Goldin & Homonoff - DataSpace at Princeton University

First, consider the effect of the shift on A’s welfare. Recall that ∂xA ∂xA ∂xA = = ∂tr ∂tp ∂ p
R
R
R
so that
dVA
= Ux (xA,yA) 1 +
dtr
∂tp
∂xA
∂tr ∂ p +Uy
(xA,yA) 1 + ∂tp
∂yA
∂tr ∂ p
Differentiating A’s budget constraint with respect to p yields ∂yA
∂ p = −x − (p +tp +tr) ∂xA
∂ p
assuming that (xA,yA) constitutes an interior solution in A’s budget set, we have
Ux (xA,yA) = (p +tp +tr)Uy (xA,yA).
. Additionally,
Substituting both of these pieces into the above expression and cancelling terms yields the effect of the
shift on A’s welfare:
dVA
dtr
R
d(tp +tr)
= −Uy (xA,yA)xA
. (6)
dtr
Because we know that a revenue-neutral shift towards register taxes reduces the combined tax rate,
< 0, we can conclude that the shift unambiguously increases the welfare of the attentive agent.
R
d(tp+tr)
dtr
This is the main result of the section, and the intuition is straightforward. Replacing a posted tax with
a register tax raises total revenue because only attentive agents reduce their demand for x in response to
the higher after-tax price. The extra revenue accommodates a reduction in the combined tax rate on x,
generating a positive income effect for attentive consumers. 5
What about the inattentive agent? The change in utility for B from a revenue-neutral shift towards
register taxes is given by
dVB
dtr
R
= Ux (xB,yB) ∂xB
∂ p
∂tp
∂tr
R
R
∂yB
+Uy (xB,yB)
∂ p
∂tp
∂tr
R
+ ∂yB
∂tr
Differentiating B’s budget constraint with respect to the price and the register tax yields:
∂yB
∂ p = −x − (p +tp +tr) ∂xB
∂ p and
5 This result can be weakened by endogenizing agents’ decisions about whether to pay attention to register taxes. If a small
increase in the register tax causes a large number of formerly inattentive agents to start taking register taxes into account, the
shift might necessitate an increase in the combined tax rate. In such cases, the shift to register taxes would actually generate
a negative income effect, reducing the welfare of all agents. Consequently, the results presented here are most applicable to
situations in which small changes in the tax rate do not induce dramatic shifts in which agents are attentive.
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