Goldin & Homonoff - DataSpace at Princeton University

Hence, the net effect of a revenue-neutral shift on the after-tax price of x is given by:
dpx
dtr
R
= ∂ p
=
=
∂tr
R
∂xb
∂ p
∂x ∂s
∂ p − ∂ p
∂x
∂ p −
+ ∂tp
∂tr
+ 1
R
1 − tr+tp
∂s
x ∂ p
tr+tp ∂x ∂s
− x ∂ p ∂ p
1 − tr+tp
∂s
x ∂ p
1 − tr+tp
x −
∂xb
∂ p
The shift positively affects A’s welfare if and only if
∂x
∂ p
∂xb
∂ p
∂s
∂ p
∂s
∂ p
1 − tr+tp
∂s
x ∂ p
1 − tr+tp
> 0 (20)
x
∂s
∂ p
− ∂s
∂ p
When will (20) hold? Some algebra yields the following sufficient conditions:
ε s > p
tr +tp
ε < p
tr +tp
where ε s and ε d are the elasticities of supply and demand, both defined to be positive. 34
When demand is too elastic, or supply is too inelastic, the shift from posted to register taxes causes a
net increase in the after-tax price of x. 35 Intuitively, this result emerges because the shift to register taxes
is equivalent to a reduction in the elasticity of aggregate consumer demand. When demand is relatively
elastic and supply is relatively inelastic, much of the posted tax will have been shifted onto producers.
Hence the change in incidence due to the shift will be large. In contrast, when supply is relatively elastic
and demand is relatively inelastic, the change in incidence will be small, and as a result, the revenue
mechanism described in Part I will dominate.
34 These conditions are sufficient but not necessary for (20) to hold. In particular, as supply becomes more elastic, the
elasticity of demand may be greater than p/(tr +tp) without (20) being violated.
35 Of course, consumers may ultimately benefit from the higher after-tax price when firms’ income is distributed to its
owners and employees. The final distributive effects of the shift will thus depend on how producer income is divided between
attentive and inattentive agents. Incorporating such elements into the analysis is outside the scope of this paper.
34
(21)
(22)