as water surrounded by concrete. Water flows, 

 as noted earlier, vary in quantity and tem- 

 perature. Both of these physical dimensions 

 are largely outside the control of management. 

 Although some low flow augmentation is ac- 

 complished, the usual result of low flows during 

 summer months has been an inability to fully 

 utilize rearing space. Since the rearing ponds 

 are fairly small and numerous, low flows are 

 adjusted for by maintaining water volume 

 in some ponds and temporarily retiring others. 

 Thus, the rearing space actually used is also 

 fairly divisible, although some seasonal excess 

 capacity may exist. 



Although our initial inclination was that 

 separate marginal factor productivities might 

 be estimated, discussions with hatchery man- 

 agers soon revealed the similarity of practices 

 in combining controlled inputs. Levels of 

 inputs and outputs at larger hatcheries seem- 

 ed to be constant multiples of those found at 

 smaller hatcheries, although opportunities for 

 variable input proportions seemed to be present 

 in a physical sense. One could, for example, 

 stock rearing ponds with fingerlings at dif- 

 ferent rates, or spread existing water flows 

 over all rearing ponds. Centralized manage- 

 ment, of course, may not be conducive to such 

 experiments. On the other hand, it may well 

 be that past "experiments", intended or other- 

 wise, have revealed that other factor combin- 

 ations involve a greater degree of risk. For 

 example, disease spreads rapidly in rearing 

 ponds; overcrowding of fingerlings might be 

 disastrous. Similarly, lower water levels in 

 all ponds would increase water temperature 

 and accelerate the spread of disease. 



Our hypotheses of fixed factor proportions 

 and constant returns to size were equivalent 

 to expecting that the Fish Commission acts 

 as if the isoquants for hatchery production of 

 fingerlings are right-angled, whether they 

 actually are or not. The hypothesis was strong- 

 ly dependent, of course, on our prior decision 

 to analyze Fish Commission hatcheries. A 

 cross-section analysis over various agencies, 

 in retrospect, would possibly have yielded more 

 empirical information. 



The non-controlled variable, water tempera- 

 ture, can be quite important during periods 

 of either cold or warm weather. Extremes of 

 either type seem to effect primarily the volun- 



tary rate of metabolic activity, rather than 

 the efficiency of food conversion (Paloheimo 

 and Dickie, 1966). It was expected, then, that 

 growth would be retarded in the upper and 

 lower limits of observed water temperature. 

 This noncontrolled variable, then, was viewed 

 as the principal shifter of a constant returns 

 production function. 



Exploratory Estimation 



The time period selected for analysis was 

 October 1, 1968 through April 30, 1970. This 

 19-month period allowed the propagation pro- 

 cess to be observed for at least one brood 

 year for each species of interest (Figure 1). 

 These included coho, spring chinook, fall 

 Chinook, chum, and steelhead. In the absence 

 of cost data which were separable by species, 

 it was necessary to estimate an aggregate 

 function over all species.*' 



In view of the fixed proportions hypothesis, 

 the initial attempt at estimation involved 

 several of the factors which were thought to 

 be jointly combined. We were limited in this 

 analysis by the absence of data on either actual 

 water flows or rearing space used. As a fairly 

 unsatisfactory proxy, these variables were re- 

 placed by a measure of the replacement value 

 of all fixed facilities. This variable, along with 

 food, operating expenses (largely labor), and 

 cumulative water temperature units" for the 

 warm weather period and the cold weather 

 period, constituted the five independent vari- 

 ables in the initial run. 



As anticipated, a high degree of intercorre- 

 lation resulted between food, operating ex- 

 penses, and the value of fixed facilities in both 

 Cobb-Douglas and linear estimations. Correla- 

 tion coefficients between these three variables 

 approached or exceeded 0.80, and resulted in 

 a considerable infiation of standard errors. 

 Since it appeared that some degree of factor 

 substitution could be estimated between any 



" An interagency effort is now underway to explore 

 cost accounting systems by species. 



^ A cumulative temperature unit (CTl') is defined 

 for each day in which the average water temperature 

 exceeds 32 °F by one degi'ee. One month of 40° water 

 temperature, for example, would constitute 240 CTU's. 



136 



