Econ 203
Excise vs lumpsum tax
Economic policy: excise vs lump-sum taxes
- income and substitution effects in practice
Question: given a fixed amount to be raised by
tax, what is best form of tax?
"best"? - highest utility for consumers
Options:
1. excise tax: tax per unit of a particular good
- original price p, tax t
o
- new price is p′ = ( p + t )
2. Lump-sum tax: fixed amount of tax
- independent of quantities consumed
- reduces income
o
- tax T, new income is M ′ = M − T
Effects on budget set?
Notation:
o
initially {M ,
p1o , p2 o }
p1′ = p1o + t
o
o
post tax, have {M , p1′ , p2 }
o
Assume: p2 = 1: composite commodity
excise tax on good 1:
Econ 203
Excise vs lumpsum tax
Revenue from Excise tax?
- depends on quantity purchased
- bundle B′ = ( x1′ , x2′ )
- tax revenue collected?
- expenditure on good 1
= p1′ x1′ = p1 x1′ + tx1′
- expenditure on good 2?
o
x2′ = M o − pl′ x1′ = ( M o − p1o x1′ ) − tx1′
- in diagram: vertical axis is $
tx1′ = x2 − x2′
o
o
(where x2 ≡ M − p1 x1′ : see diagram)
- then tax revenue is
Equal lump-sum tax?
If, instead of excise tax, lump-sum tax so that
{M ′, p1o ,1} with M ′ = M o − tx1′, would this
consumer be better or worse off?
p1o
Diagram? BL through B′ , slope = − o
p2
Can do better than B′ ?
Why?
(Role of prices? GST exemptions?)
Econ 203
Excise vs lumpsum tax
Income and subst'n effects: numerical example
1. utility function: U ( x1 , x2 ) =
x1 x2
2. MRS? partial derivatives: U1 ( x1 , x2 ) = x2 ,
U1 ( x1 , x2 ) x2
=
and U2 ( x1 , x2 ) = x1. MRS =
U 2 ( x1 , x2 ) x1
3.{M
o
, p1o , p2 o } = {$72,$9,$1} Slope BL= -9
4. Initial optimum? on BL, so
9 x1 + x2 = 72 ⇒ x2 = 72 − 9 x1
at bundle where MRS = p1 / p2 ⇒ x2 = 9 x1
These 2 eq'ns give
x1 = 4, x2 = 36
5. {M , p1′ , p2 } = {$72,$4,$1}
6. New optimum? on new BL, so
o
o
4 x1 + x2 = 72 ⇒ x2 = 72 − 4 x1
at bundle where MRS = p1 / p2 ⇒ x2 = 4 x1
Solving, x1 = 9, x2 = 36
(Note: good 2 unchanged -CD function)
Econ 203
Excise vs lumpsum tax
7. Income and substitution effects?
what bundle would just yield
(U ( x1o , x2 o ) = x1o x2 o = 3 × 36 = 144
at new prices - where on this IC is MRS = 4?
144
Two eq'ns in two unknowns: x2 =
= 4 x1
x1
yields x1 = 6, x2 = 24
So:
subst'n effect: movement along original IC:
p1o =9 to p1o = 4
x1 increases by 2 (from 4 to 6)
and x2 decreases by 12 (from 36 to 24)
income effect: to new IC at new prices:
x1 increases from 6 to 9
x2 increases by 12 (from 24 to 36)
Note: C-D function - both normal goods,
effects on good 2 of change in price of good 1
cancel out.