Recent work has formulated an MPC strategy for a sustainable development problem, focused on the control of a stochastic, non-linear, economic model called PROMETHEUS. This work also takes PROMETHEUS to be the system. To use MPC an analytic approximation of PROMETHEUS is required, with previous work focusing on linear and non-linear time invariant models. Global optimality of the solution could not be guaranteed, since to achieve reasonable accuracy in iterative fitting was required which destroyed convexity of the optimization. In this paper an LTV model is considered and is shown to reduce the approximation error. It is demonstrated that the model can be finitely parameterized and that the predominant time variation in PROMETHEUS is from a decaying exponential weighting on the predicted input sequence. It is suggested that this variation is a representation of inflation. The sustainable development MPC methodology is recast for such a model. Convexity of the MPC optimization with an LTV model guarantees global optimality; results are presented which demonstrate the improvement in performance which this allows.