In this talk we propose a calculus of variations approach to an optimal consumption problem with isoelastic preferences over an infinite horizon. Specifically we consider a complete market with a single state variable on which all model coefficients can depend. Under some mild assumptions we characterise the value function as the unique solution to a convex variational problem which is far more amenable to numerical methods. This approach circumvents the need to solve the associated Hamilton-Jacobi-Bellman (HJB) equation. This is a desirable situation as explicitly solving the HJB equation is often intractable and even numerics cannot be readily employed due to the lack of boundary conditions. We illustrate the utility of this approach by providing examples of models which cannot be solved using existing methods in the literature but can be solved using our approach. Additionally we highlight how this approach may be extended to solve similar optimisation problems in incomplete markets.