The rise of foundation models has driven the emergence of AI supply chains, where upstream foundation model providers offer fine-tuning and inference services to downstream firms developing domain-specific applications. Downstream firms pay providers to use their computing infrastructure to fine-tune models with proprietary data, creating a co-creation dynamic that enhances model quality. Amid concerns that foundation model providers and downstream firms may capture excessive consumer surplus, along with increasing regulatory measures, this study employs a game-theoretic model involving a provider and two competing downstream firms to analyze how policy interventions affect consumer surplus in the AI supply chain. Our analysis shows that policies promoting price competition in downstream markets (i.e., pro-price-competitive policies) boost consumer surplus only when compute or data preprocessing costs are high, while compute subsidies are effective only when these costs are low, suggesting these policies complement each other. In contrast, policies promoting quality competition in downstream markets (i.e., pro-quality-competitive policies) always improve consumer surplus. We also find that under pro-price-competitive policies or compute subsidies, both the provider and downstream firms can achieve higher profits along with greater consumer surplus, creating a win-win-win outcome. However, pro-quality-competitive policies increase the provider's profits while reducing those of downstream firms. Finally, as compute costs decline, pro-price-competitive policies may lose their effectiveness, whereas compute subsidies may shift from ineffective to effective. These findings offer insights for policymakers seeking to foster AI supply chains that are economically efficient and socially beneficial.