Abstract
This paper develops a mathematical model to explore the impact of energy subsidies on market
dynamics and environmental sustainability in a recessionary economy. The model examines how
subsidies influence energy demand, government costs, and carbon emissions, with a focus on the
trade-offs between short-term economic recovery and long-term environmental impact. The
findings suggest that while subsidies can stimulate demand and support economic recovery, they
can also lead to increased emissions, particularly when applied to non-renewable energy sources.
The optimal subsidy level is determined by balancing consumer welfare gains against
environmental costs. The model provides policymakers with a framework to design energy
subsidies that promote both economic growth and sustainability, particularly in times of economic
downturn. Future research should explore non-linear market relationships and validate the model
using empirical data.