prices. In this analysis, however, it is necessary to correct the prices 

 of land and cows for annual taxes. This is done in the following proce- 

 dure. The first step corrects the prices for direct taxes; the second 

 step determines the inverse ration of their prices; and the third 

 step finds their marginal rates of substitution. ••' 



(1) Add the capitalized value of annual taxes on cropland (at the 

 desired rate of return) to the price of cropland. Add the 

 capitalized value annual taxes on cows to the price of cows. 



(2) Form a ratio of the corrected price of cows to the corrected 

 price of land. 



(3) Compare this ratio with the marginal rates of substitution of 

 cows for cropland in appendix IV. The optimum combination 

 of cows and cropland will be at the place where these quant- 

 ities are equal. 



As an example of the calculation of the optimum ratio of cows 

 to cropland the situation illustrated in table 7 follows: 



Assume: Hay sales not allowed 



Milk price = $5.00 cwt. 

 Milk response =^ Medium 

 Price of land = $100 acre 

 Annual taxes on land = $4.50 acre 

 Desired rate of return = 15% 

 Price of cows = $450 

 Annual taxes on cows = $11.00 head 

 Step 1 (a) $100 + $4.50 = $130 corrected price of land 



.15 

 (b) $450 + $11.00 = $523 corrected price of cows 

 .15 

 Step 2 Inverse Ratio of Prices = $523 = -4.2 



^130 



Step 3 Marginal rates of substitution of cows for cropland at the 

 assumed milk price and milk response: (Table 7) 



.40 ratio = -2.1 

 .35 ratio = -4.5 

 .30 ratio = -5.6 



'■' The problem is to find R, the gross annual return necessary to pay the direct 

 taxes and provide the desired rate of return on the purchase price of the 

 asset. 



iP =- R - T 

 where: R =^- gross annual return 

 T ^^ annual direct tax 

 P = purchase price 

 i = desired rate of return 

 this foi-mula transposes to R = iP + T 



For simplicity in exposition this analysis is presented in terms of the present 

 value of R in perpetuity V = R i 



where V =^ present value of an asset which returns R annually in perpetuity. 

 V-P + T i 



34 



