∂Zuh (z,x,y) yhμ (i = 2,3) and the adding up condition d-+qχ ∂χh+qydyh = -xh,
this expression can be rewritten as
∂W ' X λhugh{
xh
xh
∂xh du2ι (z,χ,y) h ∂yh
∂ qx ∂ z y μ ∂ qx
∂u2(z,x,y) κ I I
u1 d z—y y μ ∣.
(26)
Multiplying through by qx , and turning derivatives into elasticities, we finally
get
- dW ` X λhegh ½ a xh - Uhh μh δh qxx + εh ∙1 + δh qyy ^∩ ¾ (27)
qx ∂t ' / v λ u1 ^qxx μy ^εxxδxz zh + εyx 1 + δyz zh j J' (27)
where the Marshallian price elasticities and the demand price elasticities are
defined as
h = ∂χh qx hh = ∂yh qx δh = du1 z δh
xx ∂qx xh, yx ∂qx yh, xz ∂z V2 , yz
∂ u3 z
u1 z
∂z u3 .
u1
(28)
Similar operations lead to an analogue expression for — qy ∂∂W :
ι+δhz ⅞yh]) }■ (29)
-qy dwW ` X λhu,9gh {''"∙' yh - μyh (εhy δhz qzχ^+εhy
with similar definitions for εhxy and εyhy. Notice how the existence of a (de)merit
good argument corrects both MC expressions in a similar way.
Writing μyh = ηqyyh, the curly bracket terms can in principle be calculated
using expenditure data (expenditures on x and on y, and expenditures on x and
y relative to z ) and uncompensated price and quantity elasticities. If these elas-
ticities are not available at the household (or income decile) level, they can as
an approximation be replaced by the aggregate elasticities. One can then pro-
duce different rankings of the marginal costs, for different values of the (de)merit
parameter η .
7 Discussion and concluding remarks
In this paper, I have questioned the scaling approach proposed by Besley (1988)
to model merit good arguments on the ground that it often leads to counterin-
tuitive policy prescriptions. I have proposed a different approach which directly
interferes with the marginal willingness to pay for a (de)merit good.
Which approach to choose? If one is convinced that a (de)merit good argu-
ment should at least in a first best world precribe the subsidisation (taxation)
of that good, then the approach presented here meets this criterion better than
10
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