38 BULLETIN NO. 161 



Using equation No. 1 for the man who heats we have : 

 B ( s k ) c n (igr +L) Dh IP=iP ( 1 ) 

 When no heating is done the equation becomes : 

 b( S k) c IP=i 2 P. (5) 



We are assuming that S 1 =s 2 , k 1 =k 2 , c 1 =c 2 , Pi=p 2 , I 1 =I 2 

 i. e. farms are exactly alike except that B>b or the one that 

 heats gets more fruit and that ii>i 2 i. e. that the profits are 

 different 



Subtracting equation (5) from (1) gives: 

 B (s k) c b (s k) -fc n (gr+L) Dh= (i, L) P 

 To make it pay to heat i x must be larger than i 2 and this will 

 make the right side of the equation positive and hence the left 

 side must also be positive. For the left side to be positive 



Bs Bk bs+bk>n(gr+L)+Dh or s(B b) k (B b) > 

 n(gr+L)+Dh 



Let B b=Ab then we obtain by substitution: 

 A b(s k)>n(gr+L)H-Dh. (6) 



This equation means that in order for the farmer who heats 

 to make more money than his neighbor who does not, everything 

 else being exactly the same, the value df the excess of his crop 

 over the others without being picked must be more than the 

 entire cost of heating that year. 



In examining this equation further let us assume that the 

 man who heats makes the same profits as the one who does not 

 for the purpose of noting the relation between the variables and 

 we will write instead of >, which will give us 

 Ab(s k)=n(GR+L)+Dh 



Ab(s k) Dh. 



Solving for n gives us n= 



(gr+L) 



which shows that the man can afford to heat many times and yet 

 break even with the one who does not if he gets much more fruit 

 than the other, (the other lost fruit by frost) if the selling 1 price 

 of the fruit is large and if the cost of heating one night is small 

 because of cheap oil and labor. With the same excess of fruit if 

 he can heat a less number of times, then he is ahead of the other 

 fellow financially, 



The equation may also be written in this form : 

 Ab (s k) Dh 



gr+L gr+L 



the plot of which is a straight line with (s k) / gr-f-L as the 

 slope and Dh / gr-j-L as intercept, n and b being the variables. 



