The paper provides an analytic integrated assessment model of climate change (AIAM). Quantitatively, the model competes with its numeric deterministic counterparts used in policy advising. I employ the model for an economic evaluation of the major climate change uncertainties. Here, the analytic solution overcomes Bellman’s curse of dimensionality. I show the different welfare implications of  “objective” uncertainty, epistemological uncertainty, and anticipated learning. Under certainty, the persistence of atmospheric carbon dioxide (carbon cycle) is the main amplifier of the carbon tax, whereas uncertainty mostly acts through the ocean-atmosphere temperature dynamics (climate system). Apart from deriving new insights, the analytic nature the model helps to convey assumptions and implications of integrated assessment modeling to a broad audience.