figure that seems consistent with the literature 

 in fisheries biology (Paloheimo and Dickie, 

 1966). Adding one day with water temperature 

 one degree in excess of 32 °F (i.e., one CTU) 

 during the cold season would add about 30 

 pounds to total output; one additional CTU 

 during the warm season would reduce output 

 by about 15 pounds. Third, the high R- values 

 support the hypothesis of fixed factor propor- 

 tions, although we recognize that another 

 analysis, covering several agencies and systems 

 of management, might well yield different 

 results. Fourth, the evidence appears to sup- 

 port the "constant returns" hypothesis, al- 

 though this is somewhat conjectural. Summing 

 the coefficients for Cobb-Douglas forms is 

 hindered by the negative coefficient on warm 

 season water temperatures. One might, as we 

 did, view the water temperature variables as 

 "shifters" of food-input relationship. If so, 

 the coefficients on the food variable do not 

 differ significantly from unity .^ 



Our estimates of marginal productivities 

 thus enabled us to ask, "What would be the 

 change in hatchery output if one were to in- 

 crease (or decrease) water temperatures by a 

 given amount?" A 10% reduction in CTU's 

 during the warm season would reduce average 

 water temperature from 52.97°F to 50.87°F 

 and cause output to increase by 5,684 pounds, 

 or about 4.36% of the mean hatchery output. 

 Raising cold season water temperatures from 

 43.99°F to 45.19°F would add 6,218 pounds 

 of output, or about 4.77% of mean hatchery 

 output. 



Factor Substitution 



If controlled inputs are combined in fixed 

 proportions, as evidenced above, the data ob- 

 viously do not allow estimation of substitution 

 possibilities. On the other hand, our analysis 

 does permit us to identify degrees of sub- 

 stitution between the fixed proportion input, 

 using food as a proxy variable, and changes 



" The negative intercept on the linear model was 

 significantly different from zero at the 0.10 level. This 

 gives some evidence of increasing returns, and is 

 consistent with the h, estimates of 1.106 and 1.047 

 for the log-linear models. Acceptance or rejection of 

 "constant returns" thus, depends partly on one's pref- 

 erence for significance levels. 



in the noncontrolled water temperature vari- 

 ables. The marginal rates of factor substitu- 

 tion, as estimated from both linear and log- 

 linear functions, are shown in Table 3. Al- 

 though log-linear models no doubt conform 

 more closely to biological reality, linear rates 

 of substitution may be appropriate for some 

 decisions. The degree of isoquant curvature is 

 largely a matter for the judgment of fisheries 

 biologists; experimental work in this area 

 should be useful in checking and refining our 

 estimates. Our confidence in the linear rates 

 would be greatest in the neighborhood of mean 

 CTU values (e.g.. Figure 2). 



Table 3. — Linear rates of factor substitution between 

 inputs.' 



9 IKoodlA-,)] 



8 [FoodCA",)] 



Functional formd |Summer CTU's (-A",) ) 9 (Winter CTU's (Jir3)l 



1. (a) Linear 



I. (b) Linear 



II. (a) Log-linear 

 II. (b) Log-linear 



-27.462 

 -29.714 

 -18.186 

 -25.867 



-58.309 

 -52.762 

 -50.972 

 -33.935 



' Estimates are based on mean values. The sign on the X vari- 

 able (warm season water temperatures) is reversed here for 

 convenience since decision makers would attempt to reduce 

 summer temperatures and increase winter temperatures. 



Increased environmental control, as through 

 controlling water temperature, is in fact one 

 means that Pacific Coast fishery agencies are 

 now considering for output augmentation. Thus 

 far, the agencies have primarily adapted to, 

 rather than controlled, this aspect of the en- 

 vironment. The hatching of fry is concentrated 

 to some degree in those hatcheries which have 

 water temperatures most conducive to this 

 operation; other hatcheries tend to specialize 

 in the rearing of fingerlings. Control of tem- 

 peratures would allow both food and transport 

 costs to be lowered, although empirical data 

 on factor price ratios were not available. It 

 was our thinking that the estimates of factor 

 substitution in Table 3, together with a step- 

 by-step presentation of "output maximization, 

 given budget constraints" would aid agencies 

 in increasing efficiency at the hatchery level.'" 



'" Specific attention was directed to the problem of 

 determining factor prices when there is significant 

 unused capacity at existing hatcheries. As mentioned 

 earlier, seasonal low water flows often force non-use 

 of some rearing ponds. 



138 



