A Principal-Agent Model for Optimal Incentives in Renewable Investments

TL;DR

The paper addresses how to regulate renewable investments to align with long-term climate goals using a continuous-time principal–multi-agent framework that incorporates both drift and volatility control. It compares a single-regulator, dual-technology firm to a two-firm, specialized setting, deriving explicit second-best rebate contracts and showing that cross-subsidies can improve the regulator's certainty equivalent when risk aversion is shared. The main technical contributions are closed-form contract structures and a rigorous demonstration that two interacting firms can yield higher regulatory value than a single integrated firm under realistic frictions, supported by numerical experiments. The work offers policy-relevant insights into incentive design for renewable investment and intermittency mitigation, highlighting the potential practical benefits and challenges of coordinating multiple specialized energy producers.

Abstract

We investigate the optimal regulation of energy production in alignment with the long-term goals of the Paris Climate Agreement. We analyze the optimal regulatory incentives to foster the development of non-emissive electricity generation when the demand for power is met either by a single firm or by two interacting agents. The regulator aims to encourage green investments to limit carbon emissions while simultaneously reducing the intermittency of total energy production. We find that the regulator can achieve a higher certainty equivalent by regulating two interacting firms, each investing in one technology, rather than a single firm managing both technologies. This higher value is achieved thanks to a greater degree of freedom in the incentive mechanisms, which involve cross-subsidies between firms. Moreover, we find that it is optimal to compensate firms for shutting down their emissive production assets. We provide closed-form expressions of the second-best contracts and show that they take a rebate form, involving time-dependent prices for each state variable. A numerical study quantifies the impact of the designed second-best contract in both market structures compared to the business-as-usual scenario.

Figures (8)

• Figure 1: A comparison of business-as-usual (BU) and second-best (SB) implications for the single producer setting without volatility control, in which the constant volatilities, $\sigma_{1,\cdot }$ and $\sigma_{2,\cdot }$, are taken from \ref{['tab:FixedParameterCost_Agents']}. (a): Investment efforts $a^{{\rm sb,m}}$ in energy production of the single firm. (b): Energy production in the single producer setting.
• Figure 2: The single producer setting with volatility control. (a): Firm's optimal volatility control $b^{{\rm bu,m}}$ in the business-as-usual case. (b): Firm's optimal volatility control $b^{{\rm sb,m}}$ under the second-best contract.
• Figure 3: The single producer setting under the second-best contract with volatility control (DVC) and without volatility control (DC, i.e. with constant uncontrolled volatilities $\sigma_{1,\cdot }$ and $\sigma_{2,\cdot }$ given by Table \ref{['tab:FixedParameterCost_Agents']}). (a): Firm's optimal investments $a^{{\rm sb,m}}_j$ in energy production. (b): Energy production in the single producer setting.
• Figure 4: A comparison of the market structures, one (M) and two firms (C), in the business-as-usual case without volatility control. (a): Investment efforts $a^{{\rm bu},\cdot}$. (b): Energy production.
• Figure 5: A comparison of the market structures, one (M) and two firms (C), under a second-best contract without volatility control. (a): Investment efforts $a^{{\rm sb},\cdot}$. (b): Energy production.

Theorems & Definitions (10)

• Definition 2.1: Production firms in Nash equilibrium
• Remark 2.1
• Proposition 3.1
• Theorem 3.1
• Proposition 4.1
• Proposition 4.2
• Proposition 4.3
• Proposition 5.1
• Proposition 5.2
• Proposition 5.3