The Law of Demand 83 



tion, we are able, by means of the laws of demand for 



the several commodities, to measure their respective 



degrees of elasticity of demand. It will be recalled that, 



in the form in which the laws of demand have been 



presented in preceding pages, the variable x has been 



taken to represent the relative change in the quantity 



of the commodity, and the variable y, the corresponding 



relative change in the price. The coefficient of the 



dx 

 elasticity of demand, therefore, is equal to -j- when x is 



zero. All that is needed to obtain the measure of the 

 degree of elasticity of demand is to differentiate y with 

 respect to x in the equation to the law of demand, 

 place x = zero, and then take the reciprocal of the result. 

 The method may be illustrated in case of the four 

 representative commodities, corn, hay, oats, and pota- 

 toes. The law of demand for corn — see Figure 17 — is 



y = .94- 1.0899x + .02391x*- .000234a: 3 

 Therefore, j~ = - 1-0899 + 2(.02391)x-3(.000234)a;2 



When x = 0, ^ = -1.0899, ^ =- 77^ = -.92 

 dx ay 1.0899 



and consequently the coefficient of the elasticity of 



demand for corn is —.92. Since the law of demand for 



hay is 



y = 4. 17-.946Z -.0077** + .000385z s 



-r = —.946 when x = zero, 

 dx 



and the coefficient of elasticity of demand is — 1.06. 

 For similar reasons the degrees of elasticity of demand 



