Firm $1$: MCC$1=120-4$ E$1$

Firm $2$: MCC$2=100-2$ E$2.$

Where MCCi is marginal abatement cost for firm i$,$ and Ei is the ith firm$$s emission level.

You must show all work for numerical problems or no credit will be earned.

$1.$ What is the unregulated level of emissions for firm $1($E$1)?$ Justify your answer.

$2.$ What is the unregulated level of emissions for firm $2($E$2)?$ Justify your answer.

$3.$ Find the emission level for each firm and the total industry emission level $($E$1+$ E$2),$

associated with a per$-$unit tax of $$16.$

$4.$ Find the emission level for each firm and the total industry emission level $($E$1+$ E$2),$

associated with a per$-$unit tax of $$24.$

$5.$ Find the emission level for each firm and the total industry emission level $($E$1+$ E$2),$

associated with a per$-$unit tax of $$32.$

$6.$ Explain why the industry emission level decreases as the tax rate increases.

$7.$ When the per unit tax is $$32,$ what is the total tax paid by firm $1?$ What is the total policy

cost to firm $1($i$.$e$.$ control $($abatement$)$ cost plus tax payment$)?$

$8.$ When the tax is $$32,$ what is the total tax paid by firm $2?$ What is the total policy cost to

firm $2($control $($abatement$)$ cost plus tax payment$)?$

$9.$ What is total industry policy cost of implementing a $$32$ pollution tax policy?

$10.$ Now assume that instead of a tax, a marketable pollution permit system is instituted and the

government auctions off $56$ emission permits $($that is the EPA determined the optimal

emission level is $56$ units and firms need a permit for each unit of emission$).$ The $56$

permits is equal to the total industry emission level under the $$32$ per unit tax policy. $(1)$

$2$

How many permits does each firm purchase at auction? $(2)$ What auction price results in the

sale of all $56$ permits?

$11.$ Given your answer to question $10,$ for each firm determine total control cost and total

policy cost $($sum of permit cost and total control cost$).$ What is total industry under the

auction system? Carefully explain why, or why not, your answers are different from your

answers for questions $7,8$ and $9.$

$12.$ Now, assume the government freely provides $28$ pollution permits to each firm at zero cost

and allows each firm to sell$/$purchase the allocated permits. Issuing $28$ permits to each firm

will result in the optimal industry emission level. Recall, a firm needs a permit for each unit

of pollution the firm emits. This type of policy, where a fixed number of permits are

allocated to an industry and firms can sell$/$purchase the allocated permits, is a cap$-$and$-$trade

policy. Note that the sum of $28$ permits provided to each firm $(56$ total permits$)$ is identical to

the $56$ permits auctioned off in question $10.$ If we assume each firm wishes to minimize their

total policy cost, the sum of pollution control cost plus permit purchase cost, the two firms

will engage in trade if their marginal control costs are not equal when each firm uses $28$

permits. After all profitable trades$/$sales are completed how many permits does each firm

sell$/$buy and what is the total control cost for each firm? What is the industry total policy

cost of the tradable permit system? Is total firm and industry policy cost different from the

values for the tax and$/$or auction policies $($questions $7,8,9,$ and $11)?$ Use economic

reasoning to explain any differences.