An alternative way to model merit good arguments

The proof, of which the details are spelled out in the appendix, goes roughly as
follows. (i) means that the MWPs are homogenous of degree zero in its arguments.
(ii), (iv) and (v) then imply that the individual (first best) tax rates are identical
across consumers. With (i), all substitution effects are proportional in income,
which makes the (common) vector of first best tax rates proportional to the vector
the government uses, the factor of proportionality being ”the average β plus the
covariance of the βs with supernumerary incomes”. But with (i), income effects
are independent of income and by (iii) and (23) β^h =1 (all h), which means the
factor of proportionality is 1 as well.

Implementation of the first best allocation is thus not incompatible with an
unequal income distribution. But the combination of assumptions for this to
happen is quite stringent and in general second best tax rates will be a genuine
weighted average of the first best ones.

6 Tax reform analysis

The tax rules derived in the previous sections characterise the optimal solution
under first and second best. For a policy maker, these rules may not be of
primary interest (i) because income distribution policy is not necessarily on the
same agenda as commodity tax policy, and (ii) because the existing commodity
tax structure puts a straightjacket on what can be achieved trough a reform.
More interesting are then the rules that indicate in which direction marginal tax
changes should occur, and that can easily be expressed in terms of accounting
and statistical data.

For this purpose, one is interested in the marginal cost in terms of social
welfare, W , of raising government revenue, R, with one Euro by changing the tax
on commodities x and y:

Expressions of this kind have been discussed in detail by Ahmad & Stern
(1984), who show that a neat parameterisation is obtained by multiplying nom-
inator and denominator by the respective after tax prices. Since the (de)merit
good arguments only affect the nominators, I limit myself to this part of the
MC-expressions. Let me for simplicity assume that μ(y) ≡ μ and y^g = 0.

For commodity x, we then have that
where a ~ above a marginal utility denotes that it is evaluated at the bun-

h

dle (z^h + μy^h,x^h,y^h). Using the first order Taylor approximation eh ` q_i +

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