Transcript EEP 101:LECTURE 6

EEP 101:LECTURE 6
DAVID ZILBERMAN
OUTLINE
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COST EFFECTIVENESS
SHADOW PRICING
HETEROGENEITY
TAXES VS. DIRECT CONTROL
UNCERTAINTY-THE WEITZMAN MODEL
COST EFFECTIVENESS
• Policy makers frequently do not know the
externality cost
• They therefore set a target level of externality
control and design a policy to meet it.
• Cost effective policy attains a target policy at least
cost
Cost effective tax& competition
Target level 1
Q2
Q1
A
AB tax target level 2
CD tax target level 1
The tax levels are shadow prices
of pollution constraints
C
B
D
MPC
Target
level 2
Qc
Shadow prices=the benefits lost by tightening a constraint
Policies to achieve cost effectiveness
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A tax,subsidy, Tradable trading among firmse
MB = 20-2Q
MPC =4 Initial equilibrium 20-2Q-4=0 Hence
Hence Qc=8,Pc=4
When Target is Q1=4 shadow price=20-8-4=8
Total Subsidy cost (8-4)*8=32
When Target is Q1=2 shadow price=20-4-4=12
Total Subsidy cost (8-2)*12=72
Heterogeneity
Q1
P1
REDUCTION FROM Q0 TO Q1
TAX =AB QUANITITES MOVE FROM
BLUE TO RED
A TD=D1+D2+D3
D1
D2
D3
B
MPC
Q0
NUMERICAL HETEROGENEITY
MB1=20-Q,MB2=20-2Q,MB3=20-4Q MPC=2
Quantity as function of price
D1=20-P,D2=10-.5P D3=5.-.25P
Aggregate demand
TD=35-1.75P or P=20-1/1.75Q
Competition
P0=2 2=20-Q*4/7 TQ0=18*7/4=31.5
Initial quantities
Q10=18.Q20=9,Q30=4.5
First scenario Q1=20.
P1=20-20*4/7;P1=20*3/7=8.57
and Q11=11.44. Q21=5.74, Q31=2.82
Heterogeneity &Tradable permits• If everyone is allotted the same quantity of permits
trading will occur
IF Q=20 and each gets 6.66
• the first firm will buy and the other will sell
pollution rights price of right 6.57
Second scenario Q1=10.
P1=20-10*4/7=14.28
Q12=5.72 Q22=2.85, Q32=1.43
• Trading occurs if there are differences among firm
Heterogeneity with fixed
coefficients
• Assume many firms each has labor/ output X and
pollution/output x coefficients
• 1<x<10
• 1<z<10
• A unit with x=2 and z=2 is clean and efficient
• z=9 and x=9 is inefficient and dirty
• Output price =P Labor class
• Pollution is either tax by v or has an upper bound Z
ExampleP=10,w=1
firm x
z
1
2
3
4
5
6
7
5
2
4
3
2
2
1
2
4
4
5
6
7
8
num V=2 Z=3 W=2
V=1
10 n
n
y
5
y
y
y
5
n
n
n
10 n
y
n
5
y
y
n
10 n
y
n
5
y
y
n
W=2
Z=3
y
y
n
y
n
n
n
Q=15 Q=35 Q=15 Q=25
TZ= TZ= TZ=
TZ=90
25
65
60
Labor per
unit of
out put, x
G
H
A
B
P /w
F
II
C
I
III
D
0
z
P ollution per unit of out put , z
E
P /v
Standa rdsA re LessE fficient than Taxe s, But Result in Higher Output
Con sider three group s of firms in the figure:
 Group I w ill surv ive unde r either a pollution tax or a po llution
standard (firms in the area OACD).
 Group I I will survive only unde r a standard (firms in the area ABC)
 Group I II will surviveon ly unde r a tax (firms in the area CED)
For Group I , let:
z(I) = pollution p er un it of ou tput of group I
Q(I) = ou tput of group I
Z(I) = pollution o f group I
[i.e., Z(I) = z(I)Q(I)]
where a simi lar de finition app lies for Group II and III.
Compari ng the outcomes of taxes and standards:
Under a pollution t ax: Total pollution = Z(I) + Z(III)
Under a pollution st andard: Total pollution = Z(I) + Z(II).
If the same level of total pollution is to be achieved in the economy under
either the tax or the standard, then it must be the case that Z(II) = Z(III).
Note that, by definition:
Z(II) = z(II)Q(II), and
Z(III) = z(III)Q(III).
Since z(III) > z(II), it must be the case that Q(II) > Q(III).
Now, since
Q(standard) = Q(I) + Q(II), and
Q(tax)
= Q(I) + Q(III),
it must be the case that Q(tax) < Q(standard
Conclusions
 Taxes achieve environmental targets at the least cost (highest
efficiency).
 Standards achieve environment al targets at a lower level of
economic efficiency, but with less impact on output and
employment.
 Taxes cause the least-efficient plants to close, but some highly
polluting firms may remain open
 Standards cause the most highly polluting plants to close, but may
allow some inefficient plants to remain open
Risk
• True demand is MB0-policy maker chooses
• MBH with 50% probability
• MBL with 50% probability-The MC is constant
BLUE Quantity control
RED tax control
MBL
TAXA
TAXB
B
*
A
MB0
WHEN DEMAND IS INELASTIC,
TAX IS BETTER THAN
QUANTITY.
Outcomes closer to optimal
MBH
Elastic demand case
BLUE Quantity control
RED tax control
P
r
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c
e
TAX A
TAX B
B
*
A
WHEN DEMAND IS
ELASTIC, QUANTITY IS
BETTER THAN TAX.
MBO MBH
MBL
Q
Quantity
Lesson
• When policymakers don’t know the true demand for
pollution
• If demand is inelastic, prices lead to lower expected
error than quantities.
• If demand is elastic, quantities are preferable to
taxes as they lead to lower expected error.
• When regulating polluting materials with no
substitutions, financial incentive works better.
• But when regulating polluting materials with
substitutions, quantity works better.