The parameters of the short-run cost function are estimated for three vessel types taking part in the Norwegian pelagic fisheries: purse seine vessels, trawlers, and coastal vessels. The generalized translog functional form is used. Estimates of returns to scale are calculated and the results indicate that there are substantial economies of scale in all vessel classes. It is further investigated whether excess capacity varies with vessel size and age. The analysis suggests increased quotas per vessel to avoid rent dissipation. With the total allowable catch given, the number of participating vessels must be reduced.