# UC Davis Efficient Taxation of Diamond Goods Theoretical Explanation

**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?

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