Within the framework of an optimal growth model with a non renewable resource, this paper seeks to answer the question of whether a production function that ignores the constraints of physics on the production process (such as the Cobb-Douglas) can generate a good medium-term approximation of the trajectory of the economy obtained with a “true” production function, which takes these constraints into account. Two functions that respect these constraints are considered: (i) the CES function and (ii) a function called ATF, designed specifically for the purposes of this paper and which has the property of being closer to the Cobb-Douglas than is the CES. The approximation generated by the Cobb-Douglas can be rough, at least for some variables. When the “true” production function is the CES, this is explained by two effects: (i) the difference in technologies and (ii) the fact that the Cobb-Douglas totally changes the long-term path of the economy compared to that induced by the CES. In the case of the ATF, only the second effect acts. If accuracy is a concern, then whatever the “true” function the obtained results do not argue in favour of a positive answer to the above question. The Cobb-Douglas is only acceptable when the constraints of physics act weakly, which unfortunately is not always empirically verified (especially in the case of energy). If accuracy is not the first concern, then the answer seems positive, to the extent that the medium term paths generated by the Cobb-Douglas and the “true” function have a similar shape and the orders of magnitude are preserved. Previous article in issue