Goldin & Homonoff - DataSpace at Princeton University

tax types:
R(tp,tr) = (tp +tr)(xA + xB). (4)
If both agents were fully attentive to both types of tax, a revenue-neutral one dollar increase in the register
tax would require a one dollar decrease in the posted tax; changing the balance between register and
posted taxes would not affect the combined tax rate necessary to raise a given amount of revenue. When
some agents are inattentive, however, the demand reduction that typically accompanies a tax increase
will be muted. As a result, an incremental increase in the posted tax will, all else equal, raise less revenue
than an incremental increase in the register tax: 4
∂R
∂tp
∂xA ∂xB
= (xA + xB) + (tp +tr) +
∂ p ∂ p
∂xA
< (xA + xB) + (tp +tr) =
∂ p
∂R
∂tr
The reduction in the posted tax associated with a revenue-neutral increase in the register tax can be
found by totally differentiating the government’s budget constraint and solving for ∂tp
:
R
∂tp
∂tr
R
= −
Note that the denominator is positive as long as ∂R(tp,tr)
∂tp
raising the tax rate would actually decrease revenue.
xA + xB + (tp +tr) ∂xA
∂ p
xA + xB + (tp +tr) ∂xA
∂ p + (tp +tr) ∂xB
∂ p
∂tr
. (5)
> 0, i.e., that demand is not so sensitive that
How does a revenue-neutral increase in the register tax affect the combined tax rate, tp + tr? The
effect of the shift is given by d(tp+tr)
= dtr R ∂tp
+1. Because demand is downward-sloping ( ∂tr R ∂xB
∂ p < 0), (5)
implies that ∂tp
< −1. Consequently, a revenue-neutral increase in the register tax is associated with
∂tr R
< 0.
R
an overall reduction in the combined tax rate, d(tp+tr)
dtr
What are the welfare effects of a revenue-neutral shift towards register taxes? Indirect utility is given
by Vi (tp,tr) = U (xi (tp,tr),yi (tp,tr)). The welfare effect of the shift is thus:
dVi
dtr
R
∂xi
= Ux (xi,yi) +
∂tr
∂xi
∂tp
∂yi
+Uy (xi,yi) +
∂tp ∂tr
∂tr
∂yi
∂tp
∂tp ∂tr
4 The 2-good nature of the model guarantees ∂xB
∂ p
< 0.
R
7
R