An alternative way to model merit good arguments

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

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

u^g(z, x, y).                                        (4)

It takes individual behaviour (3) as given and is concerned with solving:

max u^g(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 q_x = p_x + t_x and q_y = p_y + t_y .

⁴ Subscript i with a function denotes a partial derivates w.r.t. the ith argument.

<<   1   2   3   4   5   6   >>

More intriguing information