72 Economic Cycles: Their Law and Cause 



manded and relative change in price is linear. We shall 

 see later on that the two variables are even more 

 intimately associated than would be suggested by the 

 high coefficients of correlation. Just now we wish to 

 know the form of the law of demand when the restric- 

 tion involved in the assumption of linearity of regres- 

 sion is removed. What will be the statistical laws of 

 demand for the representative commodities corn, hay, 

 oats, and potatoes, if the regression of relative change in 

 price upon relative change in quantity of commodity is 

 assumed to be skew and of the type y = a-\-bx-\- cx 2 -\- dx*t 

 The question is answered by fitting, according to the 

 Method of Least Squares, the equation y = a+bx+cx z + 

 dx* to the data of Tables I, II, III, IV of the Appendix 

 to this chapter. The results of the computations are 

 exhibited in Figures 17, 18, 19, 20 of the text. 



The statistical laws of demand for the commodities 

 corn, hay, oats, and potatoes present the fundamental 

 characteristic which, in the classical treatment of de-. 

 mand, has been assumed to belong to all demand 

 curves, namely, they are all negatively inclined; that is 

 to say, speaking from the point of view of average 

 results, "the greater the amount to be sold, the smaller 

 will be the price at which it will find purchasers, or, in 

 other words, . . . the amount demanded increases 

 with a fall in price and diminishes with a rise in price." 1 



1 Marshall: Principles of Economics, 4th edit., p. 174. In case of 

 the law of demand for hay, there is a slight upward turn at the ex- 

 tremity of the curve. This is due to one extreme observation, and 

 the variation is not a significant exception to the above general rule. 



