among alternative expressions of particular as- 

 pects of the Forest Service mandate. 



The FOREST Model 

 Elaborated 



On the basis of the preceding statement, 

 we now consider the model in symbolic form 

 as a more complete statement of Forest Serv- 

 ice goals. As such, it is adaptable as a decision- 

 making tool. 



* Symbolic Statement 



The mandate to maximize the weighted 

 value of the National Forests subject to con- 

 straints in the form of site productivity, sus- 

 tained yield, and budget, can be expressed in 

 the following manner: 



GOAL 



Maximize the sum of the weighted values 

 of the FOREST resources. 



MAXIMIZE 



,F* + 0*+ R*. 



* * # 

 E + S + .T 



The symbols are interpreted according to the 

 following pattern: 



F* is the value of fish and wildlife. It may 

 be derived from the actual physical output 

 multiplied by a unit market price or some 

 other estimator. 57 The output is determined 

 partly by technology and the levels of produc- 

 tive inputs used in the production (or manage- 

 ment) of fish and wildlife (that is, capital Kp, 

 labor lp, land Lp). In the light of ecological 

 interaction it is also determined in part by the 

 levels of physical output of the other FOREST 

 resources. Thus, F = function of Kp, lp, Lp, 



0, R, E, S, T, that is, the production function. 



The lower case f, in the symbolic state- 

 ment of the goal above, indicates the weight 

 or premium placed on values derived from use 

 or production of fish and wildlife. 



CONSTRAINTS 



1. Site Productivity 



Total productive capability of the FOREST 

 in the future must not be impaired relative 



More precisely, the imputed unit value may be a 

 market price, a shadow price, or a Lagrangian multi- 

 plier and would show up as a coefficient f*. Thus f*F 

 = F*. 



to such productive capability of the FOREST 

 today. 



(FOREST) p+1 > (FOREST) p 



where p = current period, p+1 = future period. 



2. Sustained Yield 



' Growth or net periodic increments in each 

 of the resources in the future must be main- 

 tained at a level at least equal to the present 

 level of growth. Under no circumstances are 

 the current levels of harvesting or use of the 

 resources to be greater than the net periodic 

 increment or ability of the resources to renew 



themselves (p period = p-^, P2, 

 ods of undefined length). 



> 



Net periodic 

 increment of 

 resource in 

 future 

 period(s) 



G F(p+l) ^ 



Net periodic 

 increment of 

 resource in 

 current 

 period 



> 



G 



F(p) 



> 



. , p n ; pen- 



Per iodic 

 harvest of 

 resource 



IT 



G T(p+l) - G T(p) H T 



3. Budget Restrictions 



Actual expenditures on the separate re- 

 sources may vary by as much as 7 percent of 

 the amount budgeted, but such variation is 

 limited in that the total actual expenditures 

 may not exceed the total amount budgeted. 



The subscript a indicates actual expendi- 

 tures; the subscript b indicates amounts budg- 

 eted for each of the separate resources. 



Total Expenditures < Total Budget Allotment 



(F Q + O a + R Q + E a + S a + T a ) < 



(F fe + O b + R b + E b + S b + T b ) 



where the above is further constrained such 

 that 



1.07 F b > F a > .93 F b 



1.07 T b > T a > .93 T b 



39 



