Environmental economics models are often too complex to be communicated in an illustrative manner. For this reason, this paper develops the Basic Climate Economic (BCE) model that features core elements of macroeconomic and climate economic modelling, while allowing for an illustrative examination of the development path. The BCE model incorporates fossil stock depletion, pollution stock accumulation, endogenous growth, and climate-induced capital depreciation. We first use graphical analysis to show the effects of climate change and climate policy on economic development. Intuition for the different model mechanisms, the functional forms, and the effects of different climate policies is provided. We then show the model equations in mathematical terms to derive closed-form solutions and to run model simulations relating to the graphical part. Finally, we compare our setup to other models of climate economics.