Natural Resources and External Economics 



Regulation of thePacitic 



Halibut Fishery 



Jack Rich' 

 ABSTRACT 



In a static, long run competitive equilibrium framework, a catch function allowing 

 for short run diminishing returns is combined with a fish growth function developed by 

 Pella and Tomlinson which facilitates the derivation of an expression for the long run 

 marginal cost of "effort" in a common property resource such as a fishery. This 

 expression takes into account both "congestion" and "growth" costs. The diagramatic 

 technique of Crutchfield and Zellner is modified to take account of these externalities. 

 The modified Crutchfield-Zellner diagrams are used to illustrate the potential economic 

 losses from maximum sustainable yield regulation or other nonoptimal output. 



INTRODUCTION 



The task of the International Pacific Halibut 

 Commission, as established by treaty between 

 the United States and Canada, is to regulate 

 the Pacific Halibut Fishery at maximum sus- 

 tainable yield (MSY). The purpose of this paper 

 is to develop a model which will permit the 

 estimation of the economic losses which may be 

 associated with MSY regulation or other non- 

 optimal output levels. The model has certain 

 inherent limitations. It is static, deterministic, 

 partial equilibrium, and ignores income dis- 

 tribution and second-best effects. Still, it may 

 be useful in analyzing a fishery not much 

 affected by others, such as the Pacific halibut 

 fishery, and in focusing attention on the potential 

 magnitude of economic losses resulting from 

 the present type of regulation and from a 

 decentralized, unregulated fishery, although, 

 at least at present, it does not provide an 

 answer to the problem of how long run equi- 

 librium is to be attained. 



THEORETICAL FOUNDATION 



The starting point for the current model is 

 the Crutchfield-Zellner model (1962). Modifica- 



' Department of Economics, Oregon State University, 

 Corvallis, Oregon. 



tions to this model are made which are designed 

 explicitly to account for technological exter- 

 nalities resulting from the common property 

 nature of the fishery, .several of the modifications 

 having been developed by Smith (1969), Carlson 

 (1969), Bell (1969), and Worcester (1969), 

 among others. The present paper develops a 

 framework for the estimation of the rent and 

 consumer surplus losses (conventionally defined) 

 resulting from MSY regulation or other non- 

 optimal output in the static framework out- 

 lined above. 



Figure 1 depicts the Crutchfield-Zellner 

 model. Growth of the fish stock biomass as a 

 function of stock size is illustrated in Part A. 

 and has the typical characteristics. The de- 

 centralized, competitive supply and demand for 

 fish are illustrated in Part B, where the in- 

 dividual "S" curves are "short run" supply 

 curves for fish and show how the amount 

 supplied varies with prices, increases in quantity 

 resulting from additional units of "effort" 

 entering the fishery at higher prices. Decreases 

 in fish stock, such as from OC to OB, result in 

 an upward shift of the S curves, from S-OC 

 to S-OB; hence, with fewer fish exposed to the 

 gear, the costs of catching any given quantity 

 of fish are increased. The curve XX "traces 

 out the locus of points on each of these supply 

 curves which are sustainable; that is, where 

 the catch at the corresponding population will 



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