In the paper, the model optimization model is analyzed for the resource productivity index in the framework of the theory of economic growth. The control parameter of the model is presented by the investment share of GDP directed to technology innovation for raising the resource productivity. The optimal control problem for the resource consumption is formalized on the basis of the Pontryagin maximum principle. Various plausible investment levels are examined in the context of the model sensitivity analysis, especially, with respect to coordinates of steady states of the Hamiltonian system. The implemented analysis provides an algorithm for construction of the stair-stepwise suboptimal approximation control satisfying phase constrains of the natural resources limitation.