A popular model of economy and climate change has logarithmic preferences and damages proportional to the carbon stock in which case the certainty-equivalent carbon price is optimal. We allow for different aversions to risk and intertemporal fluctuations, convex damages, uncertainties in economic growth, atmospheric carbon, climate sensitivity and damages, correlated risks, and distributions that are skewed in the longer run to capture climate feedbacks. We derive a non-certainty-equivalent rule for the carbon price, which incorporates precautionary, risk insurance, and climate sensitivity and damage rate hedging effects to deal with future economic and climatic and damage risks. We interpret these effects with a calibrated DSGE model.