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EEP 101:LECTURE 6. DAVID ZILBERMAN. OUTLINE. COST EFFECTIVENESS SHADOW PRICING HETEROGENEITY TAXES VS. DIRECT CONTROL UNCERTAINTY-THE WEITZMAN MODEL. COST EFFECTIVENESS. Policy makers frequently do not know the externality cost

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Eep 101 lecture 6

EEP 101:LECTURE 6

DAVID ZILBERMAN


Outline
OUTLINE

  • COST EFFECTIVENESS

  • SHADOW PRICING

  • HETEROGENEITY

  • TAXES VS. DIRECT CONTROL

  • UNCERTAINTY-THE WEITZMAN MODEL


Cost effectiveness
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
Cost effective tax& competition

AB tax target level 2

CD tax target level 1

Target level 1

Q2

Q1

The tax levels are shadow prices

of pollution constraints

A

C

B

MPC

D

Target

level 2

Qc

Shadow prices=the benefits lost by tightening a constraint


Policies to achieve cost effectiveness
Policies to achieve cost effectiveness

  • 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
Heterogeneity

REDUCTION FROM Q0 TO Q1

TAX =AB QUANITITES MOVE FROM

BLUE TO RED

Q1

P1

A

TD=D1+D2+D3

D1

D3

D2

B

MPC

Q0


Numerical heterogeneity
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
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
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
ExampleP=10,w=1

Q=15

TZ=

25

Q=35

TZ=

65

Q=15

TZ=

60

Q=25

TZ=90


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

WHEN DEMAND IS INELASTIC, TAX IS BETTER THAN QUANTITY.

Outcomes closer to optimal

TAXA

A

*

TAXB

B

MB0

MBH


Elastic demand case
Elastic demand case

BLUE Quantity control

RED tax control

Pr ice

WHEN DEMAND IS ELASTIC, QUANTITY IS BETTER THAN TAX.

TAX A

A

*

TAX B

B

MBH

MBO

MBL

Q

Quantity


Lesson
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.


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