190 ECONOMIC ESSAYS IN HONOR OF JOHN BATES CLARK 
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Ey 
marginal wantabilities per unit of physical quantities, may now 
be compared in exactly the same manner as were compared S;, Ss, 
Wi, Ws, relating to total income. The ratio between the number 
of “pounds” of food consumed by Cases 1 and 3 (or more strictly 
between their indexes of food consumption just mentioned) is 
Ss¢s/F 3 
S1¢1/ Fy 
Cancelling F; and F3, they being equal, we obtain 
(EY) 
Substituting for 5 its value as given by equation (3), we 
1 
obtain, as the ratio of the physical consumption of food for 
Cases 1 and 2: 
We note that the right hand member of this equation differs from 
Formula (3) only in that ¢; is now replaced by ¢3 (Fs; being 
the same as F,). 
The corresponding ratio for marginal wants of food per physical 
unit is Wor . Cancelling the equal F’s, we get the equation (4) 
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over again, 2.e.: 
Wills Ws R:/Rs (4) 
WF, Ww, F, /Fs 
Similarly, remembering that R;—R3 and again using equation 
(3), we obtain, for the sub-group rent, the two equations: 
Sas 
Bs _ (5) pz) _ p/p. Ra/Rs 
Sir \S: (2) oe tral 
D 
Avr 
hii dd 
W3R, = Ws = Ry/Ry 
WRy W, F,/F; 
or (4) once again. 
Multiplying (10) and (4) we obtain: 
S33 Ws 7 p2/ ps 
SioiW1 o/s 
ey 
oi 
(4) 
; 
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