MENDELSSOHN: USING MARKOV DECISION MODELS 



expected value? Van Hee ( 1977b) gave bounds on 

 this expected loss that are easy to compute. To 

 obtain a feel for these bounds, both (r'^ and R^ are 

 assumed to be random variables. For the Wood 

 River, /?2 could take on the values -0.6, -0.8 and 

 -1.0, and for the Branch River R^ could take on the 

 values -1.5, -1.85, and -2.00. For the Wood River, 0-2 

 could assume the values of 0.35, 0.45, and 0.55, 

 and for the Branch River a^ could assume the 

 values 0.48, 0.58, and 0.68. Three probability dis- 

 tributions were used as the present prior probabil- 



ity of the parameter values. These were (%, Vs, Va,), 

 (1/4, V2, 1/4), (Vs, %, Vs). The results of the optimiza- 

 tion using the parameters at each fixed value 

 (which are needed to calculate the bounds) are 

 given in Table 3. Table 4 gives the bounds on the 

 expected loss of value from using the present esti- 

 mates of the parameters as in Equation (1.1). 



Table 3 suggests that as cr^ varies for fixed val- 

 ues of /?j , /?2 ' the mean per period harvest varies 

 little, but the variance of the long-term harvest 

 size distribution increases significantly. As i?2 



"1 r 



1 r 



(k) C = E = 0.75 



J I L 



"I r 



"1 r 



"1 r 



(I) C=E = I.OO 



J I I L 



4 .8 12 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 4.8 4 8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 40 44 4.8 



X X 



Figure 3.— Continued. 



47 



