Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Exit Incentives for Carbon Emissive Firms

René Aïd, Xiangying Pang, Xiaolu Tan

TL;DR

This paper develops a continuous-time model in which a regulator uses a compensation scheme to incentivize exit from carbon-emissive markets, with profits following a geometric Brownian motion and social damages influencing welfare. It derives closed-form solutions for optimal exit incentives and hitting-time exit thresholds in both a single-market setting and a framework with two interacting markets, revealing a second-mover advantage and potential multiple Nash equilibria. The crude-oil application demonstrates how discounting, firm count, and market concentration affect total payments and exit timing, and it highlights the potential role of cross-country compensation to resolve coordination failures. Overall, the work contributes explicit, tractable results on the cost and timing of market exit under compensation, with clear policy implications for decarbonization strategies and international cooperation.

Abstract

We develop a continuous-time model of incentives for carbon emissive firms to exit the market based on a compensation payment identical to all firms. In our model, firms enjoy profits from production modeled as a simple geometric Brownian motion and do not bear any environmental damage from production. A regulator maximises the expected discounted value of firms profits from production minus environmental damages caused by production and proposes a compensation payment whose dynamics is known to the firms. We provide in both situations closed-form expressions for the compensation payment process and the exit thresholds of each firms. We apply our model to the crude oil market. We show that market concentration both reduces the total expected discounted payment to firms and the expected closing time of polluting assets. We extend this framework to the case of two countries each regulating its own market. The presence of a second mover advantage leads to the possibility of multiple equilibria. Applying this result to large producing countries, we find that they are unlikely to agree on the timing to exit market.

Exit Incentives for Carbon Emissive Firms

TL;DR

This paper develops a continuous-time model in which a regulator uses a compensation scheme to incentivize exit from carbon-emissive markets, with profits following a geometric Brownian motion and social damages influencing welfare. It derives closed-form solutions for optimal exit incentives and hitting-time exit thresholds in both a single-market setting and a framework with two interacting markets, revealing a second-mover advantage and potential multiple Nash equilibria. The crude-oil application demonstrates how discounting, firm count, and market concentration affect total payments and exit timing, and it highlights the potential role of cross-country compensation to resolve coordination failures. Overall, the work contributes explicit, tractable results on the cost and timing of market exit under compensation, with clear policy implications for decarbonization strategies and international cooperation.

Abstract

We develop a continuous-time model of incentives for carbon emissive firms to exit the market based on a compensation payment identical to all firms. In our model, firms enjoy profits from production modeled as a simple geometric Brownian motion and do not bear any environmental damage from production. A regulator maximises the expected discounted value of firms profits from production minus environmental damages caused by production and proposes a compensation payment whose dynamics is known to the firms. We provide in both situations closed-form expressions for the compensation payment process and the exit thresholds of each firms. We apply our model to the crude oil market. We show that market concentration both reduces the total expected discounted payment to firms and the expected closing time of polluting assets. We extend this framework to the case of two countries each regulating its own market. The presence of a second mover advantage leads to the possibility of multiple equilibria. Applying this result to large producing countries, we find that they are unlikely to agree on the timing to exit market.
Paper Structure (20 sections, 9 theorems, 131 equations, 2 figures, 2 tables)

This paper contains 20 sections, 9 theorems, 131 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The case of a single market
  3. Model
  4. Main result
  5. The case of a single firm
  6. The case of two interacting markets
  7. The setting with two regulators and Nash equilibrium
  8. The setting with one regulator
  9. The case with individual compensation scheme
  10. The case of uniform compensation scheme
  11. The social optimum without compensation
  12. Economic application
  13. Single market
  14. Two markets
  15. Conclusion
  16. ...and 5 more sections

Key Result

Theorem 2.1

Let $(\lambda_i)_{i=1,\cdots, N}$, $(\pi_i)_{i=1, \cdots, N}$ satisfy eq:lambda_pi_condition, $\gamma \ge 2$ and $\rho \in (\mu,\gamma \mu+ \frac{1}{2}\sigma^2(\gamma^2 - \gamma))$. Then the following hold true. $\mathrm{(i)}$ The constants $(\hat{x}_i)_{i=1, \cdots, N}$ defined by def:hitting_point where $c_i$ is defined in def:coef, $\hat{\tau}_0 = 0$, $\hat{\tau}_i :=\inf\{ t \ge 0 ~: X_t \ge \

Figures (2)

  • Figure 1: As a function of the number of firms $N$ (Left) Fraction of firms and of market share leaving immediatly the market. (Right) Total expected discounted payment (in trillions of dollars, left axis) and expect time of closing all production (in years, right axis). Parameters: $\mu=0.02$, $\sigma=0.08$, $\rho=0.1$, $\gamma=4$, $\pi =50\,10^6$, $\ell = 1.02\, 10^{-6}$, $\theta=0.1$.
  • Figure 2: As a function of the tail parameter $\theta$ of the size distribution of firms (Left) Fraction of firms and of market share leaving immediatly the market. (Right) Total expected discounted payment (in trillions of dollars, left axis) and expect time of closing all production (in years, right axis). Parameters: $\mu=0.02$, $\sigma=0.08$, $\rho=0.1$, $\gamma=4$, $\pi =50\,10^6$, $\ell = 1.02\, 10^{-6}$, $N=10^3$.

Theorems & Definitions (22)

  • Theorem 2.1: Optimal exit incentives for $N$ firms
  • Remark 2.1
  • Definition 3.1
  • Theorem 3.1
  • Remark 3.1
  • Proposition 3.1
  • Remark 3.2
  • Proposition 3.2
  • Remark 3.3
  • Remark 3.4
  • ...and 12 more