An alternative way to model merit good arguments

The first order conditions are shown in the appendix to provide us with the
following tax rules:

^u2 /       ʌ ^u2 /

— (z^,χ,y) ^- — (z^,χ,
u1            u₁

g

u3           u3

ty = —(^z,x,y) ^- — (^z,x,y)

u₁             u^g₁

who have the intuitive interpretation of driving a wedge between the consumer’s
marginal willingness to pay (MWP) for each good, and that of the government.

3 Besley’s scaling approach

Besley (1988) proposes the following specification for the government’s evaluation

and defines the third commodity as a merit (demerit) good whenever θ > (<)1.
This scaling approach dates back to Fisher & Shell (1967) who used it to construct
an index for the true cost of living when people’s tastes change or when products
change in quality. In the present context, the government converts the quantity
of the (de)merit good into efficiency units, but otherwise fully respects individual
preferences.

With this specification, the earlier derived tax rules become⁵

To see what these rules imply, consider the preference ordering represented
by the CES utility function u(z,x,y) = (α₁z^ρ + α₂x^ρ + a₃y^p)1^/p, with α_i > 0
(i = 1, 2, 3), and -∞ < ρ < 1. With such preferences, uu3 = αα3 (У)^P 1, τ÷ =
—θ (^θy)^ρ 1 and u² = ^ug = ^α2 (^x}^ρ 1. No tax should be levied on the standard
α1 z                      u1 u₁ α z

commodity, while for the (de)merit good, we have

ty   (1 — θ^ρ)

qy       ^θ

Whenever the elasticity of substitution is below one (-∞ < ρ < 0), we get the
paradoxical result that a merit good should be taxed while a demerit good should
be subsidised!

⁵In deriving the first best rule for the tax on the (de)merit good (8b), Besley (1988) made
a mistake. The correct rule was provided in a comment by Feehan (1990).

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