Technology innovation in evolutionary green transition: environmental quality and economic sustainability

TL;DR

The paper tackles how to engineer a green technology transition under innovation-driven abatement within an evolutionary framework where a pollution-stock–dependent environmental tax funds both abatement implementation and knowledge accumulation via $\omega$. It shows that steady states include homogeneous outcomes and internal mixed states; the latter can appear or vanish as policy shifts occur, potentially producing path-dependent transitions or backsliding depending on parameter regimes. Dynamical analysis reveals rich behavior, including stability ranges, bifurcations (flip and Neimark–Sacker), and complex attractors, implying that policy design must account for nonlinearity and multiple equilibria. Overall, the work provides a theoretical basis for when taxation and innovation funding promote environmental improvement and green diffusion, while also warning of possible unintended outcomes like oscillations or regime shifts if policies are poorly calibrated.

Abstract

We propose an evolutionary model to study the transition toward green technology under the influence of innovation. Clean and dirty technologies are selected according to their profitability under an environmental tax, which depends on the overall pollution level. Pollution itself evolves dynamically: it results from the emissions of the two types of producers, naturally decays, and is reduced through the implementation of the current abatement technology. The regulator collects tax revenues and allocates them between the implementation of the existing abatement technology and its innovation, which increases the stock of knowledge and thereby enhances abatement effectiveness. From a static perspective, we show the existence of steady states, both with homogeneous populations of clean or dirty producers and with heterogeneous populations where both technologies coexist. We discuss the mechanisms through which these steady states emerge and how they may evolve into one another. From a dynamical perspective, we characterize the resulting scenarios, showing how innovation can foster a green transition if coupled with a suitable level of taxation. At the same time, we investigate how improper environmental policies may also produce unintended outcomes, such as environmental deterioration, reversion to dirty technology, or economic unsustainability.

Figures (17)

• Figure 1: Graphical representation of different outcomes of Proposition \ref{['th:ss0']} for no investments in innovation $(\omega = 0)$. Red line denotes the level of pollution abatement, the black one the stock of emitted pollution. Internal steady state occurs when they intersect.
• Figure 2: Possible emergence/disappearance of a steady state entering/leaving the feasible region from $\boldsymbol{\xi}_0^{\ast}$.
• Figure 3: Possible simultaneous emergence/disappearance of couple of steady states entering/leaving the feasible region.
• Figure 4: Possible emergence/disappearance of a steady state entering/leaving the feasible region from $\boldsymbol{\xi}_1^{\ast}$.
• Figure 5: Sequences of steady state configurations on varying $\omega$ and $\tau_D$ when the clean technology has low emission levels. White, blue, magenta and green colors are respectively used to represent steady state sets $\mathcal{S}_0, \mathcal{S}_b, \mathcal{S}_a$ and $\mathcal{S}_2$.

Theorems & Definitions (21)

• Proposition 1
• Proposition 2
• Proposition 3
• Proposition 4
• Corollary 1
• Proposition 5
• Proposition 6
• Proposition 7
• Proposition 8
• Proposition 9