A compact operations research (OR) model is proposed to analyse the prospects of meeting the Paris Agreement targets when direct air capture technologies can be used or not. The main features of the model are (i) the representation of the economy and energy use with a nested constant elasticity of substitution production function; (ii) the representation of climate policy through the use of a safety emissions budget concept; and (iii) the representation of an international emissions trading scheme for the implementation of climate policy. Using dynamic optimisation, several contrasting scenarios are analysed and the potential use of the model in future developments of climate/economy modelling is discussed.