Review
… and the hits just keep on
coming
Consumer and Producer Surplus in the Market
Equilibrium
Price A
D
Supply
Consumer
surplus
Equilibrium
price
E
Producer
surplus
B
Demand
C
0
Equilibrium
quantity
Quantity
Copyright©2003 Southwestern/Thomson Learning
Public Goods
• Most important factor is that everyone gets
the same amount.
• We have to get some agreement as to
how much we’ll want (we’ll discuss that a
lot).
• We’ll have to get some agreement as to
how to pay for it (we’ll discuss that a lot,
also).
Sum of Marginal Benefits = Marginal Cost
If you don’t believe me ...
1
2
3
4
Schools
• Suppose another
politician promises s2.
Person 3 won’t be happy 60
anymore because you’re
s1
providing MORE school
s2
resources than he wants
… so he’ll vote against it.
s3
• KEY POINT !!! The
s4
median voter is decisive.
Eq’m school will be at s3.
s5
Each voter will pay 60 b3 in taxes and get s3.
5
b3
Bread
60
How Responsive are LPGs?
• What are the usual suspects?
• We get pretty interested in both price and
income elasticities.
• Presumably, as Income , Q .
• Presumably, as Price , Q .
• How much is it?
– A little?
– A lot?
EY = % Q / % Y.
EP = % Q / % P.
occurs when people stop moving!
Tiebout Eq’m
Model
• Assumptions
– Jurisdictional Choice -Households shop for what local
governments provide.
– Information and Mobility -Households have perfect
information, and are perfectly
mobile.
– No Jurisdictional Spillovers -What is produced in Southfield
doesn’t affect people in Oak Park.
– Community size – City manager
seeks to reach average minimum
cost of producing goods.
– Head Taxes -- Pay for things withWhat happens if people keep moving
a tax per person.
From Community 1 to Community 2?
• We get an equilibrium. People’s
preferences are satisfied.
Plethora of Studies
• If you do a citation search, you
will find that this article was like
Helen of Troy, the face that
launched 1000 ships.
• All kinds of follow-ups.
– Was this really what Tiebout
meant?
– Was the econometrics right?
– Did this work at the individual
house level, as opposed to the
community level?
Instability
• Tax financing generates inherent
instability.
• Need not be solely property tax. Happens
with any tax other than a pure benefit tax
or a head (per/person) tax.
• Incentive for one family to move to take
advantage of fiscal surplus will lead other
(or all) families to move.
Baumol’s Cost Hypothesis
• Consider two sectors. He calls them
– Progressive – subject to productivity
improvements.
– Traditional – Generally more labor intensive
and not subject to productivity improvements.
• What happens?
Privatization
Think of some
of your own
examples!
• Definition: Transfer production of
government services to private firms.
Degrees of Public and Private Involvement
Case Choice
Financing
Production
1
2
3
4
Public
Public
Public
Private
Public
Public
Private
Private
Public
Private
Private
Private
Example
Police
Trash
Sidewalks
Private Goods
10
Impacts of Grants – General v. Matching
All Other
• Suppose, instead, you
were given a matching
grant, where every $ you
raised would be
matched with a $ from
the government.
• Slope is now -0.5.
Why?
Slope = -0.5, why?
A2
A1
• Leads to much more E
and relatively less A.
E1 E2
E3
Education
Fungibility
• You have a budget of $60 per week for
entertainment. You spend:
– $20 on Pizza
– $20 on Movies
– $20 on Pepsi
• Your parents come to visit and give you a
$30 gift certificate to Pizza Hut.
Taxes and Efficiency
• Excise Tax
– Tax on a particular
good.
– Look at a unit (as
oppose to percentage)
tax.
D
S
$
P1
Con.
P0
3.0
DW
Prod.
$1
• $1 Tax Collected on
DEMANDERS
What’s DW$
Q1 Q0
Q
Ad valorem tax on supply
• Tax parameter is , so if
there is a 10% tax,  =
(1+tax) = (1+0.10) = 1.1
• Impose on Supplier
• Supply – Why?
Price
Supply
c
Ps´= a  + b  Qs
Demand
TAX
• Demand
DW
Pd = c + d Qd
If we set Ps´ = Pd, then
c  a
Q ** 
b  d
aα
a
Q** Q*
Quantity
Ad valorem tax on demand
• Tax is , so if there is
a 10% tax,  = 1.1
• Impose on Demander
• Supply
Price
Supply
c
Demand
c/α
Ps = a + b Qs
TAX
• Demand
DW
Pd´ = (c/ ) + (d / ) Qd
If we set Ps = Pd´, then
(c /  )  a
Q *** 
[b  (d /  )]
a
Q*** Q*
Quantity
Proposal A in Michigan
Proposal A Spreadsheet
Tax Rate
Rate
Year
Value
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
200,000
220,000
240,000
255,000
265,000
275,000
290,000
300,000
320,000
360,000
400,000
420,000
420,000
400,000
375,000
1.5%
Value %
CPI
Taxable
Effective Taxes on
Increase Inflation
Value Taxes
Rate
Value
10.0%
9.1%
6.3%
3.9%
3.8%
5.5%
3.4%
6.7%
12.5%
11.1%
5.0%
0.0%
-4.8%
-6.3%
2.5%
2.8%
2.9%
2.2%
1.3%
2.2%
3.5%
2.7%
1.4%
2.2%
2.6%
3.5%
3.2%
2.9%
200,000
205,017
210,808
216,992
221,766
224,704
229,723
237,686
244,183
247,581
253,131
259,713
268,868
277,516
285,472
3,000
3,075
3,162
3,255
3,326
3,371
3,446
3,565
3,663
3,714
3,797
3,896
4,033
4,163
4,282
1.50%
1.40%
1.32%
1.28%
1.26%
1.23%
1.19%
1.19%
1.14%
1.03%
0.95%
0.93%
0.96%
1.04%
1.14%
3,000
3,300
3,600
3,825
3,975
4,125
4,350
4,500
4,800
5,400
6,000
6,300
6,300
6,000
5,625
Mobility
Tax
0
225
438
570
649
754
904
935
1,137
1,686
2,203
2,404
2,267
1,837
1,343
Property tax … what do we have?
