The break-even prices of cows and cropland for the marginal- 

 value products shown in Table 7 are shown below for the following 

 situation: 



Hay sales 



Milk price 



Milk response 



Annual property tax on land 



Annual tax on dairy cows 



Desired rate of return 



Prohibited 

 $5.00 cwt. 

 Medium 

 $4.50 acre 

 $11.00 head 

 15% 



Because the marginal-value product includes both the cow and 

 the stall, very high break-even prices for cows may be obtained. This 

 also indicates the foregone income of maintaining excess barn capa- 

 city. If no stall space is available, the break-even price of cows must 

 cover the cost of providing the stall space as well as the animal. 



The desired rate of return is the individual's own preference. 

 A rate of 10 to 20 percent is not excessive, considering the risk in- 

 volved in dairy farming as opposed to alternative investments. 



The Optimum Ratio of Cows to Cropland 



The marginal rates of substitution of cows for cropland recorded 

 in Table 7 and appendix IV were derived from the inverse ratio of the 

 marginal-value products of cropland and cows.* 



From these estimates of the marginal rate of substitution of cows 

 for cropland, the optimum ratio of combination of cows and cropland 

 can be determined. Optimum combination of two inputs occurs when 

 their marginal rate of substitution equals the inverse ratio of their 



Marginal rate of substitution 

 of cows for cropland 



P milk A milk 

 A cows 



P milk A milk 

 - A cropland 



A cropland 

 A cows 



The last expression on the right of the equality is the defining formula for 

 the marginal rate of substitution of cows for cropland. The customary nota- 

 tion for this formula involves partial derivatives. However, in linear pro- 

 gramming, derivative notation and the delta notation are equivalent. 



33 



