Figure 20. — Extinction. 



AN EMPIRICAL CASE STUDY: 



THE U.S. INSHORE AMERICAN 



LOBSTER FISHERY 



The U.S. inshore American lobster fishery 

 — principally located off the coast of Maine 

 — represents a good case study for a number of 

 reasons. First, the American lobster is considered a 

 high quality seafood item and is a popularly consumed 

 species for which demand has been increasing rapidly 

 (Bell, 1972). Second, because of intensive fishing pres- 

 sure the resource has shown signs of overexploitation. 

 Third, the inshore lobster fishery is one of the few 

 grounds for which enough data are available so that 

 some rough measures of needed biological and 

 economic parameters can be derived. Our discussion 

 will be subdivided on the basis of production- and 

 demand-related estimates. 



A. The Production Function and the 

 Supply of American Lobsters. 



There are four parameters on the supply side for 

 which initial estimates are required: a, b, r, and 77. -' 

 The first three can be developed by combining statisti- 

 cal estimation and independently derived data. As- 

 sume that the biomass is instantaneously in equilib- 



rium (i.e. 



dt 



= 0). Then, taking the inverse of (14) 



and substituting it for A' in (11), we obtain: 



Kx = cK-dK 



(16) 



where 



_^, d 

 b 



b 



and .V = c~dK (17) 



Equation (16) is the familiar parabolic yield function 



-'An alternative approach suggested by Thomas (1973) uses the 

 Beverton-Holt model in developing a yield/recruit relationship. 

 However, because a stock-recruitment equation is not specified, it 

 cannot be incorporated into our bioeconomic model at this time. 



postulated by Schaefer (1954). Notice that both the 

 harvest rate, Kx, and output per vessel, x, may be 

 specified solely in terms of the number of vessels or 

 fishing effort. Similarly, the common property re- 

 source externality, as given in (17), is a function only 

 of the level of A^. Over a longer period of time the basic 

 assumption underlying equations (16) and (17) may re- 

 flect a valid representation; i.e., effort or K is the only 

 instrumental variable affecting output. There are three 

 different parameters embedded in estimates of c and d. 

 The only way that a, h, and /■ can be derived is if some 

 independent biological information is given. More 

 specifically, suppose that we have an estimate of the 

 biomass consistent with maximum sustainable yield, 

 call it X". Since X" is equal to ci/2b, it follows that the 

 following parameters may be estimated (designated by "): 



r = d/2X°, 

 h =[drr^Y\ 

 a = c bir. 



(18) 

 (19) 

 (20) 



Thus, (17) will be estimated subject to one modifica- 

 tion concerning the introduction of an environmental 

 variable. Several biologists, including Dow et al. (see 

 footnote 8), have argued that a long-term trend of de- 

 clining seawater temperature is partially responsible 

 for the decline in U.S. coastal catches. ^^ It will be 

 assumed in this study that seawater temperature (°F) 

 affects the a term in the growth function so that. 



^l]L = a(°F) X-bX\ 

 dt 



(21) 



where °F is equal to the mean annual seawater tem- 

 perature, in degrees Fahrenheit Boothbay Harbor, 

 Maine, with da/d°F = a'>0. Seawater temperature 

 can easily be incorporated into (17) in the following 

 way: 



X = c 



dK + Z(°F), 



(22) 



where ;: represents the change in output per boat as a 

 result of a one-degree change in water temperature.-^ 

 Data on the number of traps fished per year for the 

 entire inshore American lobster fishery are available 

 for the 1950-1969 period. ^^ Output per trap was re- 

 gressed against the number of traps and seawater 



^^Higher seawater temperature can affect the natural yield of lob- 

 sters by providing a climate in which "molting" is facilitated. A larger 

 number of molts will tend, ceteris paribus, to increase the yield 

 associated with any given level of the biomass. 



-^Implicit in the way the effect of seawater temperature is mea- 

 sured is the relationship: c = c' + z(°¥). 



"Unfortunately, there is no precise measure of fishing effort, for 

 the inshore lobster fishery. The traps fished series is not adjusted for 

 days fished or extent of utilization. Dow has used the traps fished 

 series as a rough proxy for fishing effort. 



40 



