We present a theoretical framework assessing the economic implications of bias in AI-powered emergency response systems. Integrating health economics, welfare economics, and artificial intelligence, we analyze how algorithmic bias affects resource allocation, health outcomes, and social welfare. By incorporating a bias function into health production and social welfare models, we quantify its impact on demographic groups, showing that bias leads to suboptimal resource distribution, increased costs, and welfare losses. The framework highlights efficiency-equity trade-offs and provides economic interpretations. We propose mitigation strategies, including fairness-constrained optimization, algorithmic adjustments, and policy interventions. Our findings offer insights for policymakers, emergency service providers, and technology developers, emphasizing the need for AI systems that are efficient and equitable. By addressing the economic consequences of biased AI, this study contributes to policies and technologies promoting fairness, efficiency, and social welfare in emergency response services.