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Homework answers / question archive / Suppose the (external) damage done by pollution is known to be MD=300+5q, and the (private) cost and benefit are given by MC=100+2q and MB=D-2q, where D is not known
Suppose the (external) damage done by pollution is known to be
MD=300+5q, and the (private) cost and benefit are given by
MC=100+2q and MB=D-2q, where D is not known.
a)If d=1000, what would be the optimal quantity? What tax would be necessary in order for that to be the equilibrium quantity?
b)Suppose that, based on the result from part (a), a cap-and-trade system is imposed to allow the optimal quantity of pollution to be produced. If D=900, what would be the dead-weight loss associated with having the wrong quantity?
c)Suppose that, based on the result from part (a), a tax is imposed to allow the optimal quantity of pollution to be produced. If D=900, what would be the dead-weight loss associated with the wrong tax level?
d)If D is not exactly known, which is likely to give better results, a cap-and-trade system or a tax? What would be the answer to this question if MD were 300+3Q instead of 300+5q
A.
At D=1000, equilibrium quantity and Marginal Private Benefit (MPB) would be:
MB=MC100+2q=D−2q100+2q=1000−2q4q=900q=225MB=100+2(225)=550MB=MC100+2q=D−2q100+2q=1000−2q4q=900q=225MB=100+2(225)=550
Optimum quantity is:
MD=MB300+5q=D−2q300+5q=1000−2q7q=700q=100MD=300+5(100)=800MD=MB300+5q=D−2q300+5q=1000−2q7q=700q=100MD=300+5(100)=800
To bring q to the equilibrium quantity to 225 from 100, tax equivalent to external damage (MD) or external cost is needed. That is MD-MC
=MD−MC=800−550=250=MD−MC=800−550=250
B.
If D=900, optimal quantity is:
MD=MB300+5q1=D−2q1300+5q1=900−2q17q=600q1=85.71MD1=300+5(85.71)=728.55MD=MB300+5q1=D−2q1300+5q1=900−2q17q=600q1=85.71MD1=300+5(85.71)=728.55
Deadweight loss associated would be:
=0.5(MD−MD1)(q−q1)=0.5(800−728.55)(1000−900)=3572.5=0.5(MD−MD1)(q−q1)=0.5(800−728.55)(1000−900)=3572.5
C.
With D=900 the correct amount of tax imposed should be:
=MD−MC=728.55−550=178.55=MD−MC=728.55−550=178.55
and tax imposed=250, the extra amount of tax would be:
=250−178.55=71.45DWL=0.5(71.45)(1000−900)=3572.5=250−178.55=71.45DWL=0.5(71.45)(1000−900)=3572.5
Where DWL is deadweight loss.
D.
Considering D is not known, cap and trade system is better one. The deadweight loss would be minimum because the sellers can trade whatever marginal damage they created. Tax is ideal only for scenario when exact D is known, otherwise there would be deadweight loss.
If MD=300+3q, optimal quantity is:
MD=MB300+3q=D−2q300+3q=1000−2q5q=700q=140MD=300+3(140)=720MD=MB300+3q=D−2q300+3q=1000−2q5q=700q=140MD=300+3(140)=720
Tax would be:
=720−550=170=720−550=170
As here, marginal damage is less, tax can be imposed. Deadweight loss would be less.
