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where X represents the undetermined lagrange multiplier. Equation (20a)

states that the vessel catch rate be adjusted to the point where price

equals direct and user cost. Similarly, equation (20b) states that mesh

size should be adjusted to the point where marginal private and social

revenue is less than or equal to the cost of changing mesh size.

Condition equation (20c) states that the marginal profitability of total

industry catch equals the marginal social cost of adding a vessel to the

fishery. Using these criteria, the socially optimal levels of the

decision variables will be realized. Of course, this assumes that the

socially optimal position of a fishery is achieved by catching MEY.

 As with previous writers, Smith (1969) concludes that in the

absence of sole ownership, an open access fishery must be regulated to

achieve economically efficient production. Smith proposes that an

extraction fee of -f3 on each pound of fish landed and a license fee of

Vc4 on each vessel would be sufficient to insure social and economic

efficiency (MEY) in an open-access fishery.

 The main goal of bioeconomic theory can be seen to be that of

representing the productive activities of fishing within the bio-

technical constraints created by the growth pattern of the resource

stock. The works discussed above are by no means exhaustive. They

merely serve to illustrate the historical development of bioeconomic

theory and the general conclusions derived concerning economic effi-

ciency in fisheries production. Under the stated assumptions of con-

stant product price, a well-behaved growth law, and homogeneous units of

effort, be they vessels or some other economic entity, the above models

all arrive at the conclusion that in the absence of restrictions of

some type, suboptimal levels of catch and effort will result.