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CHAPTER 15
TAXATION AND
EFFICIENCY
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Excess Burden Defined

A loss of welfare above and beyond taxes
collected.

Same as Deadweight Loss

$20 Tax on Candy Bars?

Consider white board example.
15-2
Excess Burden Defined

Consider a Tax on Barley

Pbt = (1+tb) Pb
Note: Different Axes from last chapter.
15-3
Pounds of corn per year
Excess Burden Defined
A
Government
levies tax on
barley
Ca
Cb
E1
C1
i
F
B0
D
B1
Pounds of barley per year
15-4
Pounds of corn per year
Effect of Tax on Consumption Bundle
A
Ca
G
E2
Cb
E1
C1
F
B0
i
ii
D
B1
Pounds of barley per year
15-5
Pounds of corn per year
Excess Burden of the Barley Tax
Note: No Excess
Burden from
Lump Sum Taxes
A
Ca
G
H
Tax
Revenues
M
Equivalent
variation
E2
Cb
E1
C1
Excess
Burden
F
B0
B3
I
i
ii
D
B1
Pounds of barley per year
15-6
Compensated vs. Uncompensated

Uncompensated Response


Consumption changes because of the tax and
incorporates effects due to both losing income
and tax-induced change in relative prices.
Compensated Response

Substitution Effect

The tendency of an individual to consume more
of one good and less of another because of a
decrease in the price of the former relative to the
latter
15-7
Income vs. Substitution Effect

Income Effect


The effect of a price change on the quantity
demanded due exclusively to the fact that the
consumer’s real income has changed
Substitution Effect

Compensated Effect
15-8
Pounds of corn per year
Questions and Answers
If the demand for a commodity does not change when it is
taxed, does this mean that there is no excess burden?
A
• Uncompensated Response (E1 to E2)
E1
Ca
• Income Effect (E1 to E3)
i
• Substitution Effect (E3 to E2)
J
•Compensated Effect
R
E2
Cb
C1
S
E3
F
B1 = B2
B3
K
ii
D
Pounds of barley per year
15-9
Questions and Answers

Lump Sum Tax Problems

Tough Politically

British Prime Minister Margaret Thatcher
15-10
Questions and Answers

Does consumer maximization help us
understand this?

Whiteboard
(1  tb ) Pb
MRS bc 
Pc
Pb
MRTbc 
Pc
15-11
Questions and Answers

Does an income tax entail an excess burden?

Whiteboard
MRS lb  MRTlb
MRS lc  MRTlc
MRS bc  MRTbc
15-12
Price per pound of barley
Excess Burden Measurement with Demand Curves
(1 + tb)Pb
Pb
a
Excess burden = ½ ηPbq1tb2
Tax revenues
Excess burden of tax
g
f
h
d
S’b
i
Sb
Db
q2
q1
Pounds of barley per year15-13
Appendix A – Formula for Excess Burden
A = ½ * base * height
= ½ * (di) * (fd)
fd = ∆Pb = (1 + tb) * Pb – Pb = tb * Pb
di = ∆q
η = (∆q/∆Pb)(Pb/q) Price Elasticity
∆q = η(q/Pb)∆Pb
since ∆Pb = tb * Pb
∆q = η(q/Pb)*(tbPb) = η * q * tb
since di = ∆q
A = ½(di)(fd)
= ½(ηqtb)*(tbPb)
= ½ * η * Pb * q * (tb)2
15-14
Appendix A – Formula for Excess Burden

What do we get intuitively?

Tax several goods small amounts.

The Squared Term!

Tax Doubles?

Excess Burden Quadruples!
15-15
Appendix A – Formula for Excess Burden

Airline-Tickets

Federal Taxes = 10%

n=1

Price Increases 1%

Quantity Decreases 1%

$86 billion = p*q

Excess Burden > (.5)(86)((0.1)2 billion $

$430 million
15-16
Price per unit of
housing services
Excess Burden of a Subsidy
Ph
m
Excess burden
n
(1 – s)Ph q
o
v
Sh
r
u
Sh’
Dh
h1
h2
Housing services per year 15-17
Wage rate per hour
Excess Burden of Income Taxation
Excess burden = ½ εωL1t2
f
w
(1 – t)w g
Excess burden
SL
d
i
h
a
L2
L1
Hours per year
15-18
Value of Marginal Product (VMP)

Dollar value of the additional output produced
for each hour worked

Downward Slope?
15-19
The Allocation of Time Between
Housework and Market Work
Excess burden = ½ (ΔH)tw2
$
b
(1 – t)VMPmkt
a
w1
$
w2
w1
(1 – t)w2
e
VMPmkt
0 Hours worked in
home per year
d
H*
c
H1
VMPhome
Hours worked in 0’
market per year
15-20
Does Efficient Taxation Matter?

Why no excess burden budget?

Is efficiency the primary objective of
government policy?

Does excess burden mean a tax is bad?
15-21