If an economy faces stochastic fluctuations of the resource availability, for example in the case of resource imports, it is optimal in the long run to increase the domestic savings rate in contrast to a deterministic world. Uncertainty is partly substituted by capital accumulation. But this is only true in the long run. The short run effects depend on the capital stock so far accumulated. It is shown that in some cases it may be optimal to lessen the domestic savings rate temporarily when uncertainty increases.