Question

In: Economics

4A. Consider two rubber companies, Firestone and Goodyear. Both companies create air pollution when they produce...

4A. Consider two rubber companies, Firestone and Goodyear. Both companies create air pollution when they produce rubber. The air pollution can be reduced by the firm, but the abatement comes at a cost. Specifically,

MAC_F = 800 – 4e_F, where e_F = tons of emissions produced by Firestone
MAC_G = 200 – e_G, where e_G = tons of emissions produced by Goodyear

the government wants to use an effluent tax to reduce emissions to 200 tons. What is the optimal number of emissions for Goodyear (firm G) under this policy?

Using the information from question 4A, what is the optimal number of emissions for Firestone (firm F) under this policy?

Given the information from question 4A, what tax level reduces emissions in the most cost-effective way for the firms when they operating at their optimal number of emissions under this policy?

Using the information from question 4A, calculate the total cost (tax cost + abatement cost) for firm F under this effluent tax policy?

Using the information from question 4A, calculate the total cost (tax cost + abatement cost) for firm G under this effluent tax policy

Solutions

Expert Solution

Given

MACF=800-4eF

In absence of any regulation,

MACF=0

800-4eF=0

eF=200

MACG=200-eG

In absence of any regulation,

MACG=0

200-eG=0

eG=200

Now regulation requires that eG+eF=200

or eF=200-eG

Optimal effluent requires that

MACF=MACG

800-4eF=200-eG

set eF=200-eG

800-4*(200-eG)=200-eG

800-800+4eG=200-eG

5eG=200

eG=40 (optimal effluent from firm G)

eF=200-eG=200-40=160 (optimal effluent from firm F)

MACF at optimal effluent=800-4eF=800-4*160=160

MACG at optimal effluent=200-eG=200-40=160

Optimal Tax=MACG=MACF=$160

In case of firm F, effluent is reduced from 200 to 160 units. Effluent is reduced bt 40 units

Total effluent by firm F=eF=Effluent in case of no regulation-abatement=200-AF

MACF=800-4eF=800-4*(200-AF)=4AF

Total abatement cost is given as

Tax payment=Effluent*Tax rate=160*160=$25600

Total Cost=3200+25600=$28800

In case of firm G, effluent is reduced from 200 to 40 units. Effluent is reduced bt 160 units

Total effluent by firm G=eG=Effluent in case of no regulation-abatement=200-AG

MACG=200-eG=200-(200-AG)=aG

Total abatement cost is given as

Tax payment=Effluent*Tax rate=40*160=$6400

Total Cost=12800+6400=$19200

Rahul Sunny answered 1 year ago

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