The objective of this study is to analyze the scope for expanding the artisanal fishery in Zanzibar and to present cointegration as an econometric method to estimate the maximum sustainable yield (MSY) in fishery. For that purpose the Schaefer and Fox surplus production models are considered. Application of cointegration is discussed to test whether there is a tendency to long run equilibrium between catch and effort as assumed by the surplus production models and implied by the MSY concept. Moreover, estimation of the parameters is dealth with. Application to data relating to artisanal fishery in Zanzibar shows that there is support for a Fox model. Moreover, we find that the current catch is only about 40 percent of the estimated MSY, but the prevalent effort is about two times bigger than the estimated optimum effort. It appears therefore that the fishery in Zanzibar is biologically overfished.