190 ECONOMIC ESSAYS IN HONOR OF JOHN BATES CLARK
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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
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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
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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
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(4)
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