The Production Function 



This study purposely does not enter into 

 the calculations necessary to implement the 

 model. Nor does it attempt to specify the na- 

 ture of the interactions between the re- 

 sources, that is, the production function for 

 each of the separate resources. We have seen 

 in the explanation of the symbols above that 

 for each resource a comprehensive production 

 function must be spelled out. This shows the 

 relation of that resource to each of the others 

 and defines its own labor, capital, land, and 

 technological input-output relationships. For 

 outdoor recreation, for example, the physical 

 output O = function of (Kq, 1q, Lq, F, R, E, 

 S, T,). To make this production function de- 

 terminate will require a total management ef- 

 fort by specialists, including silviculturists, 

 biologists, hydrologists, economists, and many 

 others. Much of this work has long been a 

 major part of agency research, using and de- 

 veloping the comprehensive data that are 

 available on the ecological and social sub- 

 systems of the forests. If it is oriented to the 

 specified goal, the work of agency specialists 

 can be redirected toward fitting together the 

 sundry pieces into a meaningful management 

 tool as required by the decision model. 



An illustration of the general pattern of re- 

 source value measurement will be helpful. The 

 value of timber is partly based on the prices 

 offered in the market for the different timber 

 species and products. These prices represent 

 an expression of value as established in the 

 market. Such prices, however, vary over time, 

 and a thorough analysis would require de- 

 mand and supply projections indefinitely into 

 the future for the various timber products. 

 Further, the value of timber will be affected 

 by the harvest program levels pursued by the 

 Forest Service as these affect the allowable 

 cut calculations. The demand for the timber 

 (harvested) will be affected by changes in 

 population, construction technology, and 

 other conditions. Further, unharvested timber 

 is valuable in itself as it interacts in the eco- 

 logical and social subsystems. Thus a 

 "market" price for timber will not be appli- 

 cable to that portion of timber which is 

 classed as wilderness. In this and other ways, 

 the estimator or index number of timber val- 



ues will be altered and shaped by the interac- 

 tion of timber resources with the other re- 

 sources of the forest. In this context the state- 

 ment in the MU-SY Act that the best combi-., 

 nation is "not necessarily the combination of 

 uses that will give the greatest dollar return or 

 the greatest unit output" is given meaning. 



An estimate of unit value for timber must 

 be comparable to the estimate of unit value of 

 watershed. The value of watershed, however, 

 may be measured in terms of water quality, 

 erosion and soil stability, yield or water flow, 

 water turbidity, or other considerations. 

 These values depend in large part on the pro- 

 gram levels applicable to the other forest re- 

 sources. Similarly, the value, of fish and wild- 

 life may be measured in total population (for 

 example, the size of an elk herd) as well as in 

 numbers of species. Again, as indicated in the 

 model, the physical output (and thus the real- 

 izable value) will be in part determined by the 

 physical outputs of the other resources. 



It is apparent that in a decision model of 

 this type, the values must be stated in terms 

 of some common unit of measurement. Nor- 

 mally, when a firm produces two or more out- 

 puts, it must have an index of values (a nu- 

 meraire) that allows the addition of diverse 

 physical outputs. (Price often serves as a nu- 

 meraire, making it possible to add the val- 

 ue of apples and the value of oranges.) Obvi- 

 ously, the FOREST model calls for such a 

 numeraire by which to estimate an imputed 

 unit value for each resource. These may be 

 shown as f*, o*, r*, e*, s*, t*. Just how these 

 unit value estimators are to be determined is 

 the problem, however. As will be seen in later 

 discussion, the agency already has trouble get- 

 ting reliable estimates of physical outputs (the 

 F, O, R, E, S, T terms in the model). How it 

 will get a suitable numeraire is not within the 

 scope of this study to suggest. The model, as 

 previously stated, is not a planning tool in it- 

 self, but rather an effort to interpret what the 

 law says is the agency goal. The weakness of 

 the model in this regard reflects the desire of 

 Congress to find some way to measure the im- 

 measurable. Implied but not specified in the 

 goal is the research required to carry out the 

 agency's responsibility as spelled out in the 

 NEPA. To that end, the act calls for insuring 



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