An alternative way to model merit good arguments

commodities (although with 3 or more commodities, the income effects are more
involved).

To fix ideas, suppose that the government considers y as a merit good, μ(χ) >
0, ∀χ ≥ 0, and that both x and y are normal goods. Then both non-numéraire
commodities should be subsidised. First, the merit good should be subsidised
with a rate at which the government’s MWP exceeds that of the consumer (μ).
But in addition, both non-numéraire goods should be subsidised for the difference
in willingness to pay for all inframarginal units. The intuition is as follows.
The government is convinced that the consumer is better off than she herself
believes she is (because she ignores the merit properties of the third good). To
the extent that the non-numéraire commodities are normal goods, it considers
both commodities as underconsumed (relative to the numéraire) and wants to
stimulate their consumption by subsidisation.

5 Second-best rules

Suppose now that there are many consumers, indexed by h, with not necessarily
the same preferences or income level, and that the government cannot differentiate
commodity taxes across consumers. Let social preferences be given by

W = X λ'^hw^gh (z^h*, xh, ∙^h = X h (~+ + ^χh μ(χ)dχ, x^h, tA .    (19)

To focus on the efficiency arguments, I assume that differentiated lump sum taxes
are available. The government’s problem is then⁸

ι≡ X λ     (z ^h(qχ, qy, m^h - T ^h),x^h(q_x, qy, m^h - T ^h),y^h(q_x, qy, m^h — T ^h

tx,ty,{T } _h

(20)

s.t. X tχX^h(qχ,qy ,m^h — T^h) + X t_y y^h(qχ,qy ,m^h — T^h) + X T^h ≥ R (γ )

def ^{h         gh}                def  ^{h         gh}

where a denotes a compensated price effect and th = -hh--2h and t^h = -⅛--3h

x    _{u1   u1}g        y    _{u1   u}g₁

⁸ I agree with Capéau and Ooghe (2003) that the reaction functions entering the social
welfare function should be those of the real agents, and not, as Besley (1988) proceeded, those
of phantom agents that are endowed with the ’right’ preferences.

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