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A simple climate-economic model described in Sec. 2 has the exact analytical solution. Moreover, its uniqueness is that it allows introducing the uncertainty in a tractable way and calculating probability distributions and moments of model state variable in closed analytical form as well. As the discussion in Sec. 4 has shown, the model yields instructive results. We believe performing the same procedure with other `toy' IAMs that can be solved analytically and semi-analytically would be an interesting direction of further research. One important issue that should be addressed in such modelling exercises is going beyond symmetric distributions for model parameters (like normal distribution adopted in the present paper) to address the problem of `fat tails' that is currently topical in economics of climate change.

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