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%3D3 œ #3Dz3 (1 - "3P8/!3)[P8 - 1/("з #3)],

œ #3DZ3 (1 - %3Q)[p8 - 1∕("3- #3)],                                  (12)

where !3 is the budget share of good i. Again, in comParison with the semilog demand
system where quality enters in a similar way (Table 1), the semilog own quality elasticity
has additional terms involving
%3Q and ("3 -#3), which gives increased flexibility.

The Marshallian cross-quality slopes are given by

'X3'Z4 œ #4Dp8("3 - #3 )e# ' !# P

œ#4Dp48(x3 -"3M),

and the Marshallian cross-quality elasticities are

`  = 'X3 . z4

'■ ■    ´ z2 X3

œ #4Dz4p8 (1 - "3P8/!3).

œ#4Dz4p48 (1 -%3Q).                                             (13)

Similarly to the price effects, the cross-quality effect in the DS system has an eXtra term,
(1
- %37), relative to the semilog system (Table 1). Combining (12) and (13) with (11),
the full set of relationships between quality, price, and income effects within a given
demand function are



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