The name is absent



In the DS system, the Marshallian income slope is 'x3(p8,M8)/'M8 = "3, so that
each good has a separate income effect ("3), unlike the semilog demand system, where all
income effects must be the same. The income elasticity for good i is, then,


_ 'X3(p8,M8) M8

%3Q ´   'M8   ■ x3


Al

X3


-p

!3


(6)


where !3 ´ p3x3∕M is the Marshallian budget share of good i. Each good has an
independent income effect, unlike the semilog system, where all income effects must be
equal.

The Marshallian own- and cross-price elasticities %33 and %34 are, respectively,


´ 'x3(p8M8) . p8

%33 -    'p8      x3


œ #3p8 1 - "!p8


(7)


and


= ⅜(p8,M8) . P8

34 ´    'p8      x3


œ#4 p48 ’1 -


"P

!3


(8)


where !3 ´ p8x3/M8 is the budget share of good i. Noting, from (6), that "3p8/!3 is the
income elasticity for good i, (7) and (8) can also be written as



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