In this paper we analyse the optimal management of a renewable resource (groundwater) with stock-dependent extraction cost and a backstop substitute, facing two-sector linear demands. Application to the Kiti region in Cyprus demonstrates the model’s performance and is used to test for the difference between optimal and myopic behaviour. It is found that the presence of a backstop resource diminishes the importance of optimal dynamic behaviour, whereas in the absence of backstop the optimal control solution yields a value for social welfare significantly larger than the myopic policy.