A SPRUCE PROBLEM. 



PREMISES : A spruce forest contains in the year 1899 per 

 acre about 4228 feet b. m., consisting of trees scaling 10 inches or 

 more at four feet from ground. 



First case : Suppose that the owner actually cuts down to 10 

 inches diameter, thus removing now 4228 feet. Then, in the year 

 1929 he will be able to again cut 2420 feet b. m., cutting again 

 down to 10 inches. Every 34 years thereafter he will have the 

 same yield of 2420 feet b. m. The price of the stumpage is $1.40 

 per thousand feet. The taxes are, on an average, 3c per acre per 

 annum. 



Second case : Suppose the owner cuts only down to 12 inches. 

 Then the forest will yield,to begin with,36o8 feet b. m. In the year 1919 

 the owner will be able to cut 2115 feet b. m., and thereafter the same 

 amount every 24 years. The value of stumpage in this case is $1.50 

 per 1000 feet. The taxes are, on an average, 4c per acre per 

 annum. 



Third case : Suppose the owner cuts only down to 14 inches. 

 Then the iirst yield will be, in the year 1899, 2846 feet b. m. In the 

 year 1919 the owner will be able to cut 2624 feet b. m., and thereaf- 

 ter every 21 years the same amount. The value of the stumpage is 

 $1.60 per thousand feet; the taxes are, on an average, 5c per acre 

 per annum. 



The owner wants to derive 5 per cent, interest and believes in a 

 gradual increase of the prices, the increase to average 2 per cent, 

 per annum. The cost of administration and protection is in all cases 

 Sc per acre. 



QUESTION : Had the owner of the forest better cut down to 

 10 inches, to i2 inches or to 14 inches? 

 POINTS : 



1. The maximum difference between expected yields and ex- 

 pected expenses determines the best course to be followed. 



2. In the 10 inch case the yields are 



4,228 X 1.40 + ^•03*^2420x1.40 

 1.03** — I 

 In the 12 inch case the yields are 



3,608x1.50 + "°^;.yiSV'° = ?8.8o 

 In the 14 inch case the yields are 



2,846 X 1.60 -1- 1-03 X 2.624 X i-6o 

 1.0321 — I 

 3, In the 10 inch case the expenses are 0.03 -|- 0.05 



0.05 



14 



$8.14 



$9-56 



$1.60 



