UC Davis Efficient Taxation of Diamond Goods Theoretical Explanation

I don’t understand this Economics question and need help to study.

Efficient Taxation of ‘Diamond’ Goods

(Ng, AER, 1987)

Consider a consumer who derives utility from three consumption goods:

x and y and z, which prices are given, respectively, by x y z p , p and p . We

let z denote the numeraire good and normalize its prices to unity. The

consumer possesses an initial endowment of Z>0 units of z.

The utility function of the consumer is given by:

U (x, y, z)= v(x) + u( y . p _y) + z

Thus, the consumer is deriving utility from the amount she spends on y

and not from the number of units consumed.

The government is seeking to raise funds in the total amount of R>0

(units of z). For this purpose it considers the following two alternative

options: (i) levying a lump-sum tax; (ii) imposing an ad-valorem tax on

consumption good y.

(1) Provide a theoretical explanation for the special form of the

utility function we employ.

(2) What would be the optimal choice of the government?