Many renewable resources are in intergenerational common pools, exploited by one generation after another. In our experiment, the stock available to each generation depends on the extent of exploitation by previous generations and on resource's growth rate, which is either slow or fast. Subjects show altruistic restraint in exploitation, but not enough to achieve the social optimum. The presence of an intergenerational link induces subjects - both in slow and in fast - to expect less resource exploitation from each other than subjects expect in a single generation control. On average, expectations are too optimistic, especially in slow, where intended free-riding behavior is predominant.