MATHEMATICAL STUDY OF SUPPLY AND 

 DEMAND IN THE HOG MARKET 



"IV yT ATHEMATICAL formulation of price-making factors is 

 -LV-1. necessary in order to know when extraordinary or strategic 

 considerations arc influencing the market. The mathematical 

 methods are highly technical, and in order to explain most clearly 

 we shall follow a specific problem thru from beginning to end. 



The problem is to determine the price of hogs from hog re- 

 ceipts (supply) and from business conditions (demand). To rep- 

 resent business conditions, we are using bank clearings outside of 

 New York City. The actual figures for heavy hog prices at Chi- 

 cago are given in the Appendix. Hog receipts at Chicago and bank 

 clearings outside of New York City are given on pages 8t-and 8^. 

 The problem is to evolve from these figures the law of hog prices. 



The first step is to determine the secular or long-time trend of 

 these figures. Find, for example, the secular trend of such a 

 seres as: 



1901 2 1904 5 1907 4 



1902 3 1905 2 1908 6 



1903 2 1906 6 1909 6 



From looking at these figures, we know that the secular trend 

 slopes upward, starting with about 2 in 1901, reaching 3 or 4 by 

 1905, and 5 or 6 by 1909. To express the matter with mathemat- 

 ical accuracy, the method as applied to this series is as follows: 

 First add all the figures together. Answer in this case, 36. Then 

 divide by the number of figures in this case 9. Thirty-six divid- 

 ed by 9 gives 4, which is the value of the secular trend for 1905, 

 which is the central year. 



The year 1904 is the 1 year, 1903 the 2 year, 1902 the 

 3 year, 1901 the 4 year, and in like manner 1906 is the +1 

 year, 1907 the +2 year, 1908 the +3 year and 1909 the +4 year. 

 Multiply the minus years by their respective values : 1 by 5, 

 2 by 2, 3 by 3 and 4 by 2, and also the plus years, +1 by 

 6, +2 by 4, +3 by 6 and +4 by 6. The totals are 26 and +56, 

 or a net of +30. Now the sum of the squares of 1, 2, 3, 

 -4, +1, +2, +3 and +4 is 60. Sixty divided into 30 gives .5, 

 which is the rate of movement of the secular trend each year, or if, 

 as we found, 4 is the secular trend value for 1905, then 3.5 is the 

 value for 1904, 3.0 for 1903, 2.5 for 1902, and 2.0 for 1901, and 

 in like manner 4.5 for 1906, 5.0 for 1907, 5.5 for 1908 and 6 for 



