The first order conditions are shown in the appendix to provide us with the
following tax rules:
tx
u2 / ʌ u2 /
(6a)
(6b)
— (z,χ,y) - — (z,χ,
u1 u1
g
u3 u3
ty = —(z,x,y) - — (z,x,y)
u1 ug1
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
function: |
ug(z, x, y) = u(z, x, θy). (7) |
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
tχ = — (z,x,y) - — (z,x, θy), (8a) u1 u1 ty = u3(z,x,y) — θu1 (z,x, θy). (8b) |
To see what these rules imply, consider the preference ordering represented
by the CES utility function u(z,x,y) = (α1zρ + α2xρ + a3yp)1/p, with αi > 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 — θρ)
(9)
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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