• The tax differentials between jurisdictions
function as excise taxes (if there is a
“national” property tax of 2%, then a
jurisdiction w/ taxes of 3% will incur excise
tax effects).
• The overall weighted property tax
functions as a national tax on capital and
land.
17
Is Property Tax Progressive, Regressive?
• This has long been debated.
• The “traditional” view was the property tax
as an excise tax.
• If so, it is passed forward to the
purchasers of the goods that are
produced.
• If this is the case, it might be thought to be
regressive. Why?
Optimal Sales Tax Analysis
• We could be more efficient if we could raise same revenue with
less DW loss.
• How can we do that?
• Raise tax on A so price ↑ by 1%. This leads revenue to ↑ by a
lot, and quantity to decrease by a little so DW ↑ by a little.
• Reduce tax on B to make revenue constant and it decreases
DWB by more than DWA increased.
DA
$
Price B
CS loss ↑
DB
1+t + tA
RA
1
1+t - tB
1
Good A
RB
CS loss ↓
Rb’
DWB
Good B
Is it a prisoner’s dilemma
Southfield
• Do we give
50% tax
abatement?
• In boxes we
have total
expected tax
receipts for the
municipalities.
No
Yes
No
TS = 2M
TW = 2M
TS = 2.5M
TW = 0.5M
Yes
TS = 0.5M
TW = 2.5M
Warren
TS = 1M
TW = 1M
20
Elasticities
A Little!
• Elasticity of intermetropolitan business
activity (A) with respect to local tax
[(A/A)/ (t/t)] varies between -0.1, and -0.6.
• Elasticity of intrametropolitan business
activity with respect to local tax varies
between -1.0, and -3.0.
• Why are they so different?
A Lot!!
Compare Education to Health
Expenditures as % of GDP
20.0
18.0
Education
16.0
Health
Percentage
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0
1960
1965
1970
1975
1980
1985
Year
1990
1995
2000
2005
2010
GTB Formula (and worksheet)
Consider a formula of the type:
Gi = B + (V* - Vi) Ri, where:
Gi = 0 + ($200,000 – $50,000) ($40/$1,000), where:
Gi = grant
B = Basic or Foundation Grant
V* = Guaranteed per-pupil tax base
Vi = Per pupil tax base in district i.
Ri = Tax rate per thousand dollars in district i.
Gi = $6000; own effort = $2000
If you raise R by $1 in your district, it is raised by (V* - V)/V times;
Here (200 – 50)/50. So a $1 tax gets a $3 match.
Implicit tax price = 1/(1+3) or 25%. Let’s look at spreadsheet.
What’s the most cost-effective
place?
Highest mean!
30
Mean = (20+0)/2 = 10
• Thought experiment.
Most cost effective
place is where we get
the highest mean
score. Why?
• We can draw a line
with a slope of –1.
This line gives us
places with equal
totals. Start with S = SE
+ SH = 10.
45o
SE+SH= max
Ed
SE+SH=20
Mean = (8+8)/2 = 8
SE+SH=10
10
Mean = (0+10)/2 = 5
10
20
Harry
Ideas for Study
It’s all about quantity.
How do we calculate Q*?
What happens if we’re not at Q*?
Know what an elasticity is.
Elasyx = % Δ y / % Δ x.
From a regression, y = bx
Elasyx = b (mean of x/mean of y)
Who pays the tax?
Depends on the elasticity.
25
Ideas for Study (2)
Know what a regression is!
If y = aX + cZ
a!
what is the impact of a change in X, or a
change in Z? c!
Current events count!
Look at them!
26
Ideas for Study (3)
• Capitalization!
• If asset rents for $R per year, its value is:
– V = DR, where D = 1/r (r = interest rate)
• If same asset rents for $R per year, but
owner must pay t% tax,
– V = DR – tDR
– V = DR/(1+Dt)
Ideas for Study (4)
• Capitalization!
• If asset rents for $R per year, its value is:
– V = DR, where D = 1/r (r = interest rate)
• If property tax t pays for public good X,
then:
– Vbig = D(Rbig + X)/(1+Dt). Big houses are
worth less.
– Vsmall = D(Rsmall + X)/(1+Dt). Little houses are
worth more.
Final Exam
• The final exam, as noted in the Winter
course schedule will be:
– Monday, April 28, 2014 from 10:40 am to 1:10
pm.
… and remember
Good Luck