FACTORS AFFECTING THE PEICE OF HOGS 
37 
relatively much more effect upon prices as a similar change in the 
supply for a single month (the regression coefficient for X 3 is 
— 0.52655, and for X 1 is but —0.09406). 
With all other factors constant, the relation of supply to price is 
given by the equation: 
(3) Log X 12 - -0.09406 log Xi-0.52655 log X 3 + (K) 
This is simply equation 2 with all variables other than X x and X 3 
dropped out. The values for X i2 given by this equation would be 
applicable only when all the other variables had their average values 
(using the geometric averages for the variables correlated in terms of 
logarithms). Since both Xi and X 3 in equation 2 are stated in the 
same units, the relation of price to supply could be stated. 
(4) Log (X 12 ) = - 0.62061 log (X0 + (K) 
for periods when both X x and X 3 have the same value. This equa- 
tion expresses the combined effect of both the trend of supply and 
the current supply upon the price, and gives an approximate measure 
of the demand curve for hog products. 
PRICE AT 
CHICAGO 
IN TERMS 
OF 1913 
DOLLAR 
PER CWT. 
9.50 
9.00 
8.50 
8.00 
7.50 
7.00 
6.50 
6.00 
5. 50 
The Curve of Supply and market price 
60 
70 
80 90 100 110 120 
SUPPLY, IN PER CENT OF TREND OF DEMAND 
130 
140 
Fig. 
-The demand curve for hogs. This shows the variations in price for given variations in 
supply, after eliminating the effects of other factors affecting price 
This net regression was tested for linearity by the approximation 
method for multiple curvilinear correlation (o), and it was found 
that the straight line (in terms of logarithms) was the best fit for 
the demand curve. 
It should be noted at this point that the first differential of equation 
4 is necessarily a constant. That is to say, a given relative change in 
Xi always causes the same relative change in X X2 , regardless of the 
value of Xi. This demand curve therefore has a constant elasticity; 
at any point on the curve, the relation between a very small per- 
centage change in supply and the percentage change in price is the 
same. Thus for an increase of 1 per cent in supply, price would 
decrease 0.62 per cent. The actual coefficient of elasticity is 1.61; 
that is, the change in quantity is at the rate of 1.61 times the rate of 
change in price. 
Figure 26 is drawn to equation 4 with the quantities expressed 
in percentages of the average supply, rather than in terms of actual 
