It is widely believed that population growth has a negative impact on global warming. Here, we set set up an integrated assessment model (a simplified DICE model) and derive analytically a condition for which a higher world population causally leads to lower long-run temperature increase under optimal carbon taxation. The condition is easily fulfilled for standard IAM parameters and independent from the discount rate, the degree of utilitarianism in the objective function, the calibration of the emission and abatement technologies, and other economic parameters. We also show that at the steady state, a larger population implies higher social and individual welfare. We also investigate a refinement of the DICE approach that could mitigate or reverse the predicted negative effect of population growth on climate change.