A Tax-Subsidy Scheme for Efficient Investment in Renewable Generation Capacity

Technical Summary: A Tax-Subsidy Scheme for Efficient Investment in Renewable Generation Capacity

Problem Statement
The paper addresses two distinct but related inefficiencies in wholesale electricity markets (WEMs) that hinder the transition to a decarbonized power system.

1. Short-Run Dispatch Inefficiency: Standard competitive market clearing, based on merit-order dispatch, minimizes operational costs but ignores pollution damages (e.g., carbon emissions). This leads to socially inefficient dispatch where polluting generators are utilized more than optimal, resulting in excessive environmental externalities.
2. Long-Run Investment Distortion: While renewable technologies often have low operating costs, their expansion can depress future wholesale spot prices. Producers, anticipating this price effect, may strategically distort their long-run capacity investment decisions. Specifically, producers may alter their investment levels to manipulate future market equilibrium prices, leading to a divergence between private investment incentives and the social-welfare optimum. Depending on the sign and magnitude of the price effect, this distortion can result in either excessive or insufficient investment relative to the social optimum.

Existing literature typically addresses these issues separately—either focusing on pollution pricing (Pigouvian taxes) for short-run dispatch or analyzing strategic capacity expansion without jointly correcting for both the pollution externality and the price-distortion effect of investment.

Methodology
The authors propose a unified two-stage framework involving a generator-specific Pigouvian tax and a generator-specific investment subsidy. The analysis relies on a behavioral benchmark where the Independent System Operator (ISO) clears the spot market competitively (price-taking behavior in dispatch), while producers act strategically in the long-run investment stage, anticipating how their capacity decisions affect future spot prices.

1. Derivation of the Pigouvian Tax:

   • The authors formulate a social planner's problem that maximizes total utility minus operational costs and pollution damages.
   • They compare the Karush–Kuhn–Tucker (KKT) conditions of the social optimum with those of the competitive market clearing (which omits damages).
   • The missing term is the marginal damage of pollution. The authors derive a tax $\Phi_{g,t}$ charged to generator $g$ in interval $t$, equal to the marginal contribution of that generator to total pollution damages. This aligns the generator's private marginal cost with the social marginal cost, ensuring the competitive dispatch outcome matches the social optimum.

2. Derivation of the Investment Subsidy:

   • The authors analyze the investment stage, where producers choose capacity $\Delta \bar{P}^G_g$ to maximize profit net of investment costs.
   • Even with the Pigouvian tax applied, a producer's profit depends on how their capacity affects the equilibrium spot price ($\Theta^*_{g,t}$). The private objective includes a term representing the effect of capacity on price ($P^*_{g,t} \frac{\partial \Theta^*_{g,t}}{\partial \bar{P}^G_g}$), which does not exist in the social welfare function.
   • To correct this, the authors derive a subsidy $\Psi_{g,t}$ that removes the price-effect profit. The subsidy is calculated based on the generator's contribution to aggregate utility (consumer surplus).
   • Specifically, the subsidy is defined as the difference between the aggregate utility of the market outcome and the aggregate utility of a counterfactual scenario where generator $g$ is fixed at zero output, minus the generator's market revenue. This aligns the private marginal return on investment with the social marginal welfare gain.

3. Implementation Requirements:

   • The mechanism does not require producers to report complete private cost functions beyond standard market submissions.
   • It requires verified emissions data, technical constraints, regulator-specified pollution-damage functions, and the ability to perform generator-specific counterfactual market re-clearing (re-optimizing the market with the generator removed).

Key Results

• Analytical Example: A single-bus, two-generator model demonstrates that without intervention, competitive dispatch favors a cheaper but polluting unit, leading to negative social welfare when damages are accounted for. The Pigouvian tax corrects the dispatch order. Furthermore, the example shows that without a subsidy, a clean generator may underinvest because additional capacity lowers the spot price in high-demand intervals, reducing revenue. The proposed subsidy restores the socially optimal investment level.
• Numerical Experiments (IEEE 24-Bus System):
  • Dispatch: Internalizing pollution damages via the tax yields a modest welfare improvement (~0.10%) in the short run, as the system already contains significant low-emission generation, but the effect is persistent.
  • Investment: The strategic investment model (without the subsidy) leads to significant overinvestment (1,835 MW vs. 66 MW in the optimal case) and a welfare loss of 4.25%. This overinvestment is characterized by low utilization rates (60.78% vs. 84.84%) and high investment costs that outweigh the benefits of reduced operating costs and pollution. The strategic case resulted in investment across all technologies, whereas the optimal case added only nuclear and fuel-oil capacity.
  • Sensitivity: The mechanism is robust to moderate errors in emissions coefficients and operating cost bids. However, it is highly sensitive to inaccurate available-capacity information; under-reporting capacity leads to significant overinvestment and welfare losses.
  • Budget: The mechanism is not inherently budget-balanced. In the baseline simulation, tax revenues covered approximately 77% of subsidy payments, leaving a deficit that requires external financing or a surplus-allocation rule.

Significance and Claims
The paper claims to fill a research gap by designing a single mechanism that simultaneously corrects the pollution externality in short-run dispatch and the distortion of capacity investment on market prices in long-run planning.

• Theoretical Contribution: The authors derive the tax and subsidy analytically from a common comparison of decentralized and social-welfare optimality conditions. The novelty lies not merely in using both instruments, but in deriving the generator-specific investment subsidy that specifically targets the price-effect term arising from strategic capacity expansion.
• Practical Implications: The mechanism aligns decentralized profit-maximizing decisions with the social-welfare benchmark without requiring new, intrusive reporting of private cost functions. It relies on existing market data, verified emissions, and counterfactual analysis.
• Limitations and Scope: The authors explicitly state that the alignment result is conditional on competitive dispatch (no strategic withholding or misreporting in the short run). The mechanism does not address operational market power, which is left for future research. Additionally, the paper acknowledges that budget balance is not guaranteed and that regulatory commitment to the rules over the investment horizon is a prerequisite for effectiveness. The study does not model energy storage, noting it as a direction for future work.

In summary, the paper argues that strategic capacity investment can lead to socially costly overinvestment and underutilization, and that a combined tax-subsidy scheme is a theoretically sound method to correct these specific market failures while respecting operational constraints.