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EEP 101:LECTURE 6

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

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  1. EEP 101:LECTURE 6 DAVID ZILBERMAN

  2. OUTLINE • COST EFFECTIVENESS • SHADOW PRICING • HETEROGENEITY • TAXES VS. DIRECT CONTROL • UNCERTAINTY-THE WEITZMAN MODEL

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

  9. 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

  10. ExampleP=10,w=1 Q=15 TZ= 25 Q=35 TZ= 65 Q=15 TZ= 60 Q=25 TZ=90

  11. 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

  12. 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

  13. 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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