Question

In: Economics

Suppose two firms, All-American Power (Firm A) and Big Energy Inc. (Firm B) have the following...

Suppose two firms, All-American Power (Firm A) and Big Energy Inc. (Firm B) have the following marginal abatement cost curves: MAC_A = 400 – 2e_A and MAC_B = 600 – 3e_B, and the government wants to use an effluent tax to keep total emissions down to 200.

(Question 7A: 2 Points) Using the Marginal Abatement Cost curves and the government constraint, calculate the optimal number of emissions for Firm A under an optimal effluent tax.

(Question 7B: 2 Points) Using the Marginal Abatement Cost curves and the government constraint, calculate the optimal number of emissions for Firm B under an optimal effluent tax.

(Question 7C: 2 Points) Using the information from question 7, calculate the optimal effluent tax set by the government

(Question 7D: 4 Points) Using the information from question 7, calculate the total cost for firm A (tax cost plus abatement cost) at their optimal number of emissions.

(Question 7E: 4 Points) Using the information from question 7, calculate the total cost for firm B (tax cost plus abatement cost) at their optimal number of emissions.

Solutions

Expert Solution

Let us calculate the emissions levels without regulations

Set MACA=0

400-2eA=0

eA=200

Now, set MACB=0

600-3eB=0

eB=200

7A)

Required level of emissions=eA+eB=200

So, eB=200-eA

Set MACA=MACB for optimal reduction

400-2eA=600-3eB

Set eB=200-eA

400-2eA=600-3*(200-eA)

400-2eA=600-600+3eA

5eA=400

eA=80 (Optimal number of emissions for firm A under regulation)

7B)

We have derived in part 7A that

eB=200-eA=200-80=120 (Optimal number of emissions for firm B under regulation)

7C)

MACA at optimal emission=MACA=400-2eA=400-2*80=$240

MACB at optimal emission=MACB=600-3eA=600-3*120=$240

Optimal effluent tax=MACA=MACB=$240

7D)

Abatement by firm A=200-80=120

We know that

Emission by a firm+Abatement by a firm=Emission by firm without regulation

eA+Aa=200

eA=200-Aa

Set eA=200-Aa in MACA relation

MACA=400-2eA=400-2*(200-Aa)=2Aa

Total Cost of abatement (TACA) is given as

Total Cost for firm A=TACA+Effluent tax=14400+(200-120)*240=$33600

7E)

Abatement by firm B=200-120=80

We know that

Emission by a firm+Abatement by a firm=Emission by firm without regulation

eB+Ab=200

eB=200-Ab

Set eB=200-Ab in MACB relation

MACB=600-3eB=600-3*(200-Ab)=3Ab

Total Cost of abatement (TACB) is given as

Total Cost for firm B=TACB+Effluent tax=9600+(200-80)*240=$38400

Rahul Sunny answered 4 weeks ago

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