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/8(p8,?) œ /(p8,?)Î)(p,M)

#!+!#зр8       !"4P8-∣

(2)


— e + ?e

Equation (2) can be rewritten to solve for the indirect utility function

Vœ


M8 +e


#!+!#3P38


—!"4P48
e


(3)


—!"4P48     #!+!(#3—"3)P38

œM8e4+e         3

where M8 œ M/)(p,M) is normalized income. From equation (3), it can be seen that in
this model, the utility index is strictly Positive.

Differentiating (2) with resPect to P38 , the Hicksian demands are

x32(p8,?)


#!+!#5P58         !"4P48

œ—#3e      + "3?e


(4)


and the corresPonding Marshallian demands, obtained by substituting in the indirect
utility function (3), are

#!+!#4P8

x3(p8,M8) œ("3—#3)e !44 +"3M8.

(5)


These Marshallian demands have a functional form that is a hybrid of the semilog and
linear demand functions: the Price effects are similar to those of the semilog system
while the income effects are linear. Notably, the income effects "3 in (5) are not
restricted as they are in the semilog demand system, where they must all take on a single
value.



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