TWO-SECTOR ECOLOGICAL AND ECONOMIC MODEL OF OPTIMAL DEVELOPMENT IN THE CONDITIONS OF REDUCING GREENHOUSE GAS EMISSIONS

Abstract

Introduction. The modern stage of global economic development is characterized by increasing attention to climate change and the growing anthropogenic impact on the environment. The main cause of global warming is recognized as the excessive concentration of greenhouse gases in the atmosphere, which necessitates the development of effective mechanisms for their reduction. Climate change leads to extreme weather events, degradation of natural resources, and reduced economic efficiency.

The international community responds to these challenges through global agreements such as the Kyoto Protocol and the Paris Agreement, which impose emission constraints. Their implementation requires effective economic mechanisms that balance economic growth and environmental sustainability.

In this context, ecological and economic modeling becomes increasingly important as it enables the formalization of interactions between economic activity and environmental processes. Existing approaches, including input–output, energy, and macroeconomic models, have limitations in capturing the full complexity of these interactions.

Therefore, there is a need to develop models that simultaneously account for production dynamics, environmental constraints, and policy instruments. A two-sector ecological and economic model provides such a framework by integrating production and environmental protection activities.

Purpose. The purpose of the study is to develop a two-sector ecological and economic model of optimal development under greenhouse gas emission constraints. The study aims to formalize the relationship between economic growth and environmental limitations.

The model integrates material and ecological balances within a unified dynamic framework. It also formulates an optimal control problem aimed at maximizing integral consumption.

An additional objective is to analyze stationary and turnpike trajectories of economic development. The results are intended to support the design of effective environmental and economic policies.

Materials and Methods. The methodological basis of the study is a systemic approach to ecological and economic analysis. The research employs economic and mathematical modeling methods, including optimal control theory and dynamic systems.

The core of the study is a two-sector model consisting of a main production sector and an auxiliary emission abatement sector. Production processes are described using neoclassical production functions.

The system dynamics are represented by differential equations describing capital accumulation, output, and emissions. The optimization problem is formulated as maximizing integral consumption over time.

The Pontryagin Maximum Principle is used to derive optimality conditions. The study is based on scientific publications, statistical data, and materials from international organizations.

Results. The article develops a two-sector ecological and economic model of optimal development under greenhouse gas emission constraints. The model integrates a material balance of production and distribution with an ecological balance reflecting emission generation and reduction. The economic system consists of a main production sector and an auxiliary sector responsible for emission abatement. Output is allocated among consumption, capital formation, and environmental expenditures, including investments in international emission reduction mechanisms and quota trading frameworks.

The dynamics of the system are described through differential equations governing capital accumulation in both sectors, labor supply growth, and emission constraints. The environmental restriction is formalized as a proportional relationship between gross output and emissions, reduced by abatement activities and external ecological investments. The condition of ecological efficiency ensures compliance with the established emission quota while maintaining positive economic growth.

The optimal development trajectory is formulated as an optimal control problem aimed at maximizing integral per capita consumption over the planning horizon. The Pontryagin Maximum Principle is applied to derive necessary optimality conditions and analyze the Hamiltonian structure of the system. The existence of stationary and turnpike trajectories is demonstrated, revealing balanced exponential growth paths consistent with emission limits.

Special attention is devoted to the case where domestic technological and financial capacities are insufficient for further emission reductions, making participation in international quota mechanisms essential. The proposed framework provides a formalized basis for analyzing the trade-off between economic growth and environmental policy instruments. The results contribute to the theoretical foundation of ecological and economic modeling and offer analytical tools for designing sustainable development strategies consistent with the objectives of the Paris Agreement.

Discussion. Future research may focus on extending the model to include international emission trading mechanisms. Incorporating uncertainty and fuzzy modeling approaches is also actual.

Further development may involve multi-sector extensions and empirical calibration using real-world data. The model can be applied to support national sustainable development strategies.