Computing power has become a key productivity in the digital era, but it still faces many problems such as insufficient computing speed and high energy consumption. A critical measure for addressing these issues is the provision of government research and development (R&D) subsidies to foster enterprise innovation, thereby advancing green and high-quality computing power development. This paper considers two competing computing power suppliers with varying market shares and investigates the optimal target for government-provided R&D subsidies aimed at maximizing social welfare. Our analysis indicates that regardless of the subsidy strategy adopted by the government, the computing power price, R&D investment, and profits for both enterprises always increase with the amount of subsidy. However, social welfare increases with the subsidy amount up to a certain threshold, beyond which further increases become detrimental to social welfare. We also show that it is always more beneficial for social welfare to subsidize the enterprise with a larger market share when the government contemplates subsidizing a single enterprise. Ultimately, we highlight the importance of the R&D coefficient of enterprises when considering the optimal subsidy target. Specifically, if the R&D coefficient is large, as long as the subsidy amount does not exceed a threshold detrimental to social welfare, subsidizing two enterprises at the same time is often the best choice.