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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
- 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

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

- 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

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

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

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

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

- 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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