Individual transferable quota (ITQ) regimes have been adopted in a number of fisheries. While the issue of market power in such regimes has been discussed, this paper contributes to the literature by solving for explicit expressions for harvesting, quota price, and efficiency loss. In addition to supporting the previous findings, the explicit solution indicates that the cost of the market leader in relation to the fringe, as well as the size of the fringe, affects the magnitude of the efficiency loss. Inspired by the Norwegian Northeast Arctic cod fishery, the paper is among the first to provide a numerical illustration of the efficiency loss of market power in a rights-based regime for fisheries. The model is simulated for two cost functions, wherein one allows for exit from the fishery. The numerical results support the theoretical findings and indicate that generally, the efficiency loss of the market power is small.