Based on existing pollution emission policies, this study addresses the relationship between innovation and energy input along with energy price. Both energy demand and innovative investment are characterized in this work. First, this paper argues that higher energy prices results in lower innovation investment in reduction of emission, higher innovation in production, lower energy demand and lower consumer surplus. Second, the increased effects of emissions on consumers yield lower innovation investment, lower energy demand and lower consumer surplus. Finally, policies for controlling emissions are also discussed in this study. Stricter policies for controlling emissions yield more innovative investments to reduce emissions and less investment to improve production efficiency, resulting in lower demand for energy and lower demand for and higher prices of products. In theory, this study develops the theory about multi-dimensional innovations and captures the relationship between innovative investments to reduce emissions and innovation to improve production efficiency.