framework, but at the same time that it can be easily remedied in a way that
preserves its twofold strength.
To show my arguments in the sharpest way, I start by explaining them in a
first best setting. This, I do in the next two sections. In section 4, I offer an
alternative way of modeling (de)merit good arguments and derive the ensuing
first best policy rules. Second-best rules are presented in section 5, and in
section 6, I derive the marginal cost expressions for tax reform analysis. Section
7 concludes.
2 Consumer behaviour and government opinion
Consider a representative consumer whose preferences over the numéraire com-
modity (z ∈ R+), a (de)merit good (y ∈ R+), and a standard commodity
(x ∈ R+ ) can be represented by the monotonic and strongly quasi-concave utility
function u(z, x, y). Let the consumer prices for these commodities be given by
(1,qx,qy) and the consumer’s exogenous disposable income equal to m - T , where
T is the lump sum tax and m is pre-tax income.
This consumer then solves the problem
max u(z, x, y) (1)
z,x,y
s.t. z + qx x + qy y = m - T.
The first order conditions are4
u2 u3
(2)
qx, qy,
u1 u1
and, together with the budget constraint, these are satisfied by the optimal com-
modity demands
z(qx,qy,m- T),x(qx,qy,m- T), and y(qx,qy,m- T). (3)
The government evaluates the allocation of resources according to the modi-
fied utility function
ug(z, x, y). (4)
It takes individual behaviour (3) as given and is concerned with solving:
max ug(z(qx,qy,m- T),x(qx,qy,m- T),y(qx,qy,m- T)) (5)
tx ,ty,T
s.t. tχx(qχ,qy,m - T)+ tyy(qχ,qy,m — T)+ T ≥ R (λ)
where qx = px + tx and qy = py + ty .
4 Subscript i with a function denotes a partial derivates w.r.t. the ith argument.