b})} + \lambda_{\textcolor{nicegreen}{g}}$$	(Jong et al., 2024)
Agent-specific carbon-aware prices	Generator: $\lambda_{P,i}+\lambda_{G,g}$; consumer: $\lambda_{P,i}-\lambda_{D,d}$	(Jiang et al., 1 Aug 2025)

In the Italian CPTR framework, the carbon component is $C_t = p_t^{CO_2} I_t$, where $p_t^{CO_2}$ is the EU ETS allowance price and $I_t$ is the carbon intensity of generation, and only a fraction $\theta$ is transmitted into the day-ahead price (Duttilo et al., 3 Apr 2026). In the western U.S. trade framework, the adjusted price is a conceptual social-price object in which the private wholesale effect is combined with the emissions externality of additional imports (Dahlke, 2018). In the dual-pricing formulation, the adjustment takes the form of a green premium $\lambda_{\textcolor{nicegreen}{g}}$ added to the usual nodal price (Jong et al., 2024). In consumer-based carbon-cost models, the adjustment is agent-specific because carbon allocation enters directly into equilibrium conditions (Jiang et al., 1 Aug 2025).

This suggests that “carbon-adjusted electricity price” is best treated as an umbrella term for a set of related constructions rather than a single metric.

2. Carbon cost pass-through and wholesale price formation

Empirical pass-through estimates vary materially by market design, generation mix, and the absolute carbon price level. In the Austrian-German power system, the pass-through from CO$$\Delta P_{\text{carbon-adjusted}} = \Delta P_{\text{wholesale}} + \lambda \cdot \Delta e$$0 emission prices to power prices is estimated between 0.69 and 0.53 as of 2017, depending on the absolute emission price level. Around 5–10 €/tCO$$\Delta P_{\text{carbon-adjusted}} = \Delta P_{\text{wholesale}} + \lambda \cdot \Delta e$$1, pass-through is about 0.57; around 25–30 €/tCO$$\Delta P_{\text{carbon-adjusted}} = \Delta P_{\text{wholesale}} + \lambda \cdot \Delta e$$2, it peaks at about 0.68; around 80 €/tCO$$\Delta P_{\text{carbon-adjusted}} = \Delta P_{\text{wholesale}} + \lambda \cdot \Delta e$$3, it declines to about 0.53. The paper attributes the nonlinearity to fuel switch, CHP generation switch, and higher average fuel efficiency as high-emission units are displaced (Wehrle et al., 2018).

In Italy under the EU ETS, carbon costs are positively and significantly transmitted to wholesale electricity prices, but pass-through remains incomplete. The national CPTR is about 0.32 in Phase 3 and 0.29 in Phase 4, i.e. around 30% overall. Heterogeneity across bidding zones is substantial: Phase 4 CPTR is approximately 0.24 in the North, 0.24 in the Centre-North, 0.05 in the Centre-South, 0.20 in Sicily, and 0.41 in Sardinia. Quantile regression finds no strong evidence that pass-through depends systematically on the price level, but zonal asymmetries remain (Duttilo et al., 3 Apr 2026).

Machine-learning evidence for EPEX emphasizes that the carbon effect is not merely additive. A random forest with 1,000 regression trees modeling 22-day changes in baseload and peakload prices from 2 January 2012 to 11 January 2022 reduces in-sample RMSE by 50.5% for baseload and 51.3% for peakload relative to OLS, with out-of-bag RMSE 0.312 and 0.353. CO$$\Delta P_{\text{carbon-adjusted}} = \Delta P_{\text{wholesale}} + \lambda \cdot \Delta e$$4 permit prices strongly impact wholesale electricity prices, their impact clearly increases post-2021, and the increase is particularly pronounced for baseload. Permit importance rises from 0.079 to 0.132 for baseload and from 0.068 to 0.080 for peakload when moving from the full sample to the post-2021 subsample. Natural gas is the single most important commodity driver, and a partial-effect surface shows electricity prices rising when both carbon permit price changes and natural-gas price changes rise (Kohlscheen et al., 2022).

Across these studies, carbon-adjusted wholesale prices are regime-dependent. The carbon component is shaped not only by the allowance price itself, but also by fuel switching, marginal fuel identity, zonal constraints, and non-linear interactions with gas and renewables.

3. Estimation and decomposition methodologies

The methodological range is unusually broad. In the EPEX study, the price object is a predictive decomposition of monthly electricity price changes: $$\Delta P_{\text{carbon-adjusted}} = \Delta P_{\text{wholesale}} + \lambda \cdot \Delta e$$5 The lagged 22-day electricity price change proxies mean reversion, while the remaining regressors capture commodity prices, weather and renewable conditions, and financial controls. The finding that the random forest dominates linear least squares is used as evidence that non-linearities and interaction effects are central in electricity pricing (Kohlscheen et al., 2022).

