%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