An important conclusion from the literature on hydropower is that if there are no other constraints than the available water reservoirs for a year, and operating costs are ignored, the competitive (and socially optimal) outcome is characterized by the (present value) price being constant through the year. A second important conclusion is that the outcome under monopoly generally will differ from this, provided that the demand functions differ across different days (or other sub-periods) of the year. We show that even if the demand function is the same all days of the year, the monopoly outcome will generally differ from the competitive outcome. The difference is caused by the profit function of a price-setting producer of hydropower being non-concave. This non-concavity can be caused by short-run capacity limits either on exports and imports of electricity, or on the supply of alternative electricity sources.