Consider an industry with two firms: Firm 1 and Firm 2. Each firm initially emit

Question

Consider an industry with two firms: Firm 1 and Firm 2. Each firm initially emits 50 tons of air pollution as part of its production process. The government seeks to reduce emissions by a total of 50 tons and can do this using an emission standard, an emission tax, or a tradable emission allowance program.

Marginal costs of controlling pollution for the firms are

MCC1 = ½ Q1 MCC2 = 2 Q2

Where Q1 and Q2 is the number of tons of pollution control by Firm 1 and Firm 2, respectively.

Using the information above, complete questions (1) – (7) below.

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Question 110 pts

Calculate the cost-effective allocation of pollution control responsibility, i.e. calculate Q1* and Q2*.

Q1* =  tons Q2* =  tons

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For questions (2) and (3) suppose the government imposes an emission standard on the firms requiring Firm 1 to reduce emissions by 30 tons and Firm 2 to reduce emissions by 20 tons.

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Question 210 pts

Does the emission standard bring about a cost-effective allocation of pollution control responsibility?

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Question 310 pts

Calculate the total cost of pollution control for Firm 1 and for Firm 2.

TCC1 = $     TCC2 = $

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For parts (4) and (5) suppose the government chooses to reach its objective of 50 tons of aggregate pollution control with a pollution tax.

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Question 410 pts

What is the amount of the per-unit tax government should impose in order to bring about a cost-effective allocation of pollution control responsibility?

Tax =  $/ton

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Question 510 pts

How much government revenue does the pollution tax system generate?

Government revenue = $

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For questions (6) and (7), suppose the government decides to achieve the 50-ton pollution reduction using tradable emission allowances. Government gives 20 tons of emission allowances to Firm 1 and 30 tons of emission allowances to Firm 2. Assume there are no transaction costs.

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Question 640 pts

After the two firms make all desirable trades, how many allowances does each firm have? How many allowances did each firm buy or sell?

Firm 1 has   allowances after trading.

Firm 2 has   allowances after trading.

Firm 1 (enter bought or sold)     allowances.

Firm 2 (enter bought or sold)     allowances.

Explanation / Answer

1)SInce Q1+Q2=50 and MCC1=1/2Q1 and MCC2=2Q2 for Cost effective allocation 1/2Q1=2Q2 this gives Q1=4Q2 so 4Q2+Q2=50 therefore Q2*=10 and Q1*=40 and total cost=(1/2+1+3/2+...20)+(2+4+6+...20)=520

2) since Q1=30 and Q2=20 total cost=(1/2+1+3/2+2+...+15)+(2+4+6+...+40)=652.5 which is higher than cost effective allocation hence answer is NO

3) Total cost of pollution control for Firm 1 =(1/2+1+...+15)=30/2(1+(29/2))=232.5 and for firm 2=(2+4+...+40)=20/2(4+(19*2))=420

4) Total COst effective allocation Cost= $520 hence to reduce 50 ton per ton cost =$520/50=$10.4

5) GOvernment Revenue=$10.4*50=$520

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