In the Italian CPTR study, the econometric object is the log-differenced electricity-fuel spread: $$\Delta P_{\text{carbon-adjusted}} = \Delta P_{\text{wholesale}} + \lambda \cdot \Delta e$$6 Here $$\Delta P_{\text{carbon-adjusted}} = \Delta P_{\text{wholesale}} + \lambda \cdot \Delta e$$7 is the Phase 3 CPTR, while $$\Delta P_{\text{carbon-adjusted}} = \Delta P_{\text{wholesale}} + \lambda \cdot \Delta e$$8 captures the change in Phase 4. Robustness variants use average daily prices, quadratic demand terms, a GAM, and quantile regression (Duttilo et al., 3 Apr 2026).

For price-based demand response, the key methodological problem is that market prices do not directly reveal the carbon consequence of a marginal load change. The merit-order study therefore approximates hourly marginal emission factors using a detailed power-plant method and a piecewise-linear method based on virtual power plants. Its marginal-cost formula,

$$\Delta P_{\text{carbon-adjusted}} = \Delta P_{\text{wholesale}} + \lambda \cdot \Delta e$$9

is the bridge between carbon pricing and carbon-adjusted electricity prices: raising $${\rm LMP}_{n}^{(\textcolor{nicegreen}{\bf g})} = {\rm LMP}_{n}^{({\bf b})} + \lambda_{\textcolor{nicegreen}{g}}$$0 increases the marginal cost of carbon-intensive plants more strongly and can reorder the merit order (Fleschutz et al., 2020).

Networked policy analysis introduces another layer. Under CBAM, a spatio-temporal GNN is used to learn a shared graph representation

$${\rm LMP}_{n}^{(\textcolor{nicegreen}{\bf g})} = {\rm LMP}_{n}^{({\bf b})} + \lambda_{\textcolor{nicegreen}{g}}$$1

with parallel heads for carbon intensity and price, plus a correlation-preserving loss,

$${\rm LMP}_{n}^{(\textcolor{nicegreen}{\bf g})} = {\rm LMP}_{n}^{({\bf b})} + \lambda_{\textcolor{nicegreen}{g}}$$2

The stated purpose is to retain the non-zero covariance between carbon intensity and electricity prices in an interconnected system (Shen et al., 5 May 2026).

Taken together, these methods imply that carbon-adjusted pricing can be estimated as pass-through, inferred from the merit order, reconstructed from optimization duals, or learned from spatio-temporal network structure.

4. Endogenous carbon-aware market designs

A prominent research direction replaces ex post adjustment with endogenous pricing rules. In dual pricing dispatch, loads submit both a willingness to pay for electricity and a premium for green electricity. The clearing problem adds a green-balance constraint, yielding two nodal prices: $${\rm LMP}_{n}^{(\textcolor{nicegreen}{\bf g})} = {\rm LMP}_{n}^{({\bf b})} + \lambda_{\textcolor{nicegreen}{g}}$$3 Because $${\rm LMP}_{n}^{(\textcolor{nicegreen}{\bf g})} = {\rm LMP}_{n}^{({\bf b})} + \lambda_{\textcolor{nicegreen}{g}}$$4, the green price is always at least as high as the black price. In a 2000-node ERCOT-like synthetic system with 50% renewables, the mechanism dispatches an extra 239 MWh of green electricity, black energy increases by only 8 MWh, and the green LMP is about \$1.78/MWh higher than the black LMP (Jong et al., 2024).

Consumer-based carbon-cost models move carbon allocation inside market clearing. The centralized problem

$${\rm LMP}_{n}^{(\textcolor{nicegreen}{\bf g})} = {\rm LMP}_{n}^{({\bf b})} + \lambda_{\textcolor{nicegreen}{g}}$$5

includes a generator-to-load allocation matrix $${\rm LMP}_{n}^{(\textcolor{nicegreen}{\bf g})} = {\rm LMP}_{n}^{({\bf b})} + \lambda_{\textcolor{nicegreen}{g}}$$6 and consumer emissions

$${\rm LMP}_{n}^{(\textcolor{nicegreen}{\bf g})} = {\rm LMP}_{n}^{({\bf b})} + \lambda_{\textcolor{nicegreen}{g}}$$7

The equivalent equilibrium yields carbon-adjusted prices $${\rm LMP}_{n}^{(\textcolor{nicegreen}{\bf g})} = {\rm LMP}_{n}^{({\bf b})} + \lambda_{\textcolor{nicegreen}{g}}$$8 for generators and $${\rm LMP}_{n}^{(\textcolor{nicegreen}{\bf g})} = {\rm LMP}_{n}^{({\bf b})} + \lambda_{\textcolor{nicegreen}{g}}$$9 for consumers. The theoretical ordering result states that lower-emitting generators receive higher carbon adjustments and consumers with higher carbon costs face higher effective prices. The same framework proves revenue adequacy and individual rationality, and shows that a uniform consumer carbon cost is equivalent to a generator carbon tax (Jiang et al., 1 Aug 2025).

