A significant increase of concentration in the UK salmon retail subsector has heightened concerns about retail firms’ ability to exercise market power in the purchase of supplies (oligopsony power). To assess the extent to which retail firms have exercised oligopsony power, we develop a dynamic error correction translog profit function to model the behaviour of retailers in the input market for smoke, fillet and whole salmon. Initial estimates indicated violations of monotonicity and convexity conditions as implied by economic theory. In order to ameliorate the problem, a Bayesian technique was used to impose inequality restrictions to correct the anomaly. The final estimated indices of market power in the models were low and statistically significant but sufficiently closer to the perfect competition benchmark to indicate that retailers as a whole behaved competitively during much of the period covered by this study.