This research investigates the effect of fiscal policy on economic growth, focusing on the intertwined relationship between public goods provision, taxation policies, and their impact on economic dynamics and growth. The study aims to contribute to this research domain by introducing an economic model within the optimal control framework that integrates taxation policies into the social constraint and incorporates public goods into the social utility function, addressing recent limitations in this research area. Through numerical analysis, the study examines the potential effects of taxes and public goods provision on consumption and economic growth, as reflected by the level of capital. Results indicate that increasing government spending on public goods can decrease private goods consumption without significant economic growth benefits. At the same time, high tax rates could potentially hinder economic growth by overly relying on government intervention. The research findings highlight the importance of an optimal approach to fiscal policy, with policy implications including the need to carefully evaluate public funds' allocation, enhance public spending efficiency, and implement optimal tax to foster economic growth.