A related DC-OPF formulation emphasizes that the model remains linear and convex by using allocation variables $\lambda_{P,i}+\lambda_{G,g}$0 rather than carbon-flow proportional sharing. In its case studies, introducing consumer-side carbon costs reduces emissions through two channels: redispatch toward cleaner units and demand reduction when carbon-sensitive loads assign high carbon costs (Jiang et al., 16 Jan 2025).

Joint electricity-carbon pricing based on primal-dual optimality conditions pursues a different objective: decentralizing the carbon-aware social optimum while preserving market properties. The proposed mechanism is proven to satisfy budget balance, individual rationality, dispatch-following incentive compatibility, and truthful-bidding incentive compatibility. In the six-generator, eight-load example, the budget-balanced parameter is $\lambda_{P,i}+\lambda_{G,g}$1, and the resulting carbon-aware social welfare equals the optimum of the social-welfare problem, whereas the comparator T2 does not attain that optimum (Chen et al., 2023).

For real-time storage participation, combined electricity-and-emission prices are defined as

$\lambda_{P,i}+\lambda_{G,g}$2

where $\lambda_{P,i}+\lambda_{G,g}$3 is the LMP and $\lambda_{P,i}+\lambda_{G,g}$4 is the Aumann-Shapley emission price. The storage operating policy is then derived as a function of $\lambda_{P,i}+\lambda_{G,g}$5, so the carbon component directly shifts the charging and discharging thresholds (Xie et al., 2023).

These market designs do not merely append a carbon surcharge. They alter dispatch, allocation, and settlement simultaneously.

5. Spatial heterogeneity, trade, and cross-border adjustment

Cross-border trade and regional heterogeneity make carbon-adjusted prices spatially non-uniform. In the western United States, each 1 GWh increase in California electricity imports is associated with an average \$0.15/MWh decrease in CAISO wholesale price, conditional on local demand. The same increase is associated with a 321 metric ton reduction in California CO$\lambda_{P,i}+\lambda_{G,g}$6 emissions and a net 70-ton average decrease in CO$\lambda_{P,i}+\lambda_{G,g}$7 emissions across the western U.S., although neighboring regions experience small increases of +283 lbs SO$\lambda_{P,i}+\lambda_{G,g}$8 and +270 lbs NO$\lambda_{P,i}+\lambda_{G,g}$9 per 1 GWh increase in trade. Imports mostly displace natural gas generation on the margin in California, and less than 10% of each GWh of imports on average is supplied by coal (Dahlke, 2018).

In simplified European power-system models with GDP-based inhomogeneous carbon prices, richer regions face higher effective carbon prices and poorer regions face lower ones. The resulting carbon-adjusted electricity costs diverge strongly across space. For $\lambda_{P,i}-\lambda_{D,d}$0 and rising heterogeneity $\lambda_{P,i}-\lambda_{D,d}$1, LCOE in Baltic, Eastern, and Balkans regions drops by about half, while LCOE in Germany, Benelux, and Scandinavia rises by more than a quarter. Conventional supply rises from about 10% at $\lambda_{P,i}-\lambda_{D,d}$2 to about 40% at $\lambda_{P,i}-\lambda_{D,d}$3, and pronounced leakage emerges for $\lambda_{P,i}-\lambda_{D,d}$4 (Schlott et al., 2021). In the 11-node version of the same problem, a strongly inhomogeneous distribution at $\lambda_{P,i}-\lambda_{D,d}$5 produces 100% higher emissions than the homogeneous case, and at $\lambda_{P,i}-\lambda_{D,d}$6 the regional CO$\lambda_{P,i}-\lambda_{D,d}$7 prices range from 79 to 413 at $\lambda_{P,i}-\lambda_{D,d}$8 and from 0 to 577 at $\lambda_{P,i}-\lambda_{D,d}$9 (Schlott et al., 2019).

CBAM adds another mechanism of heterogeneity. In the eight-country GNN-based counterfactual, CBAM is modeled as a cost on cross-border electricity transactions based on the exporter’s carbon intensity above a threshold of 50 kg CO$C_t = p_t^{CO_2} I_t$0/MWh, scaled by implementation intensity and an ETS proxy of 85 EUR/tCO$C_t = p_t^{CO_2} I_t$1. The reported effect is asymmetric: low-carbon countries such as France and Switzerland can gain a competitive advantage and may see lower domestic electricity prices, while high-carbon countries such as Poland and the Czech Republic face higher prices. The stated merit-order shift reduces coal-based import reliance from 40% to 15%, while nuclear rises from 15% to 30% and renewables from 10% to 30% (Shen et al., 5 May 2026).

A different European response is to leave the uniform clearing price unchanged but alter settlement in high-price hours. Under the proposed reform, eligible non-emitting generators are paid

$C_t = p_t^{CO_2} I_t$2

while other generators still receive $C_t = p_t^{CO_2} I_t$3. Using hourly 2025 data with $C_t = p_t^{CO_2} I_t$4 and $C_t = p_t^{CO_2} I_t$5, average expenditure falls from 104.4 to 95.5 euro/MWh in Austria, a reduction of 8.5%, and from 92.8 to 88.4 euro/MWh in Germany, a reduction of 4.7% (Finster et al., 26 Mar 2026).

These results indicate that carbon adjustment is not only a matter of adding carbon cost to marginal generation. It also redistributes rents, reshapes trade flows, and can either amplify or offset regional price differentials.

6. Demand response, buildings, and long-run system transformation

Price-based flexibility is not automatically carbon-reducing. Across 20 European countries, shifting 1 kWh each day from the most expensive hour to the cheapest hour reduces costs in all countries but increases operational carbon emissions in 8 of the 20 countries and by 2.1% on average when evaluated with MEFs. By contrast, MEF-based shifting reduces emissions by 35% on average, albeit with 56% lower monetary cost savings than price-based shifting. In Germany, the Spearman correlation between marginal cost and carbon intensity along the merit order is $C_t = p_t^{CO_2} I_t$6 at 24.9 €/t, $C_t = p_t^{CO_2} I_t$7 at 42.6 €/t, $C_t = p_t^{CO_2} I_t$8 at 100 €/t, $C_t = p_t^{CO_2} I_t$9 at 156.1 €/t, and $p_t^{CO_2}$0 at 235.6 €/t; the paper uses this to argue that adequate carbon prices are required for price-based demand response to become environmentally beneficial (Fleschutz et al., 2020).

At the retail layer, economic and emissions signals can be misaligned. A large U.S. dataset combining 1,492 commercial and industrial tariffs, 138 incentive-based demand-response programs, hourly DAM prices, MEFs, and AEFs finds that DAM prices and MEFs are positively correlated on average, while tariffs and AEFs are negatively correlated on average. The interpretation is that existing tariff structures often incentivize consumption when the grid is dirtier rather than cleaner (Chapin et al., 13 Nov 2025).

Building-level carbon-aware EMS formalizes the adjustment as an operational price signal. In CAEMS, the objective minimizes energy cost plus carbon cost,

$p_t^{CO_2}$1

with the carbon term priced through marginal carbon intensity in both DA and RT settlement. The implied effective RT price is

$p_t^{CO_2}$2

Using PJM data, the carbon-aware case at $p_t^{CO_2}$3 reduces emissions by 22.5% with only a 1.7% increase in cost relative to cost-only dispatch (Cho et al., 9 Mar 2026).

Long-run studies shift attention from short-run pass-through to endogenous structural change. In the agent-based model ElecSim, a $p_t^{CO_2}$4/tCO$p_t^{CO_2}$5 tax leads to about 70% renewable electricity by 2050, while Monte-Carlo uncertainty improves MAE by 52.5% and reduces RMSE from 10.2 to 4.41 £/MWh in price validation against UK N2EX data (Kell et al., 2019). In sector-coupled Germany, price formation transitions from fossil-fuel price setting to opportunity costs of storage and flexible demand; by 2045, the fully decarbonized system clears with non-zero prices in 75% of all hours, and demand technologies set 38% of prices versus 3% in 2020 (Geis et al., 12 Sep 2025). In a 28-country carbon-neutral European scenario, German average electricity price is about 58 EUR/MWh, while onshore wind and solar PV market values are about 41 and 37 EUR/MWh, respectively, because cross-sectoral demand bidding and renewable cannibalization jointly shape prices (Böttger et al., 2021).

The long-run implication is that carbon-adjusted electricity pricing evolves with the system itself. In fossil-dominated markets it is largely a pass-through problem; in highly renewable and sector-coupled systems it increasingly becomes a question of opportunity costs, flexibility valuation, and the carbon content of marginal demand as much as of marginal